CN107664648A - A kind of X ray differential phase contrast microscopic system and its two-dimensional imaging method - Google Patents

A kind of X ray differential phase contrast microscopic system and its two-dimensional imaging method Download PDF

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CN107664648A
CN107664648A CN201610617865.1A CN201610617865A CN107664648A CN 107664648 A CN107664648 A CN 107664648A CN 201610617865 A CN201610617865 A CN 201610617865A CN 107664648 A CN107664648 A CN 107664648A
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grating
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CN107664648B (en
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朱佩平
张凯
袁清习
黄万霞
朱中柱
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Jinan Hanjiang Photoelectric Technology Co ltd
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Institute of High Energy Physics of CAS
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    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N23/00—Investigating or analysing materials by the use of wave or particle radiation, e.g. X-rays or neutrons, not covered by groups G01N3/00 – G01N17/00, G01N21/00 or G01N22/00
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Abstract

The invention discloses a kind of X ray differential phase contrast microscopic system and its two-dimensional imaging method, the X ray differential phase contrast microscopic system includes：For producing the light source of X ray；And condenser, central stop, beam-splitting optical grating, pin hole, sample stage, object lens, annular analysis grating and the imaging detector set gradually along x-ray spread direction.The beneficial effects of the invention are as follows：The X ray differential phase contrast microscopic system, increase beam-splitting optical grating and annular analysis grating only in traditional X-ray microscope, can be achieved with phase contrast quantitative imaging, there is the advantages of simple in construction, easy to spread.In addition, X-ray source, condenser, beam-splitting optical grating can be integrated into an X ray ring-shaped gate source element, then whole X ray differential phase contrast microscopic system length can further shorten, the manufacturing cost of X-ray microscope system can be not only reduced, and the utilization ratio of light also can be improved further.

Description

A kind of X ray differential phase contrast microscopic system and its two-dimensional imaging method
Technical field
The present invention relates to nano-resolution X-ray microscope technical field of imaging, more particularly to X ray differential phase contrast to show Micromirror systems and its two-dimensional imaging method.
Background technology
Effect of the material to X ray can be represented with refractive index, and n=1- δ+i β, wherein δ are refractive index real part attenuation rates, β It is Absorption Terms.δ physical significance is to be produced by the X ray of unit length material relative to the X ray Jing Guo unit length vacuum Raw corrugated movement；β physical significance is by decreased amplitude caused by the X ray of unit length material.According to δ and β thing Meaning is managed, X ray can be obtained after a sample, its complex amplitude can be expressed asWherein
For the variable quantity by the relative X ray phase Jing Guo equal length vacuum of the X ray phase of sample, abbreviation phase Move, l is the path that X ray passes through sample；Because the integrated value outside sample is zero, the bound of integration can expand to It is infinite；
To absorb, μ is linear absorption coefficient.Because hard X ray wave band light element δ than β more than big three magnitudes, institute It is possible to produce the light intensity signal more much bigger than Change of absorption with phase place change.Dutch scientist Ze Nike (Zernik) is phase Contrast imaging it is the first.Early in nineteen thirty-five, he just proposes the microscopical theoretical and method of phase contrast in visible light wave range, For this, he has won the Nobel Prize in physics of nineteen fifty-three.People are successfully by Ze Nike phase contrasts microscope side at present Method is generalized to the X-ray microscope using zone plate as object lens, succeeds in developing the X ray phase that phase contrast is obtained using phase shift ring Position contrast microscope, as shown in figure 1, the microscope according to x-ray spread direction successively include X-ray source 10, condenser 1, Central stop 2, pin hole 3, sample stage 4, object lens 5, phase shift ring 6 and imaging detector 7.However, the phase contrast of Ze Nike inventions Imaging exists clearly disadvantageous：Its application is confined to absorb negligible weak phase samples.When absorption can not be ignored, It cannot distinguish between Intensity response caused by Intensity response caused by absorption and phase shift；When sample is not weak phase object, special sample When the phase shift of product is more than π/4, the relation of phase shift and Intensity response no longer meets linear relationship, and Intensity response will be with phase cycling Produce vibration.These deficiencies bring difficulty for quantitative study sample rate structure.
The content of the invention
An object of the present invention, there is provided a kind of high sensitivity for being capable of quantitative study sample rate structure is in conventional suction The X ray differential phase contrast microscopic system of X-ray microscope.
The second object of the present invention, there is provided one kind is used for the highly sensitive X ray differential phase contrast microscope system The two-dimensional imaging method of system.
According to an aspect of the present invention, a kind of X ray differential phase contrast microscopic system is disclosed, it can include： For producing the light source of X ray；And condenser, central stop, beam-splitting optical grating, the pin set gradually along x-ray spread direction Hole, sample stage, object lens, annular analysis grating and imaging detector；Wherein, the light source for producing X ray is homogeneous X-ray light Source；The condenser is ellipsoid capillary, tapered capillaries, zone plate or other X ray optics members with focusing function Part, for producing the focus on light beam of illumination sample；The central stop is located at condenser export center position, is come from for stopping The straight-through light of X-ray source, form the hollow cone light beam of illumination sample；The absorption that it is micron dimension in the cycle that the beam-splitting optical grating, which is, Grating, after the central stop of condenser outlet, for dividing the hollow cone light beam from condenser and central stop Beam, become the hollow cone light beam with space periodic structure；The pin hole, after beam-splitting optical grating, X is come from for stopping The straight-through light and veiling glare of ray source；The sample stage, positioned at object plane, for carrying sample, and it can translate and rotary sample； The object lens are zone plate or other optical elements with X ray lens imaging function, for having positioned at object plane The sample structure of nanometer scale is enlarged into the picture in image planes with micron dimension structure, and beam-splitting optical grating is shone by hollow cone light beam Bright annular section is formed about circular grating picture and circular grating as light beam in object lens back focal plane；The annular analyzes grating Cycle is micron or the absorption grating of sub-micrometer scale, near object lens back focal plane, its shape and size and the beam splitting Circular grating of the grating near object lens back focal plane is as identical, for the circular grating to the object lens back focal plane annex as light beam It is filtered；The imaging detector is located at image planes, for shooting the two-dimentional intensified image of sample.
Alternatively, the material of the beam-splitting optical grating and the annular analysis grating is golden or other heavy metals.
Alternatively, in the case where the beam-splitting optical grating and the annular analysis grating thickness are little, the thickness of beam-splitting optical grating The odd-multiple for π phase shifts is spent, the thickness of annular analysis grating is the even-multiple of π phase shifts.
According to another aspect of the present invention, disclose a kind of for the X ray differential phase contrast microscopic system Two-dimensional imaging method, comprise the following steps：
S1, open and adjust light source：X-ray beam caused by the light source is set to be directed at condenser；
S2, adjustment condenser, central stop and pin hole：Make hollow cone beam alignment institute caused by condenser and central stop State and sample position is carried on sample stage, central stop and pin hole is stopped straight-through light and veiling glare from the X-ray source；
S3, adjust object lens：Object lens are made to focus on imaging detector of the imaging beam the to be formed alignment positioned at image planes；
S4, feed-in beam-splitting optical grating：After the central stop of condenser outlet, feed-in beam-splitting optical grating, shine hollow cone light beam The annular section of bright beam-splitting optical grating is formed about circular grating picture and circular grating as light beam in object lens back focal plane；
S5, feed-in and adjustment ring conformal analysis grating：Make annular analysis grating alignment beam-splitting optical grating near object lens back focal plane The circular grating picture of formation, adjustment ring conformal analysis grating grizzly bar direction, make annular analysis grating grizzly bar parallel to beam-splitting optical grating grid Bar；
S6, measuring angle signal response curve：Beam-splitting optical grating is progressively moved along perpendicular to optical axis and grating grizzly bar direction, is made The circular grating of beam-splitting optical grating as opposed annular analysis grating occur shear displacemant, with imaging detector image planes measure brightness with The angle signal response curve of circular grating image displacement change；
S7, angle signal response curve is fitted with cosine curve：Angle signal response curve is similar to cosine curve, with remaining The angle signal response curve that chord curve fitting measures, makes it obtain the Analytical Expression of cosine curve；
S8, shoot sample two dimension intensified image：The circular grating picture of beam-splitting optical grating is separately fixed at the angle signal to ring Paddy position, upward slope position, peak position, the descending position of curve are answered, sample is placed on sample stage, the paddy position intensified image of sample is shot, goes up a slope Intensified image, peak position intensified image, descending intensified image；
S9, quantitative two-dimensional image of the extraction sample in object space：Put from the paddy position intensified image, upward slope intensified image, peak position of sample Sample is extracted in big picture, descending intensified image in the absorption picture of object space, dioptric image and scattering picture；From any in four kinds of intensified images Sample is extracted in three kinds of intensified images in the absorption picture of object space, dioptric image and scattering picture.
In the step S6, it is contemplated that refraction and scattering of the sample on depth of focus light pencil influence, i.e., in view of sample Influence of the caused angle signal to imaging process, therefore sample angle signal function f (xo,yo,ψx) be expressed as
Wherein (xo,yo,zo) for space coordinates at sample, M (xo,yo)、θx(xo,yo) andRespectively sample The sample absorb, required in refraction angle and scattering angular variance, and the imaging of X ray differential phase contrast microscope two-dimensional quantitative exists The absorption picture of object space, dioptric image and scattering picture, their expression formula are
Wherein (xo,yo,zo) for space coordinates at object plane, μ is linear absorption coefficient, and δ is refractive index real part attenuation rate, ωx It is perpendicular to the linear scattering coefficient in grating grizzly bar direction.
What is measured in the step S6 is angle signal response curve, and it is with fitting cosine curve Analytical Expression
Or it is expressed as
Wherein η is object lens diffraction efficiency, B0For incident beam brightness, x at object planepPosition coordinates at grating is analyzed for annular,For angular displacement of the circular grating image displacement with respect to object plane, doFor object distance of the sample with respect to object lens, p is annular analysis grating Cycle,For angle signal response curve average value, RmaxAnd RminRespectively angle signal response curve Maximum and minimum value,For the visibility of angle signal response curve, n is modulation parameter, n=0,1,2,3 Paddy position response curve, upward slope response curve, peak position response curve and descending response curve are corresponded to respectively.
In the step S8, the two-dimentional intensified image of imaging detector shooting is described with angle signal imaging equation, angle Image formation equation is the convolution of angle signal function and angle signal receptance function, and its expression formula is：
Wherein (xo,yo) it is object plane coordinate, (xi,yi) it is image coordinates, η is object lens diffraction efficiency, B0For incidence at object plane Beam brightness, n=0,1,2,3 corresponds to paddy position amplification imaging equation, the amplification imaging equation that goes up a slope, peak position amplification imaging equation respectively Amplify imaging equation with descending.
It is described that the circular grating picture of beam-splitting optical grating is fixed on angle signal response curve paddy in the step S8 Position, places sample, imaging detector photographs the paddy position intensified image of sample, and its expression formula is on sample stage
It is described that the circular grating picture of beam-splitting optical grating is fixed on angle signal response curve upward slope in the step S8 Position, places sample, imaging detector photographs the upward slope intensified image of sample, and its expression formula is on sample stage
It is described that the circular grating picture of beam-splitting optical grating is fixed on angle signal response curve peak in the step S8 Position, places sample, imaging detector photographs the peak position intensified image of sample, and its expression formula is on sample stage
It is described that the circular grating picture of beam-splitting optical grating is fixed on angle signal response curve descending in the step S8 Position, places sample, imaging detector photographs the descending intensified image of sample, and its expression formula is on sample stage
Due to
BV(xi,yi)+BP(xi,yi)=BU(xi,yi)+BD(xi,yi)
So three width seem independent in paddy position intensified image, upward slope intensified image, peak position intensified image, descending intensified image, wherein Any width picture can be expressed with its excess-three width picture；During the above is various, (xi,yi) it is image coordinates, η is the diffraction of object lens Efficiency, B0To illuminate the brightness of object plane light beam,For the average value of angle signal response curve, RmaxAnd RminPoint Not Wei angle signal response curve maximum and minimum value,For the visibility of angle signal response curve, doFor object distance of the sample with respect to object lens, p is annular analysis screen periods.
It is described to be put from paddy position intensified image, upward slope intensified image, peak position intensified image, the descending of sample in the step S9 The big extraction sample as in is as follows in the absorption picture of object space, dioptric image and scattering image space method：
Extraction sample object space absorb picture formula be
Extract sample is in the formula of object space dioptric image
Under the conditions of scattering is negligible, extraction sample is in the simplified formula of object space dioptric image
Extraction sample object space scattering picture formula be
Under the conditions of refraction is negligible, extraction sample is in the simplified formula of object space scattering picture
During the above is various, (xo,yo) it is object plane coordinate, (xi,yi) it is image coordinates, doFor sample with respect to object lens object distance,
As an alternative embodiment, the X-ray source, condenser and beam-splitting optical grating can be integrated into a week Phase for the X ray ring-shaped gate source of micron dimension element, now in the exit in the X ray ring-shaped gate source, along optical axis successively Two annular light holes are placed, make the light beam that the ring-shaped gate source is sent after two annular light holes, form illumination sample Hollow cone light beam, and be formed about ring-shaped gate source image and ring-shaped gate source image light beam in object lens back focal plane, the annular analysis light The shape and size of grid are identical with the ring-shaped gate source image.
X ray differential phase contrast microscopic system disclosed by the invention, the increase point only in traditional X-ray microscope Beam grating and annular analysis grating, can be achieved with phase contrast quantitative imaging, have the advantages of simple in construction, easy to spread.Separately Outside, X-ray source, condenser, beam-splitting optical grating can be integrated into an X ray ring-shaped gate source element, and gone out in ring-shaped gate source Opening's edge optical axis direction disposes two annular light holes successively, then whole X ray differential phase contrast microscopic system length can be with Further shorten, can not only reduce the manufacturing cost of X-ray microscope system, and the utilization ratio of light also can be carried further Height, have broad application prospects.
Brief description of the drawings
It should be appreciated that in following all accompanying drawings, identical reference represents identical or corresponding part and feature.
Fig. 1 is the light path schematic diagram of X-ray phase contrast microscopic system of the prior art.
Fig. 2 is the schematic diagram according to the X ray differential phase contrast microscopic system of one embodiment of the invention.
Fig. 3 is the two-dimensional imaging method according to the X ray differential phase contrast microscopic system of one embodiment of the invention FB(flow block).
Fig. 4 is the refraction angle image formation according to the X ray differential phase contrast microscopic system of embodiments of the invention Schematic diagram.
Fig. 5 is the angle of scattering image formation according to the X ray differential phase contrast microscopic system of embodiments of the invention Schematic diagram.
Fig. 6 is four kinds of angle signal receptance function curve maps of X ray differential phase contrast microscopic system.
Fig. 7 is the X ray differential phase microscopic system based on ring-shaped gate source according to another embodiment of the present invention Schematic diagram.
Each reference is simply described as follows in accompanying drawing：
1：Condenser
2：Central stop
3：Pin hole
4：Sample stage
5：Object lens
6：Phase shift ring
7：Imaging detector
3’：Beam-splitting optical grating
6’：Annular analysis grating
10：X-ray source
10’：X ray ring-shaped gate source
20：First annular light hole
30：Second annular light hole.
Embodiment
X ray differential phase contrast microscopic system to embodiment disclosed by the invention and for this below in conjunction with the accompanying drawings The two-dimensional imaging method of system is described in detail.
Fig. 2 is the schematic diagram according to the X ray differential phase contrast microscopic system of one embodiment of the invention.Such as Fig. 2 Shown, X ray differential phase contrast microscopic system 100 includes X-ray source 10 according to x-ray spread direction (in figure successively Be not drawn into), condenser 1, central stop 2, beam-splitting optical grating 3 ', pin hole 3, sample stage 4, object lens 5, annular analysis grating 6 ' and imaging Detector 7 is formed.The property of each element, 26S Proteasome Structure and Function are described below respectively：
X-ray source 10：The X ray object lens usually diffraction optical element with lens imaging function, such as zone plate, So the X-ray source 10 used in X ray differential phase contrast microscopic system can be homogeneous X-ray light source, as electronics is hit Hit characteristic spectral line X-ray source caused by metallic target, laser plasma X-ray source, synchrotron radiation homogeneous X-ray light source.
Condenser 1：Can be ellipsoid capillary, tapered capillaries, zone plate or other X ray with focusing function Optical element, its effect is to provide focused subbeams for sample.
Central stop 2：It is too strong straight from the X-ray source for stopping positioned at the export center part of condenser 1 Thang-kng illuminates sample and detector, makes the focus on light beam of illumination sample turn into hollow cone light beam.
Beam-splitting optical grating 3 '：Can be the cycle be micron dimension absorption grating, positioned at condenser 1 export central stop 2 Afterwards, for being split to the hollow cone light beam from condenser 1 and central stop 2, become with space periodic structure Hollow cone light beam.
Pin hole 3：It is too strong straight-through from the X-ray source for stopping before beam-splitting optical grating 3 ' afterwards sample stage Light and veiling glare illumination sample and detector.
Sample stage 4：Between pin hole 3 and object lens 5, for carrying sample, translation and rotary sample, its position is hung down Directly it is referred to as object plane in the plane of optical axis.
Object lens 5：It can be the optical element with X ray lens imaging function, such as zone plate, be a block period with half The circular grating that footpath increase tapers into, has lens function to homogeneous X-ray, therefore be referred to as X ray lens；Its effect has Two, first effect is that the sample structure amplification positioned at object plane with nanometer scale is imaged in image planes, and formation has micron The picture of scale structure, second effect is after imaging in object lens 5 by the annular section of hollow cone beam lighting on beam-splitting optical grating Focal plane is formed about circular grating picture and circular grating as light beam.
Annular analysis grating 6 '：Can be the absorption grating for being micron dimension or sub-micrometer scale in the cycle, positioned at object lens 5 Near back focal plane, its shape and size is with beam-splitting optical grating 3 ' during n.s by the annular section of hollow cone beam lighting in object lens 5 Circular grating near back focal plane as identical, for the circular grating near the back focal plane of object lens 5 as light beam is filtered.
Imaging detector 7：(such as X ray CCD) is formed by two-dimensional array pixel arrangement, each pixel has independent visit The strong function of light-metering, for measurement angle signal response curve, detection light intensity spatial position change, the intensified image for shooting sample, Its position is referred to as image planes perpendicular to the plane of optical axis.
Further, although beam-splitting optical grating 3 ' and annular analysis grating 6 ' are all absorption gratings, in grating thickness not In the case of big, have partial x-ray and pass through gratings strips, make through X ray produce phase shift, in order to avoid what phase shift was brought bears Face effect, the thickness of beam-splitting optical grating 3 ' are the odd-multiple of π phase shifts, and the thickness of annular analysis grating 6 ' is the even-multiple of π phase shifts.
In addition, the material of beam-splitting optical grating 3 ' and annular analysis grating 6 ' is golden or other heavy metals.
The X ray differential phase contrast microscopic system of embodiments of the invention is traditional X-ray microscope and beam splitting Grating 3 ' and annular analysis grating 6 ' are combined into, and on the basis of the imaging process of traditional X-ray microscope system, are added The physical content of two aspects：First, consider that refraction and scattering of the sample on depth of focus light pencil influence, that is, consider caused by sample Influence of the angle signal to imaging process；Second, consider the circular grating picture of angle signal regulation and control beam-splitting optical grating of sample in ring Shear displacemant on conformal analysis grating, angle signal is set to obtain Intensity response.
Fig. 3 is the two-dimensional imaging method according to the X ray differential phase contrast microscopic system of one embodiment of the invention FB(flow block), as shown in figure 3, the two-dimensional imaging method for described X ray differential phase contrast microscopic system, including Following steps：
S1, open and adjust light source：X-ray beam caused by the light source is set to be directed at condenser；
S2, adjustment condenser, central stop and pin hole：Make hollow cone beam alignment institute caused by condenser and central stop State and sample position is carried on sample stage, central stop and pin hole is stopped straight-through light and veiling glare from the X-ray source；
S3, adjust object lens：Object lens are made to focus on imaging detector of the imaging beam the to be formed alignment positioned at image planes；
S4, feed-in beam-splitting optical grating：After the central stop of condenser outlet, feed-in beam-splitting optical grating, shine hollow cone light beam The annular section of bright beam-splitting optical grating is formed about circular grating picture and circular grating as light beam in object lens back focal plane；
S5, feed-in and adjustment ring conformal analysis grating：Make annular analysis grating alignment beam-splitting optical grating near object lens back focal plane The circular grating picture of formation, adjustment ring conformal analysis grating grizzly bar direction, make annular analysis grating grizzly bar parallel to beam-splitting optical grating grid Bar；
S6, measuring angle signal response curve：Beam-splitting optical grating is progressively moved along perpendicular to optical axis and grating grizzly bar direction, is made The circular grating of beam-splitting optical grating as opposed annular analysis grating occur shear displacemant, with imaging detector image planes measure brightness with The angle signal response curve of circular grating image displacement change；Wherein, the angle signal measured in each pixel of imaging detector Response curve is essentially identical, and during measurement angle signal response curve, the light intensity signal that detector obtains is stronger, beam-splitting optical grating movement Step-length is more intensive, and the data SNR measured is higher；When the circular grating picture and annular analysis grating of beam-splitting optical grating are completely superposed When, circular grating is minimum as light beam percent of pass, and whole visual field turns into details in a play not acted out on stage, but told through dialogues, extreme lower position-paddy with angle signal response curve Position is corresponding；When the circular grating picture and annular analysis grating of beam-splitting optical grating stagger a quarter cycle, circular grating picture light Beam half is by the way that second half is blocked, and whole visual field turns into half bright field, corresponding with the upward slope position of angle signal response curve； When beam-splitting optical grating circular grating picture and annular analysis grating stagger the half cycle when, circular grating as light beam percent of pass most Height, whole visual field turn into bright field, corresponding with extreme higher position-peak position of angle signal response curve；When the annular of beam-splitting optical grating Grating image and annular analysis grating stagger 3/4ths cycles when, circular grating is blocked as light beam half, and second half passes through whole Individual visual field turns into half bright field, and the descending position that shifting curve is responded with angle signal is corresponding；
S7, angle signal response curve is fitted with cosine curve：Angle signal response curve is similar to cosine curve, with remaining The angle signal response curve that chord curve fitting measures, makes it obtain the Analytical Expression of cosine curve；Wherein, it is fitted angle signal During response curve, the light intensity signal that detector obtains is stronger, and beam-splitting optical grating moving step length is more intensive, and the data SNR measured is got over Height, the cosine curve of fitting are more accurate；
S8, shoot sample two dimension intensified image：The circular grating picture of beam-splitting optical grating is separately fixed at the angle signal to ring Paddy position, upward slope position, peak position, the descending position of curve are answered, sample is placed on sample stage, the paddy position intensified image of sample is shot, goes up a slope Intensified image, peak position intensified image, descending intensified image；
S9, quantitative two-dimensional image of the extraction sample in object space：Put from the paddy position intensified image, upward slope intensified image, peak position of sample Sample is extracted in big picture, descending intensified image in the absorption picture of object space, dioptric image and scattering picture；Because paddy position intensified image and peak position Intensified image sum is equal to upward slope intensified image and descending intensified image sum, so only having three kinds of intensified images to be in above-mentioned four kinds of intensified images It is independent, can be extracted from any three kinds of intensified images in four kinds of intensified images sample the absorption picture of object space, dioptric image and Scatter picture.
In the step S6 of the two-dimensional imaging method of the X ray differential phase contrast microscopic system, in view of sample Refraction on depth of focus light pencil and scattering influence, i.e., in view of influence of the angle signal caused by sample to imaging process, because This obtains the mathematic(al) representation of sample angle signal function, specifically, it is necessary to establish the mathematical modeling that sample is acted on X ray Method is as described below：
Define the rectangular coordinate system (x of sampleo,yo,zo), to being a little defined in sample, in two-dimensional imaging, sample A bit (x on the object plane of placeo,yo), it is not a two-dimensional geometry point, but one with (xo,yo) centered on thing cell area Δ x Δ y, Δ x and Δ y size are determined by the numerical aperture and detector resolution of object lens.Illustrate herein, it is cited below Object point, its implication are thing cell area.
It is dissipation process that an X-ray energy is converted into heat energy in the sample to absorb (including inelastic scattering), sample In a bit (xo,yo) depth of focus light pencil is absorbed, cause depth of focus light pencil brightness decay.A bit (x in sampleo,yo) to passing through this The absorption of the depth of focus light pencil of point can be expressed as：
WhereinRepresent Dirac function (to avoid obscuring with refractive index real part attenuation rate δ, with top tape labelTable Show Dirac function),For the deflection angle vector for the depth of focus light pencil being incident on sample,
Wherein μ (xo,yo,zo) be sample linear absorption coefficient.The physical significance of formula (1) is that absorption causes the thin light of depth of focus Beam energy loses, and causes depth of focus light pencil luminance-reduction, but does not change the depth of focus light pencil direction of propagation, is zero degree signal.Formula (1) it is also denoted as component form：
Wherein ψxAnd ψyRespectivelyAlong xoDirection and yoThe component in direction.
Fig. 4 is the refraction angle image formation according to the X ray differential phase contrast microscopic system of embodiments of the invention Schematic diagram, the arrow in partial enlarged drawing describe the refractive direction of depth of focus light pencil.It is as shown in figure 4, poly- from beam-splitting optical grating Jiao can be divided into multiple depth of focus light pencils, each depth of focus light pencil illuminates one in the hollow cone light beam of sample in object plane Object point (xo,yo), object point (xo,yo) to producing refraction by the depth of focus light pencil of the point, cause the ring near the back focal plane of object lens 6 Shape grating image opposed annular analysis grating is subjected to displacement, and makes to reach image planes picture point (x by annular analysis grating 7i,yi) photon Number occurs increase or reduced, (xo,yo) and (xi,yi) between be conjugate imaging relation, it is mutually unique corresponding.
Refraction is the process of a conservation of energy, according to Fig. 4, a bit (x in sampleo,yo) refraction to depth of focus light pencil can To be expressed as
WhereinFor refraction angle vector, the physical significance of formula (4) is that refraction changes the propagation side of depth of focus light pencil To, but depth of focus light pencil energy is not lost, do not cause depth of focus light pencil luminance-reduction.Formula (4) can also be written as component form,
Wherein θx(xo,yo) and θy(xo,yo) be respectivelyIn the x-direction with the component in y directions.Make δ (xo,yo,zo) Representative sample refractive index real part attenuation rate, thenIn (xo,yo) weight expression of rectangular coordinate system is
Fig. 5 is the angle of scattering image formation according to the X ray differential phase contrast microscopic system of embodiments of the invention Schematic diagram, arrow depicts scattering and causes depth of focus light pencil to expand to multiple sides from a direction of propagation in partial enlarged drawing To.As shown in figure 5, the hollow cone light beam for focusing on sample from beam-splitting optical grating, it is thin can be divided into multiple depths of focus in object plane Light beam, each depth of focus light pencil illuminate an object point (xo,yo), object point (xo,yo) to being produced by the depth of focus light pencil of the point Scattering, causes the striped of the circular grating picture near the back focal plane of object lens 6 to obscure, and makes to reach image planes picture by annular analysis grating 7 Point (xi,yi) number of photons occur increase or reduce, (xo,yo) and (xi,yi) between be conjugate imaging relation, it is mutually unique right Should.
Scattering (herein means and reflected inside cell area caused by little particle) is the process of a conservation of energy, scattering and refraction Difference be that refraction is studied using a cell area on sample object plane as an entirety, i.e., one on sample object plane Individual cell area is scattered then using this cell area as one block of ground glass as one piece of prism, studies the uneven of its inside Particle, bubble, crystallite, impurity inside property, such as cell area etc..Therefore, for each cell area, the thin light of depth of focus of outgoing Beam only has a refractive direction, but there is multiple scattering directions.In other words, scattering is the scattered process of a depth of focus light pencil.Cause Have certain thickness for sample, along the depth of focus light pencil direction of propagation inside cell area, each little particle distribution be it is random, it is front and rear Refraction caused by two little particles is separate that the angle that little particle reflects deviation depth of focus light pencil incident direction every time is Random, so according to central-limit theorem, angle of scattering is the normal state statistical distribution centered on incidence angle, can with variance come Scattering angular distribution scope is described.
It is small inside cell area as depth of focus light pencil is walked in the sample when depth of focus light pencil injects sample according to Fig. 5 The continuous generation of particle refraction event, scattering angular variance are gradually widened.Because gathering the angle signal of sample using grating, It is necessary scattering angle signal to be decomposed.A bit (x of sampleo,yo) (x is scattered in depth of focus light pencilo,yo) rectangular co-ordinate The weight expression of system is
WhereinWithFor (xo,yo) at point sample integral thickness respectively in xoDirection and yoProduce in direction Raw scattering angular variance.According to formula (7) and formula (8), although beam energy is not lost in scattering, scattering causes depth of focus light pencil Angle of flare increases.OrderThe scattering angular variance of representative sample integral thickness, subscript κ can be x or y, then It is X ray by a series of Δ z on pathoThe scattering angular variance of thin sliceSum, so sample is overall thick The scattering angular variance of degree can be expressed as the integration of scattering angular variance, i.e.,：
Wherein ωκ(xo,yo,zo) it is perpendicular to linear scattering coefficient of the light beam along κ directions.
Consider above-mentioned three kinds to act on, a bit (x in sampleo,yo) effect to the depth of focus light pencil by the point can be with With the angle signal function f (x of sampleo,yo,ψκ) be expressed as：
Wherein subscript κ can be x or y.
According to formula (10), it is known that perpendicular to light beam along κ directions, exit Xray carry sample three kinds of angles letter Number, zero degree signal：M(xo,yo), refraction angle signal：θκ(xo,yo), scattering angle signal：They can be represented For line integral, this just obtains sample three-dimensional structure using data for projection for computer tomography and has established Fundamentals of Mathematics.
In the step S6 of the two-dimensional imaging method of the X ray differential phase contrast microscopic system, it is contemplated that sample Angle signal regulation and control beam-splitting optical grating circular grating picture annular analysis grating on shear displacemant, make angle signal obtain light Strong response.Therefore, it is necessary to establish the angle signal receptance function of X ray differential phase contrast microscopic system, specific method is such as It is lower described：
In traditional X-ray microscope, beam propagation process during n.s can be described as follows.From X ray light The diffusion light beam in source is assembled by condenser and central stop stops, forms the hollow cone light beam for focusing on sample, can be in thing The hollow cone light beam of focusing is divided into multiple depth of focus light pencils, each depth of focus light pencil shines by face according to spatial coherence area A bright object point position.It is coherent light inside depth of focus light pencil, and it is mutually incoherent between two adjacent depth of focus light pencils.By thing Behind face, each depth of focus light pencil becomes the relevant hollow cone light beam spread one by one again, by the focussing force of object lens, respectively spreads Relevant hollow cone light beam becomes the relevant hollow cone light beam focused on one by one again, and picture point one by one is formed in image planes.Propagating During, it is relevant inside relevant hollow cone light beam, and be incoherent between two relevant hollow cone light beams.Focusing on When, each relevant hollow cone light beam all forms depth of focus light pencil, disconnected from each other on object plane and image planes, but before and after focusing, example It is spatially mutual weight such as in condenser, central stop, object lens, object lens back focal plane position, these relevant hollow cone light beams Close.In traditional X-ray microscope imaging theory, only consider sample absorption and phase shift, do not consider sample refraction and Scattering, or even if sample has refraction and scattering, but in the absence of the response mechanism for refraction and scattering being changed into light intensity, pass The X-ray microscope imaging theory of system thinks, after being put into sample, in addition to sample absorbs and causes beam brightness decline and phase shift, Without difference when beam propagation process and n.s.
One piece of beam-splitting optical grating is inserted after the condenser outlet of traditional X-ray microscope system, central stop, in object lens Back focal plane nearby inserts one block of annular analysis grating, the X ray differential phase contrast being formed in one embodiment of the invention Microscope.The effect of beam-splitting optical grating is hollow cone light beam to be divided into the hollow cone light beam with space structure, and make beam splitting light Grid are formed about circular grating picture and circular grating as light beam by the annular section of hollow cone beam lighting in object lens back focal plane.Ring The shape and size and beam-splitting optical grating of conformal analysis grating shape near object lens back focal plane by the annular section of hollow cone beam lighting Circularize that grating image is identical, its effect is as light beam is filtered to the circular grating near the object lens back focal plane.By This is understood, in X ray differential phase contrast microscope, beam propagation process during n.s can be described as follows：Carry out autohemagglutination The hollow cone light beam of light microscopic and central stop, by beam-splitting optical grating beam splitting, form the sky for focusing on sample with space structure The heart bores light beam.In object plane according to spatial coherence area, the hollow cone light beam of focusing is divided into multiple depth of focus light pencils, each Depth of focus light pencil illuminates an object point.It is coherent light inside depth of focus light pencil, and mutual not phase between two adjacent depth of focus light pencils It is dry.After object plane, each depth of focus light pencil becomes the relevant hollow cone light beam spread one by one again, makees by the focusing of object lens With again the relevant hollow cone light beam respectively spread becomes the relevant hollow cone light beam focused on one by one, not only attached in object lens back focal plane Respective circular grating is closely formed as light beam, and picture point one by one is formed in image planes.Although each relevant hollow cone light beam exists The circular grating that object lens back focal plane is formed about mutually coincides as light beam, but each of which independent propagation, mutually incoherent.
If placing sample on the microscopical object plane of X ray differential phase contrast, a little to passing through the point in sample Depth of focus light pencil produces refraction and scattering process, the depth of focus light pencil is produced two kinds of angle signals of deflection and diverging, this two Kind angle signal will necessarily cause the circular grating picture of the depth of focus light pencil that position movement and bar occurs on annular analysis grating Line is obscured, and causing is increased or reduced by the number of photons of annular analysis grating, and the angle signal of any will be in picture in sample Intensity response is obtained in the picture point in face.Therefore, filter action of the annular analysis grating to the circular grating picture of beam-splitting optical grating, is X Ray differential phase contrast microscope provides angle signal response image-forming mechanism.Because sample reflects the ring for causing beam-splitting optical grating The position movement of shape grating image, and beam-splitting optical grating equivalence is artificially moved during n.s, so in n.s, can be taking human as movement Beam-splitting optical grating, circular grating is measured as caused by the shear displacemant between annular analysis grating using one pixel of imaging detector Intensity response, so as to measure angle signal receptance function of the X ray differential phase contrast microscope to any on object plane.As for sample Product scattering causes the circular grating picture generation striped of beam-splitting optical grating to obscure, and is considered as circular grating picture each local opposed annular point Analysis grating does irregular shear displacemant, and resulting Intensity response can also be carried out with the angle signal receptance function measured Explain.Because the circular grating of each object point is as being to overlap near object lens back focal plane, it is possible to one piece of beam-splitting optical grating and One block of annular analysis grating can just be changed into the angle signal of each object point on object plane the Intensity response of each picture point in image planes.Change speech It, the refraction angle signal and scattering angle signal of sample each point are converted to the mechanism all same of response light intensity, have unified angle Signal receptance function.Therefore in n.s, beam-splitting optical grating can be moved once taking human as stepping, utilize each picture of imaging detector Element can measure respective angle signal receptance function parallel simultaneously.
Because beam-splitting optical grating and annular analysis grating are only capable of producing Intensity response to vertical raster grizzly bar orientation angle signal, And to not responded to parallel to the angle signal in grating grizzly bar direction, so the angle letter perpendicular to gratings strips direction need only be considered Number function.According to the circular grating picture of beam-splitting optical grating and the shear displacemant of annular analysis grating, it is known that the angle signal measured rings It is a rectilinear oscillation curve to answer curve.All it is low-angle signal due to reflecting and scattering, so not being the response of whole piece angle signal In action, but angle signal response curve is local in action for curve.Therefore, according to beam-splitting optical grating step-scan starting point not Together, angle signal receptance function curve can be divided into four types：
(i) it is completely superposed with the circular grating picture of beam-splitting optical grating and annular analysis grating as zero point, as beam-splitting optical grating walks Enter scanning, the circular grating of beam-splitting optical grating measures the song that brightness gradually rises as opposed annular analysis grating generation shear displacemant Line, referred to as paddy position response curve；
(ii) using the circular grating picture of beam-splitting optical grating and annular analysis grating stagger a quarter cycle as zero point, with point Beam grating step-scan, the circular grating of beam-splitting optical grating is as opposed annular analysis grating generation shear displacemant, along shear displacemant Augment direction, brightness progressively linearly increasing curve is measured, the direction reduced along shear displacemant, measure brightness progressively linear decline Curve, referred to as go up a slope response curve；
(iii) the half cycle is staggered as zero point using the circular grating picture of beam-splitting optical grating and annular analysis grating, with As opposed annular analysis grating shear displacemant occurs for beam-splitting optical grating step-scan, the circular grating of beam-splitting optical grating, measure brightness by Walk the curve declined, referred to as peak position response curve；
(iv) using the circular grating picture of beam-splitting optical grating and annular analysis grating staggered for 3/4ths cycles as zero point, with divide Beam grating step-scan, the circular grating of beam-splitting optical grating is as opposed annular analysis grating generation shear displacemant, along shear displacemant Augment direction, brightness progressively linear decline curve is measured, the direction reduced along shear displacemant, measure brightness progressively linear rise Curve, referred to as descending response curve.
Fig. 6 is four kinds of angle signal receptance function curve maps of X ray differential phase contrast microscopic system.According to Fig. 6, Understand that angle signal response curve is similar to cosine curve, approximation can be fitted with cosine curve, make angle signal response curve can To carry out Analytical Expression with the cosine curve of fitting, have
Or it is expressed as
Wherein xpPosition coordinates at grating is analyzed for annular,For the circular grating image displacement counterpart of beam-splitting optical grating The angular displacement in face, doFor object distance of the sample with respect to object lens, p is the cycle of annular analysis grating,Believe for angle Number response curve average value, RmaxAnd RminThe respectively maximum and minimum value of angle signal response curve, For the visibility of angle signal response curve, n is modulation parameter, and n=0,1,2,3 corresponds respectively to the response of (a) paddy position in Fig. 6 Curve, (b) upward slope response curve, (c) peak position response curve and (d) descending response curve.
According to the derivation of angle signal receptance function, it is known that angle signal receptance function describes the angle of an object point Percent of pass of the imaging subnumber of signals-modulating object point when by annular analysis grating.
According to the constant theorem of brightness, in the perfect optical system of noenergy decay, brightness is a conserved quantity.It is although true The efficiency of transmission of real optical system can not possibly reach 100%, but brightness of the true optical system in image planes be able to can be seen Make the product of object plane brightness and an efficiency of transmission.In X ray differential phase contrast microscopic system, from object plane to image planes, In addition to sample absorbs and causes brightness decline, diffraction efficiency and annular of the main contributions that brightness declines from object lens is caused to be analyzed The percent of pass of grating, thus image planes brightness is considered as brightness and object lens diffraction efficiency and the annular analysis grating percent of pass of object plane Product.During n.s, if incident beam brightness is B at object plane0, the diffraction efficiency of object lens is η, then near object lens back focal plane The brightness of beam-splitting optical grating circular grating picture be η B0.According to formula (12), during n.s, the percent of pass of annular analysis grating is exactly Angle signal receptance function, thus annular analyzes the brightness after grating, or image planes brightness is
Formula (13) is exactly to consider the angle signal receptance function of object lens diffraction efficiency.
In the step S8 of the two-dimensional imaging method of the X ray differential phase contrast microscopic system, imaging detector The two-dimentional intensified image of shooting is described with angle signal imaging equation.Therefore, it is necessary to establish angle signal imaging equation, specific method As described below：
Zoomed into for sample as, imaging of each pixel of detector to object plane each point is parallel and separate , therefore, imaging of one pixel of detector to any in sample need only be discussed, shown with regard to X ray differential phase contrast can be established Micro mirror imaging equation.Because sample each point reflects and scattered the mechanism all same for being converted to light intensity, there is translation not on object plane Denaturation, it is possible to which the X ray differential phase is derived according to the convolution of above-mentioned angle signal function and angle signal receptance function The microscopical angle signal imaging equation of contrast.Need to illustrate herein, convolution algorithm is the refraction in angle signal function Angle, angle of scattering and angle signal receptance function convolution algorithm, convolution algorithm and space coordinates are unrelated；Suction in angle signal function Receipts are zero degree signals, are not involved in convolution algorithm.
After being put into sample, an object point (x on object planeo,yo) absorption to the depth of focus light pencil by the point can be burnt after object lens Face nearby causes circular grating picture that brightness decline occurs, and refraction can cause circular grating picture that position occurs near object lens back focal plane Skew, scattering can cause circular grating picture generation striped to obscure near object lens back focal plane.After annular analysis grating filtering, Picture point (x in image planesi,yi) brightness be angle signal function and angle signal receptance function convolution.Due to beam-splitting optical grating and ring Conformal analysis grating is only capable of producing Intensity response to vertical raster grizzly bar orientation angle signal, and to parallel to grating grizzly bar direction Angle signal does not respond to, so need only consider the angle signal function and angle signal receptance function perpendicular to gratings strips direction Convolution.Thus have
Wherein (xo,yo) it is object plane coordinate, (xi,yi) it is image coordinates, B (xi,yi,ψx) it is to pass through object point (xo,yo) Jiao Deep light pencil is in picture point (xi,yi) brightness.Formula (17) be X ray differential phase contrast microscope establish angle signal into Image space journey.
In the step S8 of the two-dimensional imaging method of the X ray differential phase contrast microscopic system, described handle point The circular grating picture of beam grating is fixed on the paddy position of angle signal response curve, and sample, imaging detector are placed on sample stage The paddy position intensified image of sample is photographed, the method for specifically shooting two-dimentional intensified image in an experiment is as described below：
Before being put into sample, circular grating picture is fixed on the paddy position of angle signal response curve, even ψx=0, n=0, so After place sample, detector can photograph the paddy position intensified image of sample, and its expression formula is
In the step S8 of the two-dimensional imaging method of the X ray differential phase contrast microscopic system, described handle point The circular grating picture of beam grating is fixed on the upward slope position of angle signal response curve, the method for shooting sample upward slope position intensified image： Before being put into sample, circular grating picture is fixed on the upward slope position of angle signal response curve, even ψx=0, n=1, then place Good sample, detector can photograph the upward slope intensified image of sample, and its expression formula is
In the step S8 of the two-dimensional imaging method of the X ray differential phase contrast microscopic system, described handle point The circular grating picture of beam grating is fixed on the peak position of angle signal response curve, the method for shooting sample peak position intensified image：It is put into Before sample, circular grating picture is fixed on the peak position of angle signal response curve, even ψx=0, n=2, then place sample Product, detector can photograph the peak position intensified image of sample, and its expression formula is
In the step S8 of the two-dimensional imaging method of the X ray differential phase contrast microscopic system, described handle point The circular grating picture of beam grating is fixed on the descending position of angle signal response curve, the method for shooting sample descending position intensified image： Before being put into sample, circular grating picture is fixed on the descending position of angle signal response curve, even ψx=0, n=3, then place Good sample, detector can photograph the descending intensified image of sample, and its expression formula is
It is described from sample in the step S9 of the two-dimensional imaging method of the X ray differential phase contrast microscopic system Absorption picture, folding of the sample in object space are extracted in the paddy position intensified images of product, upward slope intensified image, peak position intensified image, descending intensified image Image and scattering image space method are as described below：Extraction sample object space absorb picture formula be：
Extract sample is in the formula of object space dioptric image：
Under the conditions of scattering is negligible, extraction sample is in the simplified formula of object space dioptric image：
Extraction sample object space scattering picture formula be：
Under the conditions of refraction is negligible, extraction sample is in the simplified formula of object space scattering picture：
In addition, as an alternative embodiment, X-ray source 10, condenser 1, beam-splitting optical grating 3 ' can be integrated into One element, i.e. cycle are the X ray ring-shaped gate source 10 ' of micron dimension, as shown in fig. 7, now in X ray ring-shaped gate source 10 ' Exit is sequentially placed two annular light holes 20 and 30 along optical axis direction, passes through the light beam from X ray ring-shaped gate source 10 ' After two annular light holes 20 and 30, formed illumination sample and the hollow cone light beam with space periodic structure, and in object lens 5 Back focal plane is formed about ring-shaped gate source image and ring-shaped gate source image light beam, the shape and size of annular analysis grating 6 ' and ring-shaped gate source As identical.This X ray differential phase contrast microscopic system 100 ' based on ring-shaped gate source 10 ' causes whole X ray differential The length of phase contrast microscopic system can further shorten, and can not only reduce the manufacturing cost of X-ray microscope system, And the utilization ratio of light also can be improved further, be had broad application prospects.
Because the above-mentioned X ray differential phase contrast based on ring-shaped gate source, ring-shaped gate source image and annular analysis grating is micro- The two-dimensional imaging method of mirror system, with the foregoing X based on beam-splitting optical grating, the circular grating picture of beam-splitting optical grating and annular analysis grating The two-dimensional imaging method of ray differential phase contrast microscopic system is similar, and here is omitted.
Above description is only the preferred embodiment of the application and the explanation to institute's application technology principle.People in the art Member should be appreciated that invention scope involved in the application, however it is not limited to the technology that the particular combination of above-mentioned technical characteristic forms Scheme, while should also cover in the case where not departing from the inventive concept, carried out by above-mentioned technical characteristic or its equivalent feature The other technical schemes for being combined and being formed.Such as features described above has similar work(with (but not limited to) disclosed herein The technical scheme that the technical characteristic of energy is replaced mutually and formed.

Claims (10)

1. a kind of X ray differential phase contrast microscopic system, including：For producing the light source of X ray；And passed along X ray Broadcast condenser, central stop, beam-splitting optical grating, pin hole, sample stage, object lens, annular analysis grating and imaging that direction is set gradually Detector, wherein：
The light source for being used to produce X ray is homogeneous X-ray light source；
The condenser is ellipsoid capillary, tapered capillaries, zone plate or other X ray optics members with focusing function Part, for producing the focus on light beam of illumination sample；
The central stop is located at the condenser export center, for stopping the straight-through light from the X-ray source, is formed Illuminate the hollow cone light beam of sample；
The absorption grating that it is micron dimension in the cycle that the beam-splitting optical grating, which is, after the central stop, for from described The hollow cone light beam of condenser and the central stop is split, and becomes the hollow cone light with space periodic structure Beam；
After the pin hole is located at the beam-splitting optical grating, for stopping straight-through light and veiling glare from the X-ray source；
The sample stage is located at object plane, for carrying sample, and can translate and rotary sample；
The object lens are zone plate or other optical elements with X ray lens imaging function, for the tool positioned at object plane Have the sample structure of nanometer scale, be enlarged into the picture in image planes with micron dimension structure, make to have micron dimension pixel into As detector can shoot the intensified image of sample, and make the beam-splitting optical grating by the annular section of hollow cone beam lighting after object lens Focal plane is formed about circular grating picture and circular grating as light beam；
It is micron or the absorption grating of sub-micrometer scale in the cycle that the annular analysis grating, which is, attached positioned at the object lens back focal plane Closely, the circular grating of its shape and size and the beam-splitting optical grating near object lens back focal plane is as identical, for the object lens Circular grating near back focal plane is filtered as light beam；
The imaging detector is located at image planes, for shooting the two-dimentional intensified image of sample.
2. X ray differential phase contrast microscopic system according to claim 1, the beam-splitting optical grating and the annular point The material for analysing grating is golden or other heavy metals.
3. X ray differential phase contrast microscopic system according to claim 1, in the beam-splitting optical grating and the annular In the case that analysis grating thickness is little, the thickness of beam-splitting optical grating is the odd-multiple of π phase shifts, and the thickness of annular analysis grating is π The even-multiple of phase shift.
A kind of 4. two-dimensional imaging side of X ray differential phase contrast microscopic system for described in claim any one of 1-3 Method, comprise the following steps：
S1, open and adjust light source：X-ray beam caused by the light source is set to be directed at condenser；
S2, adjustment condenser, central stop and pin hole：Make sample described in hollow cone beam alignment caused by condenser and central stop Sample position is carried in sample platform, central stop and pin hole is stopped straight-through light and veiling glare from the X-ray source；
S3, adjust object lens：Object lens are made to focus on imaging detector of the imaging beam the to be formed alignment positioned at image planes；
S4, feed-in beam-splitting optical grating：After the central stop of condenser outlet, feed-in beam-splitting optical grating, make hollow cone beam lighting point The annular section of beam grating is formed about circular grating picture and circular grating as light beam in object lens back focal plane；
S5, feed-in and adjustment ring conformal analysis grating：Annular analysis grating alignment beam-splitting optical grating is set to be formed about in object lens back focal plane Circular grating picture, adjustment ring conformal analysis grating grizzly bar direction, make annular analysis grating grizzly bar parallel to beam-splitting optical grating grizzly bar；
S6, measuring angle signal response curve：Beam-splitting optical grating is progressively moved along perpendicular to optical axis and grating grizzly bar direction, makes beam splitting As opposed annular analysis grating shear displacemant occurs for the circular grating of grating, and brightness is measured with annular in image planes with imaging detector The angle signal response curve of grating image change in displacement；
S7, angle signal response curve is fitted with cosine curve：Angle signal response curve is similar to cosine curve, bent with cosine The angle signal response curve that line fitting measures, makes it obtain the Analytical Expression of cosine curve；
S8, shoot sample two dimension intensified image：It is bent that the circular grating picture of beam-splitting optical grating is separately fixed at the angle signal response Paddy position, upward slope position, peak position, the descending position of line, place sample on sample stage, shoot the paddy position intensified image of sample, amplification of going up a slope Picture, peak position intensified image, descending intensified image；
S9, quantitative two-dimensional image of the extraction sample in object space：From the paddy position intensified image of sample, upward slope intensified image, peak position intensified image, Sample is extracted in descending intensified image in the absorption picture of object space, dioptric image and scattering picture；From any three kinds in four kinds of intensified images Sample is extracted in intensified image in the absorption picture of object space, dioptric image and scattering picture.
5. the two-dimensional imaging method of X ray differential phase contrast microscopic system according to claim 4, wherein, in institute State in step S6, it is contemplated that refraction and scattering of the sample on depth of focus light pencil influence, i.e., believe in view of angle caused by sample Influence number to imaging process, therefore sample angle signal function f (xo,yo,ψx) be expressed as
<mrow> <mi>f</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>o</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>o</mi> </msub> <mo>,</mo> <msub> <mi>&amp;psi;</mi> <mi>x</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mi>exp</mi> <mrow> <mo>(</mo> <mo>-</mo> <mi>M</mi> <mo>(</mo> <msub> <mi>x</mi> <mi>o</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>o</mi> </msub> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mrow> <msqrt> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> </msqrt> <msub> <mi>&amp;sigma;</mi> <mi>x</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>o</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>o</mi> </msub> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>&amp;CenterDot;</mo> <mi>exp</mi> <mo>&amp;lsqb;</mo> <mrow> <mo>-</mo> <mfrac> <msup> <mrow> <mo>(</mo> <msub> <mi>&amp;psi;</mi> <mi>x</mi> </msub> <mo>-</mo> <msub> <mi>&amp;theta;</mi> <mi>x</mi> </msub> <mo>(</mo> <msub> <mi>x</mi> <mi>o</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>o</mi> </msub> <mo>)</mo> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mrow> <mn>2</mn> <msubsup> <mi>&amp;sigma;</mi> <mi>x</mi> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>o</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>o</mi> </msub> <mo>)</mo> </mrow> </mrow> </mfrac> </mrow> <mo>&amp;rsqb;</mo> </mrow>
Wherein M (xo,yo)、θx(xo,yo) andThe respectively absorption of sample, refraction angle and scattering angular variance, and X are penetrated The sample required in the imaging of line differential phase contrast microscope two-dimensional quantitative is in the absorption picture of object space, dioptric image and scatters picture, Their expression formula is
<mrow> <mi>M</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>o</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>o</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&amp;Integral;</mo> <mrow> <mo>-</mo> <mi>&amp;infin;</mi> </mrow> <mi>&amp;infin;</mi> </munderover> <mi>&amp;mu;</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>o</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>o</mi> </msub> <mo>,</mo> <msub> <mi>z</mi> <mi>o</mi> </msub> <mo>)</mo> </mrow> <msub> <mi>dz</mi> <mi>o</mi> </msub> </mrow>
<mrow> <msub> <mi>&amp;theta;</mi> <mi>x</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>o</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>o</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mo>-</mo> <munderover> <mo>&amp;Integral;</mo> <mrow> <mo>-</mo> <mi>&amp;infin;</mi> </mrow> <mi>&amp;infin;</mi> </munderover> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>&amp;delta;</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>o</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>o</mi> </msub> <mo>,</mo> <msub> <mi>z</mi> <mi>o</mi> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>x</mi> <mi>o</mi> </msub> </mrow> </mfrac> <msub> <mi>dz</mi> <mi>o</mi> </msub> </mrow>
<mrow> <msubsup> <mi>&amp;sigma;</mi> <mi>x</mi> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>o</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>o</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&amp;Integral;</mo> <mrow> <mo>-</mo> <mi>&amp;infin;</mi> </mrow> <mrow> <mo>+</mo> <mi>&amp;infin;</mi> </mrow> </munderover> <msub> <mi>&amp;omega;</mi> <mi>x</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>o</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>o</mi> </msub> <mo>,</mo> <msub> <mi>z</mi> <mi>o</mi> </msub> <mo>)</mo> </mrow> <msub> <mi>dz</mi> <mi>o</mi> </msub> </mrow>
Wherein (xo,yo,zo) for space coordinates at object plane, μ is linear absorption coefficient, and δ is refractive index real part attenuation rate, ωxIt is vertical Directly in the linear scattering coefficient in grating grizzly bar direction.
6. the two-dimensional imaging method of X ray differential phase contrast microscopic system according to claim 4, in the step What is measured in S6 is angle signal response curve, and it is with fitting cosine curve Analytical Expression
<mrow> <msub> <mi>&amp;eta;B</mi> <mn>0</mn> </msub> <msub> <mi>R</mi> <mi>n</mi> </msub> <mrow> <mo>(</mo> <mfrac> <msub> <mi>x</mi> <mi>p</mi> </msub> <msub> <mi>d</mi> <mi>o</mi> </msub> </mfrac> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>&amp;eta;B</mi> <mn>0</mn> </msub> <mover> <mi>R</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mo>&amp;lsqb;</mo> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>V</mi> <mn>0</mn> </msub> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mrow> <mo>(</mo> <mrow> <mfrac> <mrow> <mn>2</mn> <msub> <mi>&amp;pi;d</mi> <mi>o</mi> </msub> </mrow> <mi>p</mi> </mfrac> <mfrac> <msub> <mi>x</mi> <mi>p</mi> </msub> <msub> <mi>d</mi> <mi>o</mi> </msub> </mfrac> <mo>+</mo> <mi>n</mi> <mfrac> <mi>&amp;pi;</mi> <mn>2</mn> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mo>,</mo> <mi>n</mi> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> </mrow>
Or it is expressed as
<mrow> <msub> <mi>&amp;eta;B</mi> <mn>0</mn> </msub> <msub> <mi>R</mi> <mi>n</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>&amp;psi;</mi> <mi>x</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>&amp;eta;B</mi> <mn>0</mn> </msub> <mover> <mi>R</mi> <mo>&amp;OverBar;</mo> </mover> <mo>&amp;lsqb;</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>V</mi> <mn>0</mn> </msub> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <mn>2</mn> <msub> <mi>&amp;pi;d</mi> <mi>o</mi> </msub> </mrow> <mi>p</mi> </mfrac> <msub> <mi>&amp;psi;</mi> <mi>x</mi> </msub> <mo>+</mo> <mi>n</mi> <mfrac> <mi>&amp;pi;</mi> <mn>2</mn> </mfrac> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> <mo>,</mo> <mi>n</mi> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> </mrow>
Wherein η is object lens diffraction efficiency, B0For incident beam brightness, x at object planepPosition coordinates at grating is analyzed for annular,For angular displacement of the circular grating image displacement with respect to object plane, doFor object distance of the sample with respect to object lens, p is annular analysis grating Cycle,For angle signal response curve average value, RmaxAnd RminRespectively angle signal response curve Maximum and minimum value,For the visibility of angle signal response curve, n is modulation parameter, n=0,1,2,3 Paddy position response curve, upward slope response curve, peak position response curve and descending response curve are corresponded to respectively.
7. the two-dimensional imaging method of X ray differential phase contrast microscopic system according to claim 4, in the step In S8, the two-dimentional intensified image of imaging detector shooting is described with angle signal imaging equation, and angle signal imaging equation is angle The convolution of signal function and angle signal receptance function, its expression formula are：
<mrow> <mi>B</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;psi;</mi> <mi>x</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mi>f</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>o</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>o</mi> </msub> <mo>,</mo> <msub> <mi>&amp;psi;</mi> <mi>x</mi> </msub> <mo>)</mo> </mrow> <mo>&amp;CircleTimes;</mo> <msub> <mi>&amp;eta;B</mi> <mn>0</mn> </msub> <msub> <mi>R</mi> <mi>n</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>&amp;psi;</mi> <mi>x</mi> </msub> <mo>)</mo> </mrow> <mo>,</mo> <mi>n</mi> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> </mrow>
Wherein (xo,yo) it is object plane coordinate, (xi,yi) it is image coordinates, η is object lens diffraction efficiency, B0For incident beam at object plane Brightness, n=0,1,2,3 correspond to respectively paddy position amplification imaging equation, go up a slope amplification imaging equation, peak position amplification imaging equation and under Amplify imaging equation in slope.
8. the two-dimensional imaging method of X ray differential phase contrast microscopic system according to claim 4, wherein,
It is described that the circular grating picture of beam-splitting optical grating is fixed on angle signal response curve paddy position in the step S8, Sample is placed on sample stage, imaging detector photographs the paddy position intensified image of sample, and its expression formula is
<mrow> <msub> <mi>B</mi> <mi>V</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>&amp;eta;B</mi> <mn>0</mn> </msub> <mover> <mi>R</mi> <mo>&amp;OverBar;</mo> </mover> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mi>M</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>o</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>o</mi> </msub> <mo>)</mo> </mrow> </mrow> </msup> <mo>&amp;lsqb;</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>V</mi> <mn>0</mn> </msub> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mn>2</mn> <msup> <mi>&amp;pi;</mi> <mn>2</mn> </msup> <msubsup> <mi>d</mi> <mi>o</mi> <mn>2</mn> </msubsup> <msubsup> <mi>&amp;sigma;</mi> <mi>x</mi> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>o</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>o</mi> </msub> <mo>)</mo> </mrow> <mo>/</mo> <msup> <mi>p</mi> <mn>2</mn> </msup> </mrow> </msup> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <mn>2</mn> <msub> <mi>&amp;pi;d</mi> <mi>o</mi> </msub> </mrow> <mi>p</mi> </mfrac> <msub> <mi>&amp;theta;</mi> <mi>x</mi> </msub> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mi>o</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>o</mi> </msub> </mrow> <mo>)</mo> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow>
It is described that the circular grating picture of beam-splitting optical grating is fixed on angle signal response curve upward slope position in the step S8, Sample is placed on sample stage, imaging detector photographs the upward slope intensified image of sample, and its expression formula is
<mrow> <msub> <mi>B</mi> <mi>U</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>&amp;eta;B</mi> <mn>0</mn> </msub> <mover> <mi>R</mi> <mo>&amp;OverBar;</mo> </mover> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mi>M</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>o</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>o</mi> </msub> <mo>)</mo> </mrow> </mrow> </msup> <mo>&amp;lsqb;</mo> <mrow> <mn>1</mn> <mo>+</mo> <msub> <mi>V</mi> <mn>0</mn> </msub> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mn>2</mn> <msup> <mi>&amp;pi;</mi> <mn>2</mn> </msup> <msubsup> <mi>d</mi> <mi>o</mi> <mn>2</mn> </msubsup> <msubsup> <mi>&amp;sigma;</mi> <mi>x</mi> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>o</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>o</mi> </msub> <mo>)</mo> </mrow> <mo>/</mo> <msup> <mi>p</mi> <mn>2</mn> </msup> </mrow> </msup> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <mrow> <mfrac> <mrow> <mn>2</mn> <msub> <mi>&amp;pi;d</mi> <mi>o</mi> </msub> </mrow> <mi>p</mi> </mfrac> <msub> <mi>&amp;theta;</mi> <mi>x</mi> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mi>o</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>o</mi> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mo>)</mo> </mrow> </mrow> <mo>&amp;rsqb;</mo> </mrow>
It is described that the circular grating picture of beam-splitting optical grating is fixed on angle signal response curve peak position in the step S8, Sample is placed on sample stage, imaging detector photographs the peak position intensified image of sample, and its expression formula is
<mrow> <msub> <mi>B</mi> <mi>P</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>&amp;eta;B</mi> <mn>0</mn> </msub> <mover> <mi>R</mi> <mo>&amp;OverBar;</mo> </mover> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mi>M</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>o</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>o</mi> </msub> <mo>)</mo> </mrow> </mrow> </msup> <mo>&amp;lsqb;</mo> <mrow> <mn>1</mn> <mo>+</mo> <msub> <mi>V</mi> <mn>0</mn> </msub> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mn>2</mn> <msup> <mi>&amp;pi;</mi> <mn>2</mn> </msup> <msubsup> <mi>d</mi> <mi>o</mi> <mn>2</mn> </msubsup> <msubsup> <mi>&amp;sigma;</mi> <mi>x</mi> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>o</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>o</mi> </msub> <mo>)</mo> </mrow> <mo>/</mo> <msup> <mi>p</mi> <mn>2</mn> </msup> </mrow> </msup> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <mrow> <mfrac> <mrow> <mn>2</mn> <msub> <mi>&amp;pi;d</mi> <mi>o</mi> </msub> </mrow> <mi>p</mi> </mfrac> <msub> <mi>&amp;theta;</mi> <mi>x</mi> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mi>o</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>o</mi> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mo>)</mo> </mrow> </mrow> <mo>&amp;rsqb;</mo> </mrow>
It is described that the circular grating picture of beam-splitting optical grating is fixed on angle signal response curve descending position in the step S8, Sample is placed on sample stage, imaging detector photographs the descending intensified image of sample, and its expression formula is
<mrow> <msub> <mi>B</mi> <mi>D</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>&amp;eta;B</mi> <mn>0</mn> </msub> <mover> <mi>R</mi> <mo>&amp;OverBar;</mo> </mover> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mi>M</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>o</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>o</mi> </msub> <mo>)</mo> </mrow> </mrow> </msup> <mo>&amp;lsqb;</mo> <mrow> <mn>1</mn> <mo>+</mo> <msub> <mi>V</mi> <mn>0</mn> </msub> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mn>2</mn> <msup> <mi>&amp;pi;</mi> <mn>2</mn> </msup> <msubsup> <mi>d</mi> <mi>o</mi> <mn>2</mn> </msubsup> <msubsup> <mi>&amp;sigma;</mi> <mi>x</mi> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>o</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>o</mi> </msub> <mo>)</mo> </mrow> <mo>/</mo> <msup> <mi>p</mi> <mn>2</mn> </msup> </mrow> </msup> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <mrow> <mfrac> <mrow> <mn>2</mn> <msub> <mi>&amp;pi;d</mi> <mi>o</mi> </msub> </mrow> <mi>p</mi> </mfrac> <msub> <mi>&amp;theta;</mi> <mi>x</mi> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mi>o</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>o</mi> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mo>)</mo> </mrow> </mrow> <mo>&amp;rsqb;</mo> </mrow>
Due to
BV(xi,yi)+BP(xi,yi)=BU(xi,yi)+BD(xi,yi)
So three width seem independent, any of which in paddy position intensified image, upward slope intensified image, peak position intensified image, descending intensified image Width picture can be expressed with its excess-three width picture；During the above is various, (xi,yi) it is image coordinates, η is the diffraction efficiency of object lens, B0To illuminate the brightness of object plane light beam,For the average value of angle signal response curve, RmaxAnd RminRespectively The maximum and minimum value of angle signal response curve,For the visibility of angle signal response curve, doFor For sample with respect to the object distance of object lens, p is annular analysis screen periods.
9. the two-dimensional imaging method of X ray differential phase contrast microscopic system according to claim 4, in the step In S9, the sample that extracted from the paddy position intensified image of sample, upward slope intensified image, peak position intensified image, descending intensified image is in thing The absorption picture in space, dioptric image and scattering image space method are as follows：
Extraction sample object space absorb picture formula be
<mrow> <mi>M</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>o</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>o</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mi>ln</mi> <mo>(</mo> <mfrac> <mrow> <mn>2</mn> <msub> <mi>&amp;eta;B</mi> <mn>0</mn> </msub> <mover> <mi>R</mi> <mo>&amp;OverBar;</mo> </mover> </mrow> <mrow> <msub> <mi>B</mi> <mi>U</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>B</mi> <mi>D</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>)</mo> <mo>=</mo> <mi>ln</mi> <mo>(</mo> <mfrac> <mrow> <mn>2</mn> <msub> <mi>&amp;eta;B</mi> <mn>0</mn> </msub> <mover> <mi>R</mi> <mo>&amp;OverBar;</mo> </mover> </mrow> <mrow> <msub> <mi>B</mi> <mi>V</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>B</mi> <mi>P</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>)</mo> </mrow>
Extract sample is in the formula of object space dioptric image
<mrow> <msub> <mi>&amp;theta;</mi> <mi>x</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>o</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>o</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mo>-</mo> <mo>(</mo> <mfrac> <mi>p</mi> <mrow> <mn>2</mn> <msub> <mi>&amp;pi;d</mi> <mi>o</mi> </msub> </mrow> </mfrac> <mo>)</mo> <mi>arctan</mi> <mo>(</mo> <mfrac> <mrow> <msub> <mi>B</mi> <mi>U</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>B</mi> <mi>D</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <msub> <mi>B</mi> <mi>V</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>B</mi> <mi>P</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>)</mo> </mrow>
Under the conditions of scattering is negligible, extraction sample is in the simplified formula of object space dioptric image
<mrow> <msub> <mi>&amp;theta;</mi> <mi>x</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>o</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>o</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mo>-</mo> <mo>(</mo> <mfrac> <mi>p</mi> <mrow> <mn>2</mn> <msub> <mi>&amp;pi;d</mi> <mi>o</mi> </msub> </mrow> </mfrac> <mo>)</mo> <mi>a</mi> <mi>r</mi> <mi>c</mi> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mo>(</mo> <mrow> <mfrac> <mrow> <msub> <mi>B</mi> <mi>U</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>B</mi> <mi>D</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <msub> <mi>B</mi> <mi>U</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>B</mi> <mi>D</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>&amp;CenterDot;</mo> <mfrac> <mn>1</mn> <msub> <mi>V</mi> <mn>0</mn> </msub> </mfrac> </mrow> <mo>)</mo> </mrow>
Extraction sample object space scattering picture formula be
<mrow> <msubsup> <mi>&amp;sigma;</mi> <mi>x</mi> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>o</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>o</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mo>(</mo> <mfrac> <msup> <mi>p</mi> <mn>2</mn> </msup> <mrow> <mn>2</mn> <msup> <mi>&amp;pi;</mi> <mn>2</mn> </msup> <msubsup> <mi>d</mi> <mi>o</mi> <mn>2</mn> </msubsup> </mrow> </mfrac> <mo>)</mo> <mi>l</mi> <mi>n</mi> <mfrac> <msub> <mi>V</mi> <mn>0</mn> </msub> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <mfrac> <mrow> <msub> <mi>B</mi> <mi>V</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>B</mi> <mi>P</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <msub> <mi>B</mi> <mi>V</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>B</mi> <mi>P</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mfrac> <mrow> <msub> <mi>B</mi> <mi>U</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>B</mi> <mi>D</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <msub> <mi>B</mi> <mi>U</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>B</mi> <mi>D</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> </mfrac> </mrow>
Under the conditions of refraction is negligible, extraction sample is in the simplified formula of object space scattering picture
<mrow> <msubsup> <mi>&amp;sigma;</mi> <mi>x</mi> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>o</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>o</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mo>(</mo> <mfrac> <msup> <mi>p</mi> <mn>2</mn> </msup> <mrow> <mn>2</mn> <msup> <mi>&amp;pi;</mi> <mn>2</mn> </msup> <msubsup> <mi>d</mi> <mi>o</mi> <mn>2</mn> </msubsup> </mrow> </mfrac> <mo>)</mo> <mi>l</mi> <mi>n</mi> <mo>(</mo> <mrow> <mfrac> <mrow> <msub> <mi>B</mi> <mi>V</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>B</mi> <mi>P</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <msub> <mi>B</mi> <mi>V</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>B</mi> <mi>P</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>&amp;CenterDot;</mo> <msub> <mi>V</mi> <mn>0</mn> </msub> </mrow> <mo>)</mo> </mrow>
During the above is various, (xo,yo) it is object plane coordinate, (xi,yi) it is image coordinates, doFor sample with respect to object lens object distance,
10. X ray differential phase contrast microscopic system according to claim 1, the X-ray source, condenser and Beam-splitting optical grating is integrated into the X ray ring-shaped gate source element that a cycle is micron dimension, now in the X ray ring-shaped gate source Exit, two annular light holes are sequentially placed along optical axis, the light beam that the ring-shaped gate source is sent is passed through two annular thang-kngs Kong Hou, forms the hollow cone light beam of illumination sample, and is formed about ring-shaped gate source image and ring-shaped gate source image light in object lens back focal plane Beam, the shape and size of the annular analysis grating are identical with the ring-shaped gate source image.
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