CN104949940B - A kind of apparatus and method for measuring scatterer scattering function real and imaginary parts - Google Patents
A kind of apparatus and method for measuring scatterer scattering function real and imaginary parts Download PDFInfo
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Abstract
The present invention relates to a kind of apparatus and method for measuring scatterer scattering function real and imaginary parts, line of collimation polarized laser beam is sent by laser, transmitted light beam and the reflected beams are uniformly divided into by the first spectroscope after being expanded via beam expanding lens；The transmitted light beam transmitted via the first spectroscope is reflected in the second spectroscope via after neutral density filter plate by the first speculum；Scatterer is reflexed to by the second speculum via after neutral density filter plate by the reflected beams of the first dichroic mirror, produces scattered beam coaxial superposition at the second spectroscope with modulation scattering function；Mixed light electron gun caused by superposition is detected sensor and detected, and after the pictorial information that recorded is handled via microcomputer loader, obtains scattering function complete information caused by scatterer, the real and imaginary parts comprising scattering function.
Description
Technical Field
The invention belongs to the technical field of applied optics, and particularly relates to a device and a method for measuring a real part and an imaginary part of a scattering function of a scattering object.
Background
In recent years, scattering functions of scattering objects have gained much attention of researchers, and basic characteristic parameters of the scattering objects can be extracted from the scattering functions of the objects, so that important technical bases are provided for imaging, detecting and the like of the objects. From the viewpoint of statistical mechanics, a scattering function can be generally characterized by a correlation function, where the correlation function refers to the fluctuation consistency of a point in space between different time instants (time domains) or different positions in space (space domains) at the same time, and if the fluctuation characteristics at the different time instants or different space positions have the same fluctuation characteristic, the two are completely correlated, and the correlation value is one; if the two fluctuations are completely independent, they are said to be uncorrelated and the correlation value is zero, and in general, the correlation value of the light field lies between these two extremes.
Therefore, the fluctuation correlation of the light beam in time and space can be obtained by measuring the correlation of two points in time domain or space domain, so as to restore the information of the structure, space and the like of the target object. Therefore, the measurement of the scattering function has important practical significance. However, in the previous practical application, the conventional measurement cannot recover a scattering function value (including real part and imaginary part information), but only can obtain a modulus square of the scattering function, which is obviously unable to obtain complete information of the scattering function, and meanwhile, the measurement mode has a serious limitation, which limits further application of the scattering function, and a complete method and device for recovering the scattering function have not been proposed so far. In addition, research on scattering functions has been focused on simple scattering functions for a long time, and in recent years, with the development of theory and experimental research on more complex scattering functions, deeper practical application of scattering functions is promoted, and a wider application prospect is shown.
In conclusion, the scattering function is widely applied to important fields such as astronomical observation, national defense and scientific research, medical health and the like due to the special structural characteristics, and has wide application value, but precisely due to the special structural characteristics, how to accurately measure and restore the real part and imaginary part information of the scattering function so as to obtain complete associated information is very important, and meanwhile, the scattering function has important practical significance.
Disclosure of Invention
In order to solve the technical problems, the invention aims to provide a device and a method for measuring the real part and the imaginary part of a scattering function of a scattering object.
The device for measuring the real part and the imaginary part of the scattering function of the scattering object comprises a laser, a beam expander for expanding a laser beam emitted by the laser, a first spectroscope for dividing the expanded laser beam into a transmission beam and a reflection beam which are perpendicular to each other, a first reflector and a second reflector for reflecting the transmission beam and the reflection beam by 90 degrees respectively, a second spectroscope for coaxially superposing the reflected transmission beam and the reflected beam, a detection sensor for converting the light intensity information of the superposed beam into picture information, and a microcomputer in communication connection with the detection sensor, wherein the scattering object is arranged between the first reflector and the second spectroscope or between the second reflector and the second spectroscope.
Furthermore, a neutral density filter is arranged between the first spectroscope and the first reflector and between the first spectroscope and the second reflector.
Further, the laser is a linear polarization single longitudinal mode He-Ne gas laser.
Further, the splitting ratio of the first beam splitter to the second beam splitter is 50:50.
the invention also provides a method for measuring the real part and the imaginary part of the scattering function of the scattering object, which comprises the following steps:
(1) The collimated linear polarization laser beam generated by the linear polarization He-Ne laser is expanded by a beam expander and is uniformly divided into a transmission beam and a reflection beam by a first beam splitter;
(2) The completely coherent quasi-linear polarized light beam transmitted by the first spectroscope is reflected by a neutral density filter plate through a first reflector to form a completely coherent light beam to a second spectroscope;
(3) Reflecting the completely coherent quasi-linear polarized light beam reflected by the first spectroscope to a certain scattering object through the second spectroscope after the neutral density filter to generate a scattered light beam with certain scattering function distribution;
(4) The generated scattered light beam and the completely coherent light beam are coaxially overlapped through a second spectroscope, the generated overlapped light beam source is received by the detection sensor, and data recorded by the detection sensor is transmitted to a microcomputer program to be processed to obtain the real part and imaginary part information of the scattering function.
Further, the microcomputer processing steps are as follows:
(1) The microcomputer respectively represents the light field and the light intensity information of the superposed light beam source received by the detection sensor as the vector sum of the electric fields of the two superposed light sources and the superposition of the light intensity information according to the light intensity matrix I (r) recorded by the detection sensor, and the microcomputer respectively represents the vector sum of the electric fields of the two superposed light sources and the superposition of the light intensity information according to a formula
Wherein G (2) (r 1 ,r 2 ) Is a fourth order correlation function, < is the mean value of the function, < E > α (r)，I α (r) electric field and light intensity, respectively, subscripts "l, p" representing coherent light beam and partially coherent light beam, respectively, r 1 ≡(x 1 ,y 1 ) And r 2 ≡(x 2 ,y 2 ) Respectively representing the coordinates of any two points on the plane of the detection sensor; i (r) 1 ) And I (r) 2 ) For the intensity values of these two points, Γ l (r 1 ,r 2 ) And Γ p (r 1 ,r 2 ) The scattering functions of the coherent light beam and the scattered light beam at these two points, respectively, "Re" represents the real part of the complex number. Measuring the two-dimensional distribution of the real part of the scattering function:
(2) Calculating a two-dimensional distribution of the modes of the imaginary part values of the scattering function:
wherein, "|" is a modulo symbol, "Im" is a complex imaginary symbol;
(3) Corresponding the partial derivative value of the scattering function real part to the column vector and the partial derivative value sign of the scattering function imaginary part to the row vector one by one, recovering the two-dimensional distribution of the imaginary part information of the scattering function of the scattering object, and determining the expression form of the scattering function of the scattering object: gamma-shaped p (r 1 ,r 2 )＝Re[Γ p (r 1 ,r 2 )]+iIm[Γ p (r 1 ,r 2 )]。
By means of the scheme, the device and the method for measuring the real part and the imaginary part of the scattering function of the scattering object have the advantages that:
1. the device for measuring the real part and the imaginary part of the scattering function of the scattering object (internal scattering or surface scattering) provided by the technical scheme of the invention firstly provides the method for measuring the real part and the imaginary part information of the scattering function of a scattering beam source by superposing completely coherent beams, and has originality;
2. the device for measuring the real part and the imaginary part of the correlation function, which is provided by the technical scheme of the invention, has the advantages of compact structure, accurate measurement, good operability and practicability and wide application prospect;
3. the method for measuring the real part and the imaginary part of the scattering function of the scattering object (internal scattering or surface scattering) provided by the technical scheme of the invention has wide applicability, and can measure the real part and the imaginary part information of any scattering function;
4. the measuring method for detecting and measuring the real part and imaginary part information of any scattering function by using the detection sensor can obtain the three-dimensional distribution of the scattering function, and is simple, visual, rapid and practical.
The foregoing description is only an overview of the technical solutions of the present invention, and in order to make the technical solutions of the present invention more clearly understood and to make the technical solutions of the present invention practical in accordance with the contents of the specification, the following detailed description is given of preferred embodiments of the present invention with reference to the accompanying drawings.
Drawings
FIG. 1 is a schematic structural diagram of an apparatus for measuring the real part and the imaginary part of a scattering function of a scattering object according to an embodiment of the present invention;
FIG. 2 is a contour plot of the squares of the scattering function modes of a scattering object according to an embodiment of the present invention;
FIG. 3 is a contour plot of the real part of the scattering function of a scattering object according to an embodiment of the present invention;
fig. 4 is a contour distribution diagram of imaginary parts of scattering functions of a scattering object according to an embodiment of the present invention.
Detailed Description
The following detailed description of embodiments of the present invention is provided in connection with the accompanying drawings and examples. The following examples are intended to illustrate the invention but are not intended to limit the scope of the invention.
Referring to fig. 1, an apparatus for measuring the real part and the imaginary part of the scattering function of a scattering object according to a preferred embodiment of the present invention includes a laser 1, a beam expander 2, a first beam splitter 3, a second beam splitter 9, neutral density filters 4 and 6, a first reflector 5, a second reflector 7, a scattering object 8, a detection sensor 10, and a microcomputer 11.
The laser 1 emits a linear polarization laser beam with Gaussian light intensity distribution, the laser 1 is a single longitudinal mode helium-neon laser with the power of 100mw and the wavelength of 632.8nm; a linear polarization laser beam emitted by a laser 1 is expanded by a continuously adjustable beam expander 2, the beam expander 2 is used for adjusting the beam waist size of the beam, and the beam expander 2 is a continuously adjustable coated beam expander; the expanded linear polarization laser beam is uniformly divided into a vertical transmission beam and a vertical reflection beam by a first spectroscope 3, wherein the first spectroscope 3 is a non-polarization spectroscope with a splitting ratio of 50; the transmitted light beam is reflected by the first reflector 5 after passing through the neutral density filter 4 and then irradiates the second spectroscope 9, the second spectroscope 9 is also an unpolarized spectroscope with a splitting ratio of 50; the reflected light beam reflected by the first spectroscope 3 passes through a neutral density filter 6, is reflected by a second reflector 7 and then irradiates a scattering object 8, and the neutral density filter 6 is also a continuously adjustable neutral density filter; the totally coherent light beam reflected via the first mirror 5 and the scattered light beam generated via the scattering object are coaxially superimposed at the second beam splitter 9; the generated superimposed beam source is irradiated onto the detection sensor 10, the detection sensor 10 converts the light intensity information into 0-255-level gray scale picture information, and the gray scale picture information recorded via the detection sensor 10 is stored onto the microcomputer 11.
The picture information recorded in the microcomputer 11 can be processed in the following manner: the detection sensor 10 continuously records N (N is a positive integer) pieces of gray scale image information, each piece of image information can be represented as an a × B light intensity matrix I (r), a and B are the numbers of pixel elements of the recorded image in the horizontal and vertical directions, r = (x, y), [ (x, y) ∈ (a, B) ] is a coordinate value of any pixel element on the image, I is a gray scale value of each pixel element, i.e., a light intensity value, and after the matrix is subjected to the operation shown in formula (1), the spatial distribution of a fourth-order correlation function (i.e., a modulo square of a scattering function) can be obtained, and a computer processing process is as follows:
wherein g is (2) (r 1 ,r 2 ) Is two image element points r 1 And r 2 Is the ensemble average of the function; n and N are respectively a certain frame of picture shot by the detector and the total number of shot pictures; i is n (r 1 ) And I n (r 2 ) Respectively the nth picture is in 1 And r 2 The light intensity value of the spot; Σ is the summation symbol. R can be fixed in actual processing 1 The light intensity value and the difference r at the coordinate are calculated 2 The processing method can obtain the two-dimensional plane distribution of the scattering function mode square, the measurement precision of the measurement processing method depends on the number N of the measured pictures, and N is used in the processing&Can ensure measurement at gt, 4000The accuracy of (2).
The detection sensor 10 is a charge-coupled sensor, and the light field and light intensity information of the superimposed light beam source received thereon can be respectively expressed as a vector sum of two superimposed light source electric fields and a superposition of light intensity information:
E α (r)＝E lα (r)+E pα (r),(α＝x or y) (2)
I α (r)＝I lα (r)+I pα (r),(α＝x or y) (3)
wherein E α (r)，I α (r) is the electric field and the light intensity, respectively, r ≡ (x, y) is an arbitrary coordinate perpendicular to the light beam transmission plane, subscript "α" is the polarization direction of the light field, and subscripts "l, p" represent coherent laser and partially coherent light beams, respectively.
The light intensity information recorded in the microcomputer 11 is associated in the fourth order, and the expression thereof can be expressed as:
wherein G is (2) (r 1 ,r 2 ) Is the fourth order correlation function, and is the average of the functions. r is 1 ≡(x 1 ,y 1 ) And r 2 ≡(x 2 ,y 2 ) Respectively detecting the coordinates of any two points on the plane of the sensor 10; i (r) 1 ) And I (r) 2 ) For the intensity values of these two points, Γ l (r 1 ,r 2 ) And Γ p (r 1 ,r 2 ) The scattering function of the coherent and scattered beams at these two points, respectively, "Re" represents the real part of the complex number. Equation (4) can be written as follows:
according to the previous measuring method, only the modulus square | gamma of the scattering function can be measured p (r 1 ,r 2 )| 2 The result of the one-dimensional measurement is,while the exact specific values of the complete information of the scattering function, i.e. the real and imaginary information, cannot be measured. The invention provides a method and a device for measuring a real part and an imaginary part of a scattering function, which firstly measure the two-dimensional distribution of the modulus square of the scattering function by using a method for measuring the modulus square of the scattering function by using a detection sensor 10, and secondly measure the two-dimensional distribution of the real part of the scattering function according to a formula (5) deformed by a formula (3); modulus squared | Γ from scattering function p (r 1 ,r 2 )| 2 And the real part of the scattering function Re [ gamma ] p (r 1 ,r 2 )]The two-dimensional distribution diagram of the modulus of the imaginary value of the scattering function can be calculated:
"| |" is a modulo sign, and "Im" is a complex imaginary sign.
If the scattering function of the scattering object 8 is an analytic complex function, then according to the cauchy-riemann condition: if the function f (z) = u (x, y) + iv (x, y) is determined within region D, then a sufficient requirement that f (z) is derivable at point z = x + iy ∈ D is:
1. the real part u (x, y) and imaginary part v (x, y) are differentiable at point (x, y);
2. u (x, y) and v (x, y) satisfy the cauchy-riemann equation at point (x, y):
wherein the content of the first and second substances,is a partial differential sign. The real part Re [ gamma ] of the scattering function obtained by measurement p (r 1 ,r 2 )]Expressed in the form of a two-dimensional matrix, the partial derivatives of the row vector (x direction) and the column vector (y direction) of the matrix are respectively calculated, and the values of the partial derivatives of the real part of the scattering function and the values of the imaginary part of the scattering function are respectively calculated by means of the Cauchy-Riemann decision conditionCorresponding to the sign of the partial derivative value of the row vector, the sign of the imaginary part value of the scattering function can be confirmed by the one-to-one correspondence mode, and at the moment, the two-dimensional distribution of the imaginary part information of the scattering function of the scattering object can be completely restored, so that the expression form of the scattering function of the scattering object can be determined:
Γ p (r 1 ,r 2 )＝Re[Γ p (r 1 ,r 2 )]+iIm[Γ p (r 1 ,r 2 )] (7)
the apparatus for measuring the real part and the imaginary part of the scattering function provided by this embodiment has the following specific operation steps:
1. the linear polarization single longitudinal mode He-Ne laser 1 emits a laser beam with stable phase and light intensity and Gaussian light intensity distribution;
2. the emitted laser beam is uniformly expanded by the continuously adjustable beam expander 2 and is uniformly divided into a transmission beam and a reflection beam which are vertical to each other by a first spectroscope 3 with the splitting ratio of 50;
3. the transmitted light beam is adjusted in intensity by a neutral density filter 4 with continuously adjustable attenuation intensity, reflected by a first reflector 5 and irradiated to a second spectroscope 9;
4. the reflected light beam reflected by the first spectroscope 3 is reflected by a second reflector 7 and then irradiates on a scattering object 8 after the intensity of the light beam is adjusted by a neutral density filter 6 with continuously adjustable attenuation intensity, so that a scattered light beam with a certain scattering function structure is generated;
5. the totally coherent light beam reflected via the first mirror 5 and the scattered light beam generated via the scattering object 8 are coaxially superimposed at a second beam splitter 9 with a splitting ratio of 50;
6. the generated superimposed beam source is irradiated onto the detection sensor 10 to convert the light intensity information into 0-255-level gray scale picture information, and the gray scale picture information recorded via the detection sensor 10 is stored on the microcomputer 11.
The following are exemplified:
if the scattering function of a scattering object satisfies the following scattering function:
wherein gamma (r) 1 ,r 2 ) A scattering function that is a scattering object; r is a radical of hydrogen 1 ≡(x 1 ,y 1 )，r 2 ≡(x 2 ,y 2 ) Is an arbitrary coordinate point perpendicular to the light beam transmission plane; "exp" is an exponential function; sigma 0 Is the waist radius of the scattered beam; g x (Δ x) and g y (Δ y) is the scatter function component in the x-direction and y-direction, respectively; Δ x = x 1 -x 2 ，Δy＝y 1 -y 2 The relative distances in the x direction and the y direction are respectively; delta 0 Is the coherence length of the scattered beam; a is a modulation parameter of the scattering function; i is an imaginary symbol;andrespectively, the argument in the x-direction and the y-direction.
The embodiment takes the method and the device for measuring the real part and the imaginary part of the scattering function as an example, and the contour map of the scattering function module square of the scattering object in the example is shown in fig. 2; FIG. 3 shows a contour plot of the real part of the scattering function of a scattering object in an example; figure 4 shows a contour plot of the imaginary part of the scattering function of a scattering object in an example. The data obtain consistent results in experimental measurement, and show good operability and wide application prospect.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, it should be noted that, for those skilled in the art, many modifications and variations can be made without departing from the technical principle of the present invention, and these modifications and variations should also be regarded as the protection scope of the present invention.
Claims (6)
1. An apparatus for measuring the real and imaginary components of the scattering function of a scattering object, characterized by: the laser beam expander comprises a laser, a beam expander for expanding a laser beam emitted by the laser, a first spectroscope for dividing the expanded laser beam into a transmission beam and a reflection beam which are perpendicular to each other, a first reflector and a second reflector for reflecting the transmission beam and the reflection beam for 90 degrees respectively, a second spectroscope for coaxially superposing the transmission beam and the reflection beam after reflection, a detection sensor for converting light intensity information of the superposed beams into picture information, and a microcomputer in communication connection with the detection sensor, wherein a scattering object is arranged between the first reflector and the second spectroscope or between the second reflector and the second spectroscope.
2. An apparatus for measuring the real and imaginary parts of the scattering function of a scattering object as defined in claim 1, wherein: neutral density filters are arranged between the first spectroscope and the first reflector and between the first spectroscope and the second reflector.
3. An apparatus for measuring the real and imaginary parts of the scattering function of a scattering object as defined in claim 2, wherein: the laser is a linear polarization single longitudinal mode He-Ne gas laser.
4. An apparatus for measuring the real and imaginary parts of the scattering function of a scattering object as claimed in claim 3, wherein: the splitting ratio of the first beam splitter to the second beam splitter is 50:50.
5. a method of measuring the real and imaginary parts of the scattering function of a scattering object, comprising the steps of:
(1) The collimated linear polarization laser beam generated by the linear polarization He-Ne laser is expanded by a beam expander and is uniformly divided into a transmission beam and a reflection beam by a first beam splitter;
(2) The completely coherent quasi-linear polarized light beam transmitted by the first spectroscope is reflected by a neutral density filter plate through a first reflector to form a completely coherent light beam to a second spectroscope;
(3) The totally coherent quasi-linear polarized light beam reflected by the first spectroscope is reflected to a scattering object by the second spectroscope after passing through the neutral density filter to generate a scattering light beam with certain scattering function distribution;
(4) The generated scattered light beam and the completely coherent light beam are coaxially overlapped through a second spectroscope, the generated overlapped light beam source is received by the detection sensor, and data recorded by the detection sensor is transmitted to a microcomputer program to be processed to obtain the real part and imaginary part information of the scattering function.
6. A method for measuring the real and imaginary components of the scattering function of a scattering object as recited in claim 5, wherein said microcomputer processing step is:
(1) The microcomputer respectively represents the light field and the light intensity information of the superposed light beam source received by the detection sensor as the vector sum of the electric fields of the two superposed light sources and the superposition of the light intensity information according to the light intensity matrix I (r) recorded by the detection sensor, and the microcomputer respectively represents the vector sum of the electric fields of the two superposed light sources and the superposition of the light intensity information according to a formula
Wherein G is (2) (r 1 ,r 2 ) In order to be a fourth-order correlation function,<>, mean value of the function, E α (r)，I α (r) electric field and light intensity, respectively, subscripts "l, p" representing coherent light beam and partially coherent light beam, respectively, r 1 ≡(x 1 ,y 1 ) And r 2 ≡(x 2 ,y 2 ) Are respectively asCoordinates of any two points on the plane of the detection sensor; i (r) 1 ) And I (r) 2 ) For the intensity values of these two points, Γ l (r 1 ,r 2 ) And Γ p (r 1 ,r 2 ) The scattering functions of the coherent light beam and the scattered light beam at the two points are respectively, and "Re" represents the two-dimensional distribution of the real part of the measured scattering function of the real part of the complex number:
(2) Calculating a two-dimensional distribution of the modes of the imaginary part values of the scattering function:
wherein, "|" is a modulo symbol, "Im" is a complex imaginary symbol;
(3) Corresponding the partial derivative value of the scattering function real part to the column vector and the partial derivative value sign of the scattering function imaginary part to the row vector one by one, recovering the two-dimensional distribution of the imaginary part information of the scattering function of the scattering object, and determining the expression form of the scattering function of the scattering object: gamma-shaped p (r 1 ,r 2 )＝Re[Γ p (r 1 ,r 2 )]+iIm[Γ p (r 1 ,r 2 )]。
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