CN104102017A - Structural illumination-based random scattering optical beyond-diffraction-limit imaging system and method - Google Patents

Abstract

The invention discloses a structural illumination-based random scattering optical beyond-diffraction-limit imaging system and method. The objective of the invention is mainly to solve the problems of complicated techniques, long imaging time, difficult realization of system structure and low imaging resolution of existing similar technologies. The imaging system includes a light source, a beam expander, a spatial light modulator, a lambda/4 wave plate, a beam expanding lens group, a light blocking plate, lenses, a random scattering medium, a convergence lens, and a CCD camera; light beams emitted by the light source are subjected to beam expansion of the beam expander and thereafter enter the spatial light modulator, so that 0-level light and +/-1-level light are obtained; the 0-level light and +/-1-level light pass through the lambda/4 wave plate, so that circularly polarized light can be obtained; after being subjected to beam expansion of the beam expanding lens group, the circularly polarized light reaches the light blocking plate, and the +/-1-level light is reserved; the +/-1-level light is interfered when passing through the lenses, and structural light can be generated, and an observation target can be illuminated; and the illuminated observation target enters the random scattering medium, and strong scattering occurs, and light beams enter the CCD camera through the convergence lens. The structural illumination-based random scattering optical beyond-diffraction-limit imaging system of the invention has the advantages of simple structure and high imaging resolution, and can be used for optical super resolution imaging.

Description

The super diffraction limit imaging system of random scatter optics and method based on structured light photograph

Technical field

The invention belongs to technical field of imaging, particularly a kind of optical imaging system, can be used for the imaging of optical ultra-discrimination rate.

Background technology

The resolution of traditional optical imaging is limited by diffraction limit, is difficult to measure the distance that is less than 200nm in visible-range, and the research that therefore breaks through the imaging of optical system diffraction limit is extremely urgent.

At present, around the research of the super diffraction limit imaging near field and far field, obtained the progress attracting people's attention.The super diffraction limit formation method near field mainly adopts perfect lens prepared by nano-probe, the super material of plasma and material with negative refractive index etc. to survey evanescent wave, and its resolution is not subject to the restriction of Rayleigh criterion.But because the preparation of nano-probe, the super material of plasma, material with negative refractive index need meet very exacting terms, technique is extremely complicated, and technology is ripe not enough, causes its scan-probe easily sample to be caused to damage, and is unfavorable for biological tissue to observe.

And the super diffraction limit formation method in far field, as stimulated emission loss microtechnic, random optics are rebuild microtechnic and photosensitive location microtechnic etc., they are by the spatial information of the fluorescence signal distributed acquisition sample of detection excited fluorescence molecule, detectable sample interior, can reach at present 20～50nm, and under maximum conditions, can reach the resolution of 5.8nm.But because its spatial resolution reaching is seriously to sacrifice temporal resolution as cost, cause imaging process complexity, length consuming time, be difficult to realize real-time monitored.

Summary of the invention

The object of the invention is to the deficiency for above-mentioned prior art, propose the super diffraction limit imaging system of a kind of random scatter optics based on structured light photograph and method, to simplify material preparation process, simplify imaging process, to improve imaging resolution.

Technical scheme of the present invention is achieved in that

One. technical thought is: adopt structured light as imaging source, illumination observed object, obtains image by random scattering media, and transmits it in main control computer, reconstruct final observed object by calculating formation method, obtain high-quality super-resolution image.

Two. the super diffraction limit imaging system of random scatter optics based on structured light photograph, comprise the sub-device of optics and super diffraction limit imaging device, it is characterized in that:

The sub-device of described optics, comprises light source, two aperture diaphragms, beam expander, spatial light modulator, four lens, λ/4 wave plate, three catoptrons and light barrier, the light beam of light source transmitting is successively through the first aperture diaphragm, beam expander, the first catoptron back lighting is on spatial light modulator, produce 0 grade of light, + 1 grade of light and-1 grade of light, these three grades of light are separated by parallel by first lens, through λ/4, wave plate obtains circularly polarized light, again successively by the second catoptron and the second lens, the second diaphragm and the 3rd lens expand, and keep off 0 grade of middle light by light barrier, retain+1 grade of light and-1 grade of light, after the 3rd catoptron, pass through again the 4th lens, make+1 grade of light and-1 grade of light interfere on focal plane, produce structured light to illuminate observed object,

Described super diffraction limit imaging device, comprises three lens, the 3rd aperture diaphragm, random scattering media, CCD camera; Observed object through illuminating reduces the diameter of whole light beam successively through the 5th lens, the 3rd aperture diaphragm and the 6th lens, make light beam that strong scattering occur in random scattering media, then carry out after beam energy convergence through the 7th lens, receives image by CCD camera.

Three. the super diffraction limit formation method of random scatter optics based on structured light photograph, comprises the steps:

(1) to CCD collected by camera to original image carry out brightness of image homogenization processing, to eliminate the impact on brightness of image by light source fluctuation;

(2) brightness of image homogenization image after treatment is carried out to Fourier transform operation, obtain corresponding frequency spectrum;

(3) in 0 °, 45 °, 90 ° and 135 ° of each directions, input three different phase values by controlling spatial light modulator, composition 3 × 3 systems of linear equations also solve, to isolate 0 grade ,+1 grade and-1 grade of spectral imaging information in each direction;

(4), by isolated 0 grade, the overlapping region of+1 grade and-1 grade spectral imaging information on four direction, obtain the frequency component k of four groups of Structured Illumination _i, i ∈ 0 °, and 45 °, 90 °, 135 ° };

(5) utilize the fourier transform property of cosine function, by the frequency component k of four groups of Structured Illumination that obtain _icarry out frequency splicing, frequency spectrum k is expanded ₀± k _i, wherein k ₀for original frequency component;

(6) utilize angular spectra theory in frequency field, to obtain the transmission matrix data cube E of random scattering media _m;

(7) according to the frequency spectrum k of Structured Illumination expansion ₀± k _itransmission matrix data cube E with random scattering media _m, rebuild ASCIRA algorithm by image and reconstruct observed object image.

The present invention compared with prior art tool has the following advantages:

1) the present invention is according to the principle of super diffraction limit imaging and Structured Illumination imaging, designed the super diffraction limit imaging system of random scatter optics based on structured light photograph, compared with existing optical system, material preparation process is simple, system architecture easily realizes, and imaging resolution obviously improves.

2) the present invention utilizes angular spectra theory, the random scatter optics super diffraction limit formation method of design based on structured light photograph, compared with existing formation method, had not only filtered parasitic light but also had retained the high-frequency information of observed object, and effectively reduce imaging time, improved imaging resolution.

Brief description of the drawings

Fig. 1 is the structural drawing that the present invention is based on the super diffraction limit imaging system of random scatter optics of structured light photograph;

Fig. 2 is the realization flow figure that the present invention is based on the super diffraction limit formation method of random scatter optics of structured light photograph;

Fig. 3 is the schematic diagram that intermediate frequency spectrum image-forming information of the present invention separates;

Fig. 4 is the schematic diagram of intermediate frequency spectrum expansion of the present invention;

Fig. 5 is the transmission matrix data cube schematic diagram that obtains random scattering media in the present invention.

Embodiment

Below with reference to accompanying drawing, the setting of the super diffraction limit imaging system of random scatter optics under Structured Illumination of the present invention is described clearly and completely, and the performing step of formation method.

Referring to Fig. 1, imaging system of the present invention, comprises the sub-device of optics and super diffraction limit imaging device two parts.Wherein:

The sub-device of described optics, comprises light source 1, two aperture diaphragms, beam expander 3, spatial light modulator 4, four lens, λ/4 wave plate 6, three catoptrons and light barriers 12.Wherein, light source 1 adopts the laser instrument of visible light wave range, the parasitic light of the light beam of laser instrument transmitting in the first aperture diaphragm 2 filtering light beams, expand through beam expander 3, control the incident direction of light beam in spatial light modulator 4 by the first catoptron 7, it is respectively 0 °, 45 °, 90 ° and 135 ° of four directions, in each direction, produces respectively 0 grade of light ,+1 grade of light and-1 grade of light; These three grades of light are parallel separately by first lens 5, obtain having the circularly polarized light of better polarization characteristic through λ/4 wave plate 6; This circularly polarized light changes optical path direction by the second catoptron 8, and the extender lens group forming via the second lens 9, the second diaphragm 10 and the 3rd lens 11 expands, then falls 0 grade of middle light through light barrier 12 gears, retains+1 grade of light and-1 grade of light; By the 3rd catoptron 13 change in light path, retain+direction of propagation of 1 grade of light and-1 grade of light, then by the 4th lens 14, on its focal plane, interfere, produce structured light to illuminate observed object.

Described super diffraction limit imaging device, comprises three lens, the 3rd aperture diaphragm 17, random scattering media 19, CCD camera 21, and wherein the thickness of random scattering media 19 is elected 10～20 μ m as, to reduce its absorption to light and to strengthen it to scattering of light.The reverse extender lens group that observed object through illuminating forms via the 5th lens 16, the 3rd aperture diaphragm 17 and the 6th lens 18, with the parasitic light in filtering light path and reduce the diameter of whole light beam, then make light beam pass through random scattering media 19, and there is strong scattering therein, output beam after strong scattering carries out energy convergence through the 7th lens 20, finally receives image by CCD camera 21.

Referring to Fig. 2, formation method of the present invention, implementation step is as follows:

Step 1, gathers original image and carries out brightness of image homogenization processing.

1a) by CCD collected by camera original image T (r), and upload to main control computer;

1b) main control computer is according to brightness of image homogenization principle, by the mould value of original image | T (r) | divided by original image T (r), obtain the image of brightness homogenization to eliminate the impact on brightness of image by light source fluctuation, and be kept in main control computer.

Step 2, obtains the frequency spectrum of brightness homogenization image, the image D (r) of brightness homogenization is carried out to Fourier transform, obtains the frequency spectrum of this brightness homogenization image wherein, represent Fourier transform operation.

Step 3, isolates 0 grade ,+1 grade and-1 grade of spectral imaging information in 0 °, 45 °, 90 ° and 135 ° of each directions.

Referring to Fig. 3, being achieved as follows of this step:

3a) by main control computer control spatial light modulator three different phase value φ of input arbitrarily in 0 °, 45 °, 90 ° and 135 ° of each directions respectively _j, j ∈ { 1,2,3};

3b) by three different phase value φ _jsubstitution Structured Illumination intensity expression formula, obtains structured light light intensity expression formula in 0 °, 45 °, 90 ° and 135 ° of each directions as follows:

I(r)＝I ₀[1+cos(k _i·r)+φ _j]， <1>

Wherein, I ₀for the light intensity of light source, k _ifor the frequency component of different directions Structured Illumination, i ∈ 0 °, and 45 °, 90 °, 135 ° }, r is volume coordinate;

3c) the point spread function PSF (r) 0 °, 45 °, 90 ° and 135 ° of each direction glazing intensity I (r) and whole optical system according to structured light, obtains the mathematic(al) representation of whole optical system model:

$D\left(r\right)=[O\left(r\right)\&CenterDot;I\left(r\right)]\&CircleTimes;\mathrm{PSF}\left(r\right)---<2>$

Wherein, O (r) represents observed object image, and D (r) represents the image after brightness homogenization, and PSF (r) represents the point spread function of whole optical system;

3d) formula <2> is carried out to Fourier transform, obtains the mathematic(al) representation in whole optical system frequency field:

$D\left(k\right)=I_0[S\left(k_0\right)+0.5S(k_0+k_i)e^{-i{\mathrm{\&phi;}}_j}+0.5S(k_0-k_i)e^{i{\mathrm{\&phi;}}_j}]\mathrm{OTF}\left(k\right)---<3>$

Wherein, the frequency spectrum that D (k) is brightness homogenization image, OTF (k) represents the optical transfer function of whole optical system, S (k ₀), S (k ₀+ k _i), S (k ₀-k _i) be respectively 0 grade ,+1 grade ,-1 grade spectral imaging information;

3e) by three different phase of main control computer control spatial light modulator input _j, j ∈ 1,2,3}, and substitution formula <3>, composition 3 × 3 systems of linear equations:

$\left\{\begin{array}{c}D\left(k\right)=I_0[S\left(k_0\right)+0.5S(k_0+k_i)e^{-i{\mathrm{\&phi;}}_1}+0.5S(k_0-k_i)e^{i{\mathrm{\&phi;}}_1}]\mathrm{OTF}\left(k\right)\\ D\left(k\right)=I_0[S\left(k_0\right)+0.5S(k_0+k_i)e^{-i{\mathrm{\&phi;}}_2}+0.5S(k_0-k_i)e^{i{\mathrm{\&phi;}}_2}]\mathrm{OTF}\left(k\right)\\ D\left(k\right)=I_0[S\left(k_0\right)+0.5S(k_0+k_i)e^{-i{\mathrm{\&phi;}}_3}+0.5S(k_0-k_i)e^{i{\mathrm{\&phi;}}_3}]\mathrm{OTF}\left(k\right)\end{array}\right.$

Solve this system of equations, to isolate 0 grade ,+1 grade and-1 grade of spectral imaging information, i.e. S (k in each direction ₀), S (k ₀+ k _i), S (k ₀-k _i).

Step 4, by structured light isolated 0 grade ,+1 grade and-1 grade of spectral imaging information S (k respectively on 0 °, 45 °, 90 ° and 135 ° of these four directions ₀), S (k ₀+ k _i), S (k ₀-k _i) overlapping region, obtain the frequency component k of four groups of Structured Illumination _i, i ∈ 0 °, and 45 °, 90 °, 135 ° }.

Step 5, utilizes the fourier transform property of cosine function, by the frequency component k of four groups of Structured Illumination that obtain _icarry out frequency splicing, frequency spectrum k is expanded ₀± k _i, in the image that Structured Illumination is obtained, comprise more high-frequency information, thereby contribute to the raising of resolution, wherein, k ₀for original frequency component, the frequency spectrum after expansion as shown in Figure 4.

Step 6, obtains the transmission matrix data cube E of random scattering media _m;

Referring to Fig. 5, being achieved as follows of this step:

6a) according to angular spectra theory, obtain through the plane of incidence wave field of observed object be:

$E_o(x,y)=\underset{k_x,k_y}{\mathrm{\&Sigma;}}{A}_o(k_x,k_y)e^{i(k_{x}x+k_{y}y)}---<4>$

Wherein, k _xand k _yrepresent that respectively light wave is at x axle and the axial wave component vector of y, and and incident light and optical axis between angle theta _x, θ _yrelevant, i.e. k _x/ 2 π=sin θ _x/ λ, k _y/ 2 π=sin θ _y/ λ, A _o(k _x, k _y) be called angular spectrum, represent the complex amplitude of each plane wave component;

6b) according to the angle theta between incident light in formula <4> and x axle _x, and y axle between angle theta _y, by different angles (θ _x, θ _y) laser beam irradiate successively the same position in random scattering media, when recording respectively each angle incident light and irradiating, the speckle field E producing in image planes _m(x, y, k _x, k _y) be random scattering media transmission matrix;

When 6c) different angles incident light irradiation, the different speckle field E producing in image planes _m(x, y, k _x, k _y) being superimposed has just formed random medium transmission matrix data cube E _m.

Step 7, rebuilds observed object image.

7a) by the frequency spectrum k of Structured Illumination expansion ₀± k _icarry out inverse Fourier transform, obtain the speckle field E in spatial domain _s(x, y), includes more observed object high-frequency information in this speckle field;

7b) by the speckle field E in spatial domain _s(x, y), is expressed as with angular spectrum and random scattering media transmission matrix:

$E_s(x,y)=\underset{k_x,k_y}{\mathrm{\&Sigma;}}{A}_o(k_x,k_y)E_m(x,y,k_x,k_y)---<5>$

Wherein, A _o(k _x, k _y) be angular spectrum, E _m(x, y, k _x, k _y) be random scattering media transmission matrix;

7c) by step 7a) speckle field E in the spatial domain that obtains _s(x, y) and step 6b) the random scattering media transmission matrix E that obtains _m(x, y, k _x, k _y), substitution formula <5> solves angular spectrum A _o(k _x, k _y);

7d) by the angular spectrum A obtaining _o(k _x, k _y) substitution plane of incidence wave field formula $E_o(x,y)=\underset{k_x,k_y}{\mathrm{\&Sigma;}}{A}_o(k_x,k_y)e^{i(k_{x}x+k_{y}y)},$ Solve the plane of incidence wave field E through observed object _o(x, y);

7e) to the plane of incidence wave field E through observed object _o(x, y) take absolute value after square, obtain the final observed object image T rebuilding:

T＝|E _o(x,y)| ²。

More than describing is only example of the present invention, does not form any limitation of the invention.Obviously for those skilled in the art; understanding after content of the present invention and principle; all may be in the situation that not deviating from the principle of the invention, structure; carry out various corrections and change in form and details, but these corrections based on inventive concept and changing still within claim protection domain of the present invention.

Claims (8)

1. the super diffraction limit imaging system of the random scatter optics based on structured light photograph, comprises the sub-device of optics and super diffraction limit imaging device, it is characterized in that:

The sub-device of described optics, comprise light source (1), two aperture diaphragms (2,10), beam expander (3), spatial light modulator (4), four lens (5,9,11,14), λ/4 wave plate (6), three catoptrons (7,8,13) and light barrier (12), the light beam of light source (1) transmitting is successively through the first aperture diaphragm (2), beam expander (3), the first catoptron (7) back lighting is on spatial light modulator (4), produce 0 grade of light, + 1 grade of light and-1 grade of light, these three grades of light are separated by parallel by first lens (5), obtain circularly polarized light through λ/4 wave plate (6), again successively by the second catoptron (8) and the second lens (9), the second diaphragm (10) and the 3rd lens (11) expand, and fall 0 grade of middle light by light barrier (12) gear, retain+1 grade of light and-1 grade of light, after the 3rd catoptron (13), pass through again the 4th lens (14), make+1 grade of light and-1 grade of light interfere on focal plane, produce structured light to illuminate imageable target,

Described super diffraction limit imaging device, comprises three lens (16,18,20), the 3rd aperture diaphragm (17), random scattering media (19), CCD camera (21); Imageable target through illuminating reduces the diameter of whole light beam successively through the 5th lens (16), the 3rd aperture diaphragm (17) and the 6th lens (18), make light beam that strong scattering occur in random scattering media (19), carry out after beam energy convergence through the 7th lens (20) again, receive image by CCD camera (21).

2. imaging system according to claim 1, is characterized in that, the upper 0 grade of light producing of spatial light modulator (4) ,+1 grade of light and-1 grade are in the direction of 0 °, 45 °, 90 ° and 135 °, to produce respectively.

3. imaging system according to claim 1, is characterized in that, the thickness of random scattering media (19) is 10～20 μ m, to reduce the absorption to light, strengthens scattering of light.

4. imaging system according to claim 1, is characterized in that, the laser instrument that described light source (1) is visible light wave range.

5. the super diffraction limit formation method of the random scatter optics based on structured light photograph, comprises the following steps:

(1) original image CCD camera (21) being collected carries out brightness of image homogenization processing, to eliminate the impact on brightness of image by light source fluctuation;

(2) brightness of image homogenization image after treatment is carried out to Fourier transform operation, obtain corresponding frequency spectrum;

(3) in 0 °, 45 °, 90 ° and 135 ° of each directions, input three different phase values by controlling spatial light modulator, composition 3 × 3 systems of linear equations also solve, to isolate 0 grade ,+1 grade and-1 grade of spectral imaging information in each direction;

(4), by isolated 0 grade, the overlapping region of+1 grade and-1 grade spectral imaging information on four direction, obtain the frequency component k of four groups of Structured Illumination _i, i ∈ 0 °, and 45 °, 90 °, 135 ° };

(5) utilize the fourier transform property of cosine function, by the frequency component k of four groups of Structured Illumination that obtain _icarry out frequency splicing, frequency spectrum k is expanded ₀± k _i, wherein k ₀for original frequency component;

(6) utilize angular spectra theory in frequency field, to obtain the transmission matrix data cube E of random scattering media _m;

(7) according to the frequency spectrum k of Structured Illumination expansion ₀± k _itransmission matrix data cube E with random scattering media _m, rebuild ASCIRA algorithm by image and reconstruct observed object image.

6. the super diffraction limit formation method of the random scatter optics based on structured light photograph according to claim 5, spatial light modulator that what wherein step (3) was described passing through to control is inputted three different phase values in 0 °, 45 °, 90 ° and 135 ° of each directions, composition 3 × 3 systems of linear equations also solve, and carry out as follows:

6a) by main control computer control spatial light modulator three different phase value φ of input arbitrarily in 0 °, 45 °, 90 ° and 135 ° of each directions _j, j ∈ { 1,2,3};

6b) by three different phase value φ _jsubstitution Structured Illumination intensity expression formula, obtains structured light light intensity expression formula in 0 °, 45 °, 90 ° and 135 ° of each directions as follows:

I(r)＝I ₀[1+cos(k _i·r)+φ _j] <1>

Wherein, I ₀for the light intensity of light source, k _ifor the frequency component of different directions Structured Illumination, i ∈ 0 °, and 45 °, 90 °, 135 ° }, r is volume coordinate;

6c) the point spread function PSF (r) 0 °, 45 °, 90 ° and 135 ° of each direction glazing intensity I (r) and whole optical system according to structured light, obtains whole optical system and becomes the mathematic(al) representation of image D (r):

$D\left(r\right)=[O\left(r\right)\&CenterDot;I\left(r\right)]\&CircleTimes;\mathrm{PSF}\left(r\right)---<2>$

Wherein, O (r) represents observed object image, and D (r) represents the image that whole optical system becomes, and PSF (r) represents the point spread function of whole optical system;

6d) formula <2> is carried out to Fourier transform, obtains the mathematic(al) representation of image that whole optical system becomes in frequency field:

$D\left(k\right)=I_0[S\left(k_0\right)+0.5S(k_0+k_i)e^{-i{\mathrm{\&phi;}}_j}+0.5S(k_0-k_i)e^{i{\mathrm{\&phi;}}_j}]\mathrm{OTF}\left(k\right)---<3>$

Wherein, the image that D (k) becomes for whole optical system in frequency field, OTF (k) represents the optical transfer function of whole optical system, S (k ₀), S (k ₀+ k _i), S (k ₀-k _i) be respectively 0 grade ,+1 grade ,-1 grade spectral imaging information;

6e) by controlling three different phase of spatial light modulator input _j, { composition 3 × 3 systems of linear equations also solve j ∈, to isolate 0 grade ,+1 grade and-1 grade of spectral imaging information, i.e. S (k in each direction for 1,2,3}, substitution formula <3> ₀), S (k ₀+ k _i), S (k ₀-k _i).

7. the super diffraction limit formation method of the random scatter optics based on structured light photograph according to claim 5, wherein the described angular spectra theory of utilizing of step (6) is obtained the transmission matrix data cube E of random scattering media in frequency field _m, carry out as follows:

7a) known according to angular spectra theory, obtain through the plane of incidence wave field of observed object be:

$E_o(x,y)=\underset{k_x,k_y}{\mathrm{\&Sigma;}}{A}_o(k_x,k_y)e^{i(k_{x}x+k_{y}y)}---<4>$

Wherein, k _xand k _yrepresent that respectively light wave is at x axle and the axial wave component vector of y, and and incident light and optical axis between angle theta _x, θ _yrelevant, i.e. k _x/ 2 π=sin θ _x/ λ, k _y/ 2 π=sin θ _y/ λ, A _o(k _x, k _y) be called angular spectrum, represent the complex amplitude of each plane wave component;

7b) according to the angle theta between incident light and optical axis in formula <4> _x, θ _y, by different angles (θ _x, θ _y) laser beam irradiate successively the same position in random scattering media, when recording respectively each angle incident light and irradiating, the speckle field E producing in image planes _m(x, y, k _x, k _y) be random scattering media transmission matrix;

When 7c) different angles incident light irradiation, the different speckle field E producing in image planes _m(x, y, k _x, k _y) being superimposed has just formed random medium transmission matrix data cube E _m.

8. the super diffraction limit formation method of a kind of random scatter optics based on structured light photograph according to claim 5, the wherein described frequency spectrum k expanding according to Structured Illumination of step (7) ₀± k _itransmission matrix data cube E with random scattering media _m, rebuild ASCIRA algorithm by image and reconstruct observed object image, carry out as follows:

8a) by the frequency spectrum k of Structured Illumination expansion ₀± k _icarry out inverse Fourier transform, obtain the speckle field E in spatial domain _s(x, y), includes more observed object high-frequency information in this speckle field;

8b) by the speckle field E in spatial domain _s(x, y), is expressed as with angular spectrum and random scattering media transmission matrix:

$E_s(x,y)=\underset{k_x,k_y}{\mathrm{\&Sigma;}}{A}_o(k_x,k_y)E_m(x,y,k_x,k_y)---<5>$

Wherein, A _o(k _x, k _y) be angular spectrum, E _m(x, y, k _x, k _y) be random scattering media transmission matrix;

8c) by step 8a) speckle field E in the spatial domain that obtains _s(x, y) and step 7b) the random scattering media transmission matrix E that obtains _m(x, y, k _x, k _y), substitution formula <5>, anti-solution, obtains angular spectrum A _o(k _x, k _y);

8d) by the angular spectrum A obtaining _o(k _x, k _y) substitution plane of incidence wave field formula: solve the plane of incidence wave field E through observed object _o(x, y);

8e) to the plane of incidence wave field E through observed object _o(x, y) take absolute value after square, obtain the final observed object image T rebuilding:

T＝|E _o(x,y)| ²。