CN103322940B - A kind of method obtaining microscopic image in three-dimensional shape - Google Patents

Abstract

A kind of method obtaining microscopic image in three-dimensional shape, by beam of laser by being divided into Object light wave and reference light wave after beam splitter, Object light wave carries the three-dimensional information of transparent substance, Object light wave and reference light wave form interference image on CCD target surface, interference image, to computing machine, is reproduced by unconventional method for reconstructing by this image transmitting in a computer.Wherein, in unconventional method for reconstructing, carry out Fourier transform after natural logarithm is got to interference image and obtain its spectrogram, the spectrum face size choosing a quadrant corresponding with object frequency spectrum in spectrogram carries out filtering, thus acquisition object frequency spectrum, then inverse Fourier transform is carried out, exponent arithmetic and phase compensation, thus the three-dimensional microscopic image obtaining object accurately.

Description

A kind of method obtaining microscopic image in three-dimensional shape

Technical field

Please design a kind of digital microscope formation method in this, belong to optical microphotograph imaging field.

Background technology

Traditional microscope, mainly scioptics group obtains, and the micro-image obtained so is also the intensity image of imaging object.Along with the development of semiconductor technology and laser technology, there is a kind of digital holography in present stage, and it can while the intensity image obtaining imaging object, and obtain the position phase images of imaging object, it can obtain the 3-D view of imaging object in other words.

Digital holography utilizes electrooptical device (CCD or CMOS) to replace traditional holographic dry plate recording interference fringe, then sends into computing machine also by intensity and the phase mehtod of numerical evaluation reconstruction of objects.Compared with traditional optical holography, digital hologram has many outstanding advantages, and these advantages make digital holography get the attention, and has become a study hotspot.In recent years, along with the appearance of the pulsed digital holography technology of the ultrafast transient process of record femtosecond, digital holography more shows the vigor in scientific research and optical non-destructive detection.

Traditional holography is recorded on holographic dry plate by the hologram of imaging object, then irradiates holographic dry plate with the reference light in recorded hologram or its conjugate beam, namely reproduce hologram, thus obtain the 3-D view of object; And in digital holography, replace holographic dry plate with CCD, the hologram gathering imaging object with CCD, hologram is inputted in computing machine, utilize the hologram reconstruction process of algorithm simulation reality in a computer, thus rebuild the 3-D view of object in a computer.The image that the reproduction image of hologram obtains relative to common digital camera, the reproduction image of hologram, except having intensity image, also has position phase images, i.e. the three-dimensional appearance image of object, therefore in digital holography it is crucial that the reconstruction of object phase information.

The conventional method that digital hologram position rebuilds mutually is: by obtaining its frequency spectrum (as shown in Figure 1 to hologram Fourier transform, a () is schematic diagram, b () is experimental result), then spectral filtering is carried out by unwanted 0 grade and-1 grade of frequency spectrum filtering, afterwards inverse Fourier transform is remake to filtered frequency spectrum, obtain the wavefront information of reproduction image finally by Diffraction Calculation.There are the following problems for this method: (1) owing to needing the scope determining+1 order diffraction spectrum by artificial method in process of reconstruction, significantly reduce the speed that position rebuilds mutually, thus limit digital holography carries out Real-Time Monitoring application demand to dynamic changing process.(2) often cause in filtering 0 grade of filtering of composing thoroughly and+1 grade of spectrum leach imperfect, thus cause the loss of noise and reproduction image high-frequency information, this causes the reduction of reproduction image signal to noise ratio (S/N ratio) on the one hand, cause phase measurement error, also reduce the resolution of reproduction image on the other hand; (3) discrete reconstruction can bring periodically, and this cycle equals the scope in space of hologram, within the scope of this, 0 grade, ± 1 grade exist simultaneously, and the scope of 0 grade of item is 2 times of+1 grade or-1 grade picture, and conjugate image is unnecessary, and it is unlike any information of original image multi-band.Like this, effective area has accounted for the very little share of hologram.Therefore increasing useful area by the area of oppressive undesired picture is that people expect very much; (4), in the Diffraction Calculation process of final step, because the record parameters such as recording distance can not accurately obtain and numerical reconstruction algorithm itself, larger position phase reconstruction error can all be introduced, and part high-frequency information loss in object light field.

Summary of the invention

The invention provides the real-time high-precision position phase method for reconstructing in a kind of Digital holographic microscopy, with overcome upper rheme rebuild mutually in Problems existing.No matter recording beam path and the sample what state that is recorded, the filter field selected during reproduction must be fixing.Consider that in hologram frequency spectrum, three orders of diffraction are symmetrical relative to true origin, therefore, if select+1 grade of complete quadrant (i.e. reproduction image visual field 1/4th) composing place as filter field (as shown in Figure 2), then can exempt and not fixing due to filter field and the reconstruction non real-time nature problem brought.Such Choose filtering region, can also solve the effective radio-frequency component brought not greatly in+1 grade of spectrum region simultaneously and lose problem.But meanwhile also bring the height interference of 0 grade of spectrum, therefore, unconventional method for reconstructing must be utilized in this case 0 grade of interference to be eliminated.Consider that multiplying can be converted to additive operation by homomorphic filtering technology, this thought is used for hologram reconstructing, then Object light wave and complex conjugate thereof can be separated completely, thus thoroughly eliminate the interference of 0 order diffraction, high precision, real-time ground rebuilds object light wave field.

The present invention includes following technical scheme:

Open laser instrument, the laser of generation, through the first half-wave plate, after polarization beam splitter prism, is divided into Object light wave and reference light wave; By the first reflective mirror and the second mirror reflection, Object light wave and reference light wave are intersected vertically, put into light combination mirror in intersection, make Object light wave and reference light wave overlap as light beam after light combination mirror; After the first reflective mirror, put into the first beam-expanding collimation device, transparent substance and the first microscope successively, regulate the first beam-expanding collimation device, make Object light wave become the first directional light after the first beam-expanding collimation device, utilize the first directional light to irradiate transparent substance; Make transparent substance by the first microcobjective imaging, CCD is placed in the position at described picture place; The second beam-expanding collimation device was put into before the second reflective mirror, the second microscope is put into after the second reflective mirror, regulate the second beam-expanding collimation device, make reference light wave become the second directional light after the second beam-expanding collimation device, utilize the second reflective mirror that the second directional light is imported the second microcobjective; Rotate light combination mirror, make Object light wave oblique incidence light combination mirror; Wherein the first microscope is equal to the distance of light combination mirror with the second microscope; By the hologram that CCD collection Object light wave and reference light wave are formed on CCD target surface, described hologram is transferred to computing machine; Wherein the Object light wave of CCD target surface place plane and reference light wave complex amplitude are respectively O (x, y), R (x, y), and the complex amplitude of above-mentioned hologram is H (x, y).

The feature of the method for described acquisition three-dimensional microscopic image is: comprise the following steps:

1) above-mentioned hologram is distributed divided by the reference light intensity recorded, then natural logarithm is got to it, obtain:

$\ln \left[\hat{H}(x,y)\right]=\ln [1+\hat{O}(x,y)]+\ln [1+{\hat{O}}^{*}(x,y)];$

Wherein $\hat{H}(x,y)=\frac{H(x,y)}{{\left|R(x,y)\right|}^2},$ $\hat{O}(x,y)=O(x,y)/R(x,y),$ for complex conjugate;

2) then Fourier transform is done to above formula, obtain its frequency spectrum profile wherein FT{} is Fourier transform; f _x, f _yfor the spatial frequency in x direction and y direction;

3) choose 1/4th spectrums face size (i.e. a quadrant) corresponding with object frequency spectrum in spectrogram, obtain the spectrum distribution of filtered hologram logarithm $S_{\mathrm{Fil}}(f_x,f_y)={\mathrm{FT}}_{\mathrm{Fil}}\left\{\ln \right[\hat{H}(x,y)\left]\right\};$

4) to S _fil(f _x, f _y) doing inverse Fourier transform, can obtain again exponent arithmetic is done to it, can obtain

5) bigness scale is carried out to reference light wave wave vector, obtains its propagation vector, thus obtain the reference light COMPLEX AMPLITUDE R (x, y) omited mutually:

6) by $\hat{O}(x,y)=O(x,y)/R(x,y)$ Obtain O (x, y);

7) according to automatic phase compensation method, the wavefront distortion obtained is compensated, obtain the true phase mehtod of object light wave field.

Accompanying drawing explanation

Hologram frequency spectrum simulation distribution figure during Fig. 1 conventional reconstruction; In Fig. 1, (a) is schematic diagram, and (b) is lab diagram.

Fig. 2 unconventional rebuild time hologram frequency spectrum simulation distribution figure.

Fig. 3 optical microphotograph imaging system schematic diagram.

Fig. 4 Plane reference light pre-amplified digital holographic coordinate schematic diagram.

Fig. 5 spherical reference light pre-amplified digital holographic coordinate schematic diagram.

The unconventional reconstruction FB(flow block) of Fig. 6.

The holographic resolving power test target experimental result of Fig. 7 Plane reference light pre-amplified digital; (a) hologram in Fig. 7, (b) spectrogram, (c) conventional algorithm rebuilds picture, and (d) nonlinear algorithm rebuilds picture.

The hologram of Fig. 8 erythrocyte and frequency spectrum thereof; (a) hologram in Fig. 8, the frequency spectrum of (b) (a).

The reconstructed results of Fig. 9 erythrocyte; The intensity image of (a) conventional algorithm in Fig. 9, the intensity image of (b) nonlinear algorithm, the Two-dimensional Position Entropy density deviation of (c) conventional algorithm, the Two-dimensional Position Entropy density deviation of (d) nonlinear algorithm, the three-dimensional phase mehtod of (e) conventional algorithm, the three-dimensional phase mehtod of (f) non-linear reconstruction algorithm.

Specific embodiment

One, digital hologram chart recording system

Fig. 3 is optical microphotograph imaging system schematic diagram.The wavelength sent by He-Ne laser instrument 1 is that the laser of 632.8nm is divided into light beam A and light beam B after half-wave plate 2 after polarization beam splitter prism 3, and respectively after beam-expanding collimation device 4, the plane light wave of a branch of formation illuminated sample 6 (transparent substance), and through microcobjective MO ₁(7) form the Object light wave of amplification afterwards, another bundle is through microcobjective MO ₂(8) spherical reference wave dispersed is formed afterwards, two-beam closes after bundle through prism BS (i.e. bundling device 9) and interferes, and be positioned at ccd sensor 10 records of sample image plane, be sent to computing machine 11 subsequently and process, in figure, 5 represent reflective mirror.In order to eliminate MO ₁the secondary phase aberrated beams introduced, MO ₂should with MO ₁identical, necessary its position of accurate adjustment, the spherical light wave that directional light is formed after them has identical corrugated to bend relative to CCD.Need the inclination angle of fine adjusting prism BS simultaneously, recorded hologram frequency spectrum is diagonally separated.Concrete control method is as follows: first, blocks reference light, instrumentality plane to the distance of microcobjective and CCD position, make object be exaggerated suitable multiple and become in CCD clearly as.But because diffraction effect makes to be difficult to accurately determine as plane, but we find, if put into a common wiping lens paper in object light road, the diffraction of light can be made greatly to weaken, picture planimetric position now just accurately can be determined.Secondly, not setting-out product in object light road, accurate adjustment MO ₂position, make recorded holographic fringes and reconstructed bits Entropy density deviation be parallel equidistant vertical bar line.

In figure 3, object light and reference light are before entering BS, its main beam is mutually vertical, and prism BS has a small angle inclination (tiltangleθ is about 2 ~ 3 °) relative to optical axis, result makes reference light main beam produce same inclination relative to object light main beam, thus realizes from axle record.

Two, the recording and reconstruction of digital hologram

1, the record of Digital Holography with Plane Reference Wave figure and reproduction

Fig. 4 is the coordinate system schematic diagram that before Plane reference light image, pre-amplified digital holographic microphotography record and reproduction adopt.Wherein, MO has used simple lens equivalently represented, and focal length is f; x ₀-y ₀, x _φ-y _φ, x-y, x _i-y _irepresent object, MO, hologram and reproduction image plane successively, z-axis along system optical axis direction and by the center of above plane; R (x, y) is from axial plane reference light, and the angle of its direction of propagation and main shaft is 2 ~ 3 °.In addition, d in figure ₀for object distance, the d of MO _φ+ d=d _ifor the reproduction distance that its image distance, d are hologram.

Succinct in order to what express, in deriving below unless otherwise indicated, general one-dimensional form.

If the COMPLEX AMPLITUDE of object under test is o (x ₀), the aperture function of MO is according to means of Fresnel diffraction, ignore inessential constant phase factor, then the diffractive light field complex amplitude on the forward and backward surface of MO is respectively

$U^{\′}\left(x_{\mathrm{\φ}}\right)=\underset{-\∞}{\overset{\∞}{\∫}}O\left(x_0\right)\exp \left[\frac{\mathrm{jk}}{{2d}_0}{(x_{\mathrm{\φ}}-x_0)}^2\right]{\mathrm{dx}}_0---\left(1\right)$

$U\left(x_{\mathrm{\φ}}\right)=U^{\′}\left(x_{\mathrm{\φ}}\right)P\left(x_{\mathrm{\φ}}\right)\exp [-\frac{\mathrm{jk}}{2f}{x}_{\mathrm{\φ}}^2]---\left(2\right)$

CCD plane object optical field distribution

$O\left(x\right)=\underset{-\∞}{\overset{\∞}{\∫}}U\left(x_{\mathrm{\φ}}\right)\exp \left[\frac{\mathrm{jk}}{{2d}_{\mathrm{\φ}}}{(x-x_{\mathrm{\φ}})}^2\right]{\mathrm{dx}}_{\mathrm{\φ}}---\left(3\right)$

In like manner, reference light in the COMPLEX AMPLITUDE of CCD plane is

R(x)＝R ₀exp[-j2π(f _xx)] (4)

F in formula _xfor Plane reference light wave is in the spatial frequency in x direction, R ₀for its amplitude.The fringe intensity that object light and reference light are formed in CCD plane is distributed as

$H\left(x\right)=|O\left(x\right){|}^2+R_0^2+R^{*}\left(x\right)O\left(x\right)+O{\left(x\right)}^{*}R\left(x\right)---\left(5\right)$

The digital hologram of CCD record is

$H_D\left(x\right)=[H\left(x\right)\⊗\mathrm{rect}\left(\frac{x}{\mathrm{\α\Δx}}\right)]\mathrm{comb}\left(\frac{x}{\mathrm{\Δx}}\right)\mathrm{rect}\left(\frac{x}{L_x}\right)---\left(6\right)$

Δ x and L in formula _xbe respectively CCD pixel dimension in the horizontal direction and photosurface size, α is its fill factor, curve factor.

In order to the convenience discussed, still carry out the reproduction of light wave fields with continuous light format of field.Adopt former reference light wave R to irradiate hologram, obtain | R| ²o, can obtain original image through diffraction propagation in the image planes of MO, is real image, and its image field light wave is distributed as

$U_{+1}\left(x\right)=R_0^2\underset{-\∞}{\overset{\∞}{\∫}}\mathrm{rect}\left(\frac{x}{L_x}\right)O\left(x\right)\exp \left[\frac{\mathrm{jk}}{2d}{(x_i-x)}^2\right]\mathrm{dx}---\left(7\right)$

Rect (x/L in formula _x) effect be restriction CCD record light field scope.Just can obtain the intensity distributions of reproduction image by formula (7) and contain the parcel phase mehtod of secondary and a phase aberrated beams, being compensated and separate the continuous phase mehtod that parcel computing can obtain object by suitable phase aberrated beams.

2, the record of Digital Hologram under Spherical Reference light Wave and reproduction

Fig. 5 is the pre-amplified digital holographic light path and the coordinate system schematic diagram that utilize spherical reference optical recording.Be spherical light wave with Fig. 4 unlike reference light, δ (x in figure _r, y _r) represent the position of spherical reference point source, if be located at (in figure, F is MO focus) on the focal plane of MO, the bending thing in is formationed corrugated of etc.ing joins light image face digital holography, is conducive to phase aberrated beams compensation and position separates correctly carrying out of parcel mutually.

Because CCD photosurface is less, can think that the amplitude of spherical reference light in record plane is constant, if it is R ' ₀, then the light field complex amplitude that spherical reference light is formed in CCD plane is

$R\left(x\right)=R_0^{\′}\exp \left[\frac{\mathrm{jk}}{2(d_i-f-d)}{(x-x_r)}^2\right]---\left(8\right)$

For pre-amplified digital holography, want to obtain reproduction image clearly in the image planes of MO, after reproducing light-wave irradiation hologram, should be the diffractive light field O (x of object what be close to that hologram rear surface obtains, y), for this reason, reproducing light wave should be the spherical light wave with record reference light iso-curvature.Consider x _r, y _raccurately cannot obtain, therefore, reproduce light wave and adopt the sphere point source be positioned on optical axis.Without loss of generality, if its amplitude in CCD plane is 1, then its expression formula is:

$C\left(x\right)=\exp \left[\frac{\mathrm{jk}}{2(d_i-f-d)}{x}^2\right]---\left(9\right)$

The COMPLEX AMPLITUDE obtaining original image light field is thus

$U_{+1}\left(x_i\right)=\underset{-\∞}{\overset{\∞}{\∫}}\mathrm{rect}\left(\frac{x}{L_x}\right)C\left(x\right)R^{*}\left(x\right)O\left(x\right)\×\exp \left[\frac{\mathrm{jk}}{2d}{(x_i-x)}^2\right]\mathrm{dx}$

$=A\underset{-\∞}{\overset{\∞}{\∫}}\mathrm{rect}\left(\frac{x}{L_x}\right)O\left(x\right)\exp \left[j2\mathrm{\π}\frac{x_r}{\mathrm{\λ}(d_i-f-d)}x\right]\×\exp \left[\frac{\mathrm{jk}}{2d}{(x_i-x)}^2\right]\mathrm{dx}---\left(10\right)$

Wherein A is constant factor.

3, the recording and reconstruction of image planes digital hologram

Record plane in Fig. 4 and Fig. 5 is moved to the imaging plane place of system, plane and spherical reference light image face digital holography can be realized.Now, d _φ=d _i, i.e. x _i-y _iplane overlaps with x-y plane.

Image planes digital holography record be object itself picture field information, therefore, no matter be plane or spherical reference light image face digital hologram, as long as irradiate hologram with the plane light wave being parallel to optical axis, just can obtain the picture light field of object in the plane after being close to hologram.But in order to eliminate the interference of Zero-order diffractive item and conjugate image, need to carry out spectral filtering to hologram.The two-dimentional COMPLEX AMPLITUDE of original image light field is as follows:

U ₊₁(x，y)＝FT ^-1{FT[H(x，y)]·W(x，y)}＝R ^*(x，y)O(x，y) (11)

" FT " and " FT in formula ^-1" representing two-dimensional Fourier transform and inverse transformation thereof respectively, W (x, y) represents transparent spectral window function.

Three, position rebuilds mutually

1, conventional position phase method for reconstructing

1), fresnel transform method

Fresnel transform reconstruction method be suggested the earliest, be also a kind of method for reconstructing with the most use, it is simple, quick, and therefore, first we discuss it.Fresnel transform reconstruction method is based on fresnel diffraction theory, and demand fulfillment Fresnel approximation condition, this condition is

$z_0\≥{\left\{\frac{\mathrm{\π}}{4\mathrm{\λ}}{[{(x_0-x)}^2+{(y_0-y)}^2]}^2\right\}}_{\max }^{1/3}---\left(12\right)$

Wherein, z ₀for viewing plane x-y and diffraction aperture plane x ₀-y ₀between distance.

According to the definition of means of Fresnel diffraction and Fourier transform, if reconstructed wave is distributed as C (x, y) in CCD plane, at the complex amplitude as the diffraction light wave in plane be then

$U(x_i,y_i)=\frac{\exp \left({\mathrm{jkz}}_i\right)}{{\mathrm{j\λz}}_i}\underset{-\∞}{\overset{\∞}{\∫}}\underset{-\∞}{\overset{\∞}{\∫}}C(x,y)H(x,y)\exp \left\{\frac{\mathrm{jk}}{{2z}_i}\right[{(x_i-x)}^2+{(y_i-y)}^2\left]\right\}\mathrm{dxdy}$

$=\frac{\exp \left({\mathrm{jkz}}_i\right)}{{\mathrm{j\λz}}_i}\exp \left[\frac{\mathrm{jk}}{2z_i}({x_i}^2+{y_i}^2)\right]\mathrm{FT}\left\{C(x,y)H(x,y)\exp \right[\frac{\mathrm{jk}}{{2z}_i}(x^2+y^2)\left]\right\}---\left(13\right)$

Wherein, FT{} represents two-dimensional Fourier transform, and H (x, y) is recorded hologram, z _ifor the distance between picture plane and hologram plane.In reality, above formula is realized by the fast algorithm (FFT) of discrete Fourier transformation.But in order to the convenience expressed, in this and following analysis, usually only write out corresponding conitnuous forms.

From formula (13), utilize fresnel transform reconstruction algorithm, only need work Fourier transform can obtain the distribution of picture light field.

Fresnel transform is rebuild expression formula (13) and is got by means of Fresnel diffraction, and light is always forward direction in space, therefore, and parameter z in formula _irepresent the distance of light wave propagation, always on the occasion of.This situation correspond to reproduction image plane and is positioned at CCD plane rear, and namely reproduction image is the situation of real image.So, how the virtual image in digital hologram is reproduced?

From the angle of system, what formula (13) was expressed is a kind of conversion, can be called fresnel transform.Object light wave is a diffraction process from CCD plane propagation to its rear as the process of plane, can represent with Fresnel formula, if we regard positive fresnel transform as this conversion, then the process that light wave finally oppositely converges to the formation virtual image of its front from CCD planar diffraction just can be equivalent to a process against fresnel transform.That is, in digital hologram, the calculating of virtual image light field also can calculate in the conversion expressed of through type (13), only at this moment should by the distance z of formula _ichange-z into _i.This conclusion not only can be used in fresnel transform reconstruction method, for convolution reconstruction method, angular spectrum reconstruction method are also applicable below.

2), convolution method

Kirchhoff diffraction integral formula and Rayleigh one Suo Mofei diffraction integral formula are all the accurate description of diffraction in space, and convolution reconstruction method obtains based on Rayleigh one Suo Mofei diffraction integral formula and lineary system theory.According to Rayleigh one Suo Mofei diffraction integral formula, the Complex Amplitude of above-mentioned diffractional field is

$U(x_i,y_i)=\frac{1}{\mathrm{j\λ}}\underset{-\∞}{\overset{\∞}{\∫}}\underset{-\∞}{\overset{\∞}{\∫}}C(x,y)H(x,y)\frac{\exp \left(\mathrm{jk\ρ}\right)}{\mathrm{\ρ}}\cos \mathrm{\θdxdy}---\left(14\right)$

Wherein $\mathrm{\ρ}=[z_i^2+{(x_i-x)}^2+{(y_i-y)}^2{]}^{1/2},$ $\cos \mathrm{\θ}=\frac{z_i}{\mathrm{\ρ}}.$ By lineary system theory, (14) formula can be write as following convolution form:

$U(x_i,y_i)=\underset{-\∞}{\overset{\∞}{\∫}}\underset{-\∞}{\overset{\∞}{\∫}}C(x,y)H(x,y)g(x_i-x,y_i-y)\mathrm{dxdy}---\left(15\right)$

In formula

$g(x,y)=\frac{1}{\mathrm{j\λ}}\frac{\exp \left[\mathrm{jk}{(z_i^2+x^2+y^2)}^{1/2}\right]}{z_i^2+x^2+y^2}---\left(16\right)$

For the pulsion phase of free space should.According to convolution theory, the Fourier transform form that (15) formula can be expressed as:

U＝FT ^-1[FT(H·C)·FT(g)] (17)

From formula (17), utilizing convolution method to rebuild needs work three Fourier transforms, and Fresnel approximation reconstruction method only needs work Fourier transform, and thus Fresnel approximation method rebuilds speed.In addition, the two has following difference at all: if hologram plane is considered as spatial domain, then after the conversion of (13) formula, reproduction image has arrived frequency domain, and therefore reproduce the pixel size of image planes, namely the sampling interval is

${\mathrm{\Δx}}_i=\frac{{\mathrm{\λz}}_i}{N_x\mathrm{\Δx}},$ ${\mathrm{\Δy}}_i=\frac{{\mathrm{\λz}}_i}{N_y\mathrm{\Δy}}---\left(18\right)$

This interval is consistent with the resolution of reproduction image.And spatial domain has finally been got back in the conversion represented by (17) formula, therefore the pixel size of convolution method reconstruction image planes has been

Δx _i＝Δx，Δy _i＝Δy (19)

According to principle of holography, the resolution of digital hologram imaging is determined by the numerical aperture of hologram during record, and therefore, record high-NA hologram, can realize high-resolution imaging.But if adopt convolution method to reproduce, because the sampling interval of reproducing image planes equals the Pixel size of CCD, even if can reach high resolution in theory, the fine structure in actual reproduction, object plane being less than CCD pixel dimension also can not be out reproduced.That is, conventional convolution reproduces the resolution that method limits digital holographic imaging systems.

3), angular spectrum method

Angular spectra theory is the Plane wave theory of diffraction, and it strictly defers to the Helmholtz equation of scalar diffraction, and without any restrictive condition, therefore it is the accurate description of diffraction phenomena at frequency domain.Its expression formula is as follows

G(f _x，f _y)＝G ₀(f _x，f _y)G _B(f _x，f _y) (20)

Wherein

$G_B(f_x,f_y)=\exp \left[j\frac{2\mathrm{\π}}{\mathrm{\λ}}z\sqrt{1-{\left({\mathrm{\λf}}_x\right)}^2-{\left(\mathrm{\λ}{f}_y\right)}^2}\right]---\left(21\right)$

For light wave is in the transport function of free space, G ₀(f _x, f _y) be the angular spectrum of light wave fields in aperture plane.Formula (20) have expressed light wave fields propagates into the film viewing screen being z apart spectral change relation from diffraction screen.Following relation is had between the transport function of free space and impulse response:

G _B(f _x，f _y)＝FT{g(x，y)} (22)

By principle of holography, when irradiating hologram with reconstructed wave C (x, y), the frequency spectrum being close to the light wave fields of diffraction screen rear surface is

G ₀(f _x，f _y)＝FT{C(x，y)H(x，y)} (23)

According to angular spectra theory, can obtain from hologram plan range be z _ipicture plane x _i-y _ithe frequency spectrum of upper reproduction light field, is the COMPLEX AMPLITUDE of playback light wave field do inverse Fourier transform to it.

U＝FT ^-1{FT[C·H]·G _B} (24)

Visible, rebuilding hologram by angular spectrum method needs through once positive Fourier transform and an inverse Fourier transform, and therefore the pixel size of reproduction image plane also equals the pixel dimension of CCD.

In addition, means of Fresnel diffraction also can be write as convolution form and angular spectrum form.Therefore, except above-mentioned based on except the convolution reconstruction method on strict diffraction theory and angular spectrum reconstruction method, the convolution reconstruction method based on fresnel diffraction theory and angular spectrum reconstruction method should also be there is.

According to lineary system theory, fresnel transform reconstruction formula (13) also can be write as following convolution form:

U＝[H(x，y)C(x，y)]*g _F(x，y) (25)

Wherein

$g_F=\frac{\exp \left({\mathrm{jkz}}_i\right)}{{\mathrm{jkz}}_i}\exp \left[\frac{\mathrm{jk}}{2z_i}(x^2+y^2)\right]---\left(26\right)$

For the impulse response of Fresnel Diffraction System.Under paraxial approximate condition, formula (26) can be obtained by formula (16).Utilize convolution theorem, (24) formula can be written as

U＝FT ^-1[FT(H·C)·FT(g _F)] (27)

The method for reconstructing that formula (27) is expressed can be called Fresnel convolution method.

Fourier transform is done to formula (26), obtains

$\mathrm{FT}\left\{g_F\right\}=\exp \left({\mathrm{jkz}}_i\right)\exp \left[{-\mathrm{j\π\λz}}_i(f_x^2+f_y^2)\right]---\left(28\right)$

Be the same with the result obtained under Fresnel approximation condition by formula (21), be therefore called the transport function of Fresnel Diffraction System, and use G _frepresent.This pattern (27) can be written as again

U＝FT ^-1[FT(H·C)·G _F] (29)

Similar to formula (24), the reconstruction algorithm that formula (29) is expressed can be called Fresnel angular spectrum method.

2, unconventional position phase method for reconstructing

If the Object light wave of hologram plane and reference light wave complex amplitude are respectively O (x, y), R (x, y), be distributed as at CCD plane hologram

H(x，y)＝|O(x，y)+R(x，y)| ²＝|O(x，y)| ²+|R(x，y)| ²+O(x，y)R ^*(x，y)+O ^*(x，y)R(x，y) (30)

| O (x, y) | ²and 0 of thing functional dependence grade of item that it represents the auto-correlation of thing function.This elimination is the key that digital hologram reproduces.Formula (30) can be write as form below:

$H(x,y)={\left|R(x,y)\right|}^2{|1+\frac{O(x,y)}{R(x,y)}|}^2=A^2{|1+\hat{O}(x,y)|}^2=A^2[1+\hat{O}(x,y)][1+{\hat{O}}^{*}(x,y)]---\left(31\right)$

Wherein wherein for complex conjugate, A ²=| R (x, y) | ²for recording the light distribution of reference light.Following relation can be obtained by formula (31):

$\ln \left[\frac{H(x,y)}{{\left|R(x,y)\right|}^2}\right]=\ln [1+\hat{O}(x,y)]+\ln [1+{\hat{O}}^{*}(x,y)]---\left(32\right)$

Can prove, | R (x, y) | > | O (x, y) | when, if be distributed in a certain quadrant scope (as I quadrant) completely, then must be positioned at completely and the quadrant of its symmetry (III quadrant).Like this, just can be by thoroughly leach, again exponent arithmetic is done to it afterwards, can obtain object light wave COMPLEX AMPLITUDE can be obtained thus $O(x,y)=\hat{O}(x,y)R(x,y).$

Visible, utilize above-mentioned nconventional method to rebuild hologram, following condition must be met:

(1) reference light intensity is greater than object light intensity, namely | and R (x, y) | ²> | O (x, y) | ².Reference beam intensity ratio object light is powerful must be more, rebuild and are accurate to higher (in holographic recording process, with reference to the light intensity 3-5 that normally object light is strong doubly, thus this condition is satisfied);

(2) spectral range of object is within the scope of a quadrant, and+1 of the hologram recorded and-1 grade of spectrum can not be overlapping in space, and will along the diagonal arrangement in spectrum face;

(3) reference light needs to know in advance (can record with CCD at any time in recording process) in the intensity distributions of hologram plane.

3, unconventional position phase reconstruction procedures

Visible according to analysis above, hologram function can regard the product of two functions as, therefore can rebuild it with the homomorphic signal processing technique based on multiplying signal, and its process flow block diagram is as shown in Figure 6 in figure, H (x, y) is recorded digital hologram.

The unconventional reconstruction procedures of hologram is as follows:

(1) hologram of record is distributed divided by the reference light intensity recorded, then natural logarithm is got to it, obtain:

$\ln \left(\hat{H}(x,y)\right)=\ln [1+\hat{O}(x,y)]+\ln [1+{\hat{O}}^{*}(x,y)];$

(2) then Fourier transform is done to above formula, obtain its frequency spectrum profile

(3) choose 1/4th spectrums face size (i.e. a quadrant) corresponding with object frequency spectrum in spectrogram, obtain the spectrum distribution of filtered hologram logarithm $S_{\mathrm{Fil}}(f_x,f_y)={\mathrm{FT}}_{\mathrm{Fil}}\left\{\ln \right[\hat{H}(x,y)\left]\right\};$

(4) to S _fil(f _x, f _y) doing inverse Fourier transform, can obtain again exponent arithmetic is done to it, can obtain

(5) bigness scale is carried out to reference light wave wave vector, obtains its propagation vector, thus obtain rough reference light COMPLEX AMPLITUDE R (x, y)=| R (x, y) | exp [j2 π (k _xx+k _yy)];

(6) by $\hat{O}(x,y)=O(x,y)/R(x,y)$ Obtain O (x, y);

(7) utilize angular spectrum diffraction formulae discovery as the light wave fields COMPLEX AMPLITUDE (for image planes digital holography, Diffraction Calculation can be omitted) of plane;

(8) according to automatic phase compensation method, the wavefront distortion obtained is compensated, obtain the true phase mehtod of object light wave field.

Four, the rectification of phase aberrated beams

1, double exposure method

Double exposure method refers to and records a width hologram respectively having in sample and n.s. two kinds of situations, then utilizes identical method for reconstructing to carry out position respectively to two width holograms and rebuilds mutually, finally two the position phasors obtained are subtracted each other the phase mehtod that can obtain object.

2, automatic phase compensation method

In phase diagram, choose the region that a part of noise is little, and set up X-axis on the area, and perpendicular Y-axis; Obtain the position phase data of some along X-axis, obtain the position phase data corresponding with the upper phase amount of X-axis along Y-axis simultaneously, and perform least square method, extract position phase data; Described least square method is preferably based on the least square method of lateral shearing interference; Linear fit is carried out to the position phase data extracted, obtains every fitting coefficient of X-axis and Y direction respectively, thus obtain actual phase aberrated beams expression formula, phase of ascending the throne mask; The position phase images of the phase-only pupil filter obtained and acquisition is subtracted each other, corrects a phase aberrated beams, thus obtain the position phase images of phase aberrated beams rectification.

3, frequency displacement method

For the phase aberrated beams introduced from axle record, can by after acquisition hologram+1 spectral centroid coordinate, this frequency spectrum is moved to rebuilding plane center, and filtering 0 grade simultaneously and-1 grade of spectrum, then carry out position and rebuild mutually.

4, the method for average

The phase aberrated beams that the method is only applicable to light field equally compensates.The method of average utilizes the linear change character reproducing phase of the field, along level and vertical direction, local derviation is asked respectively to the phase mehtod of flat site near sample, then its mean value is obtained respectively, thus obtain a phase aberrated beams distribution, subtract each other with raw bits Entropy density deviation again, distortionless phase mehtod can be obtained.

Five, experimental result

In order to verify non-linear reconstruction algorithm feasibility in an experiment, first Plane reference light pre-amplified digital holographic microphotography light path is utilized to test resolution test plate, as shown in Figure 7, wherein Fig. 7 (a), (b), (c) and (d) are the holograms of resolving power test target to result respectively, the spectrum distribution of hologram, the conventional algorithm intensity intensity of rebuilding picture and nonlinear algorithm rebuilds picture.In experiment, reference light and object light angle theta are about 1.51 °, beam intensity ratio γ is about 1.53.Visible, the result utilizing non-linear reconstruction algorithm to obtain obviously is better than the result that conventional algorithm obtains.What is more important, utilizes nonlinear algorithm to avoid the manual process choosing filter window, thus really can realize the real-time reproduction of hologram.

Keeping above light path constant, resolving power test target is changed to human body erythrocyte, in order to ensure that system has higher imaging resolution and better imaging picture element, reducing the image-forming range of microcobjective to d _i=273mm, recording distance is to d=44mm, result as shown in Figure 8, wherein scheme the hologram that (a) is erythrocyte, b spectrum distribution that () is hologram, it is overlapping but separated from one another that the positive and negative one-level spectrum in figure and zero level compose part, first carries out filtering to this spectrogram, shown in the region that the filter range of two kinds of algorithms is irised out as figure white box and white dashed line respectively, part zero level is had to compose in the region being included in and reproducing light field.Then conventional algorithm and non-linear reconstruction algorithm is utilized to carry out numerical reconstruction to hologram, reconstructed results as shown in Figure 9, Fig. 9 (a) that conventional algorithm obtains receives the impact of zero level spectrum, noise ratio is more severe, thus directly affects the quasi real time property of the reconstruction of a phase, the two and three dimensions phase mehtod that Fig. 9 (c), (e) reproduce for conventional algorithm, by position phase precompensation with based on the multi-thread phase information to still high not reproducing erythrocyte after average automatic phase compensation algorithm accurately; And the result adopting non-linear reconstruction algorithm to obtain can suppress zero-order term well, result is as shown in Fig. 9 (b), after after the phase precompensation of position, connect the two and three dimensions position phase result obtained shown in Fig. 9 (d) He (f), cell surface is smooth, form is high-visible.Experimental result and theoretical analysis, Computer simulation results are identical, and indicate non-linear reconstruction algorithm high precision, reproduction feature quasi real time based on homomorphic signal processing technique, lay a good foundation for digital holographic microscopy further develops.

Claims (2)

1. obtain a method for microscopic image in three-dimensional shape, open laser instrument, the laser of generation, after the first half-wave plate and a polarization beam splitter prism, is divided into Object light wave and reference light wave; By the first reflective mirror and the second mirror reflection, Object light wave and reference light wave are intersected vertically, put into light combination mirror in intersection, make Object light wave and reference light wave overlap as light beam after light combination mirror; After the first reflective mirror, put into the first beam-expanding collimation device, transparent substance and the first microcobjective successively, regulate the first beam-expanding collimation device, make Object light wave become the first directional light after the first beam-expanding collimation device, utilize the first directional light to irradiate transparent substance; Make transparent substance by the first microcobjective imaging, CCD is placed in the position at described picture place; The second beam-expanding collimation device was put into before the second reflective mirror, the second microcobjective is put into after the second reflective mirror, regulate the second beam-expanding collimation device, make reference light wave become the second directional light after the second beam-expanding collimation device, utilize the second reflective mirror that the second directional light is imported the second microcobjective; Rotate light combination mirror, make Object light wave oblique incidence light combination mirror; Wherein the first microcobjective is equal to the distance of light combination mirror with the second microcobjective; By the hologram that CCD collection Object light wave and reference light wave are formed on CCD target surface, described hologram is transferred to computing machine; Wherein the Object light wave of CCD target surface place plane and reference light wave complex amplitude are respectively O (x, y), R (x, y), and the complex amplitude of above-mentioned hologram is H (x, y);

The feature of the method for described acquisition three-dimensional microscopic image is: comprise the following steps:

1) above-mentioned hologram is distributed divided by the reference light intensity recorded, then natural logarithm is got to it, obtain;

$\ln \left(\hat{H}(x,y)\right)=\ln [1+\hat{O}(x,y)]+\ln [1+{\hat{O}}^{*}(x,y)];$

Wherein $\hat{H}(x,y)=\frac{H(x,y)}{{\left|R(x,y)\right|}^2},\hat{O}(x,y)=O(x,y)/R(x,y),$ for complex conjugate;

2) then Fourier transform is done to above formula, obtain its frequency spectrum profile wherein FT{} is Fourier transform; f _x, f _yfor the spatial frequency in x direction and y direction;

3) choose 1/4th spectrum face sizes corresponding with object frequency spectrum in spectrogram, i.e. a quadrant, obtains the spectrum distribution of filtered hologram logarithm $S_{\mathrm{Fil}}(f_x,f_y)={\mathrm{FT}}_{\mathrm{Fil}}\left\{\ln \right[\hat{H}(x,y)\left]\right\};$

4) to S _fil(f _x, f _y) doing inverse Fourier transform, can obtain again exponent arithmetic is done to it, can obtain

5) bigness scale is carried out to reference light wave wave vector, obtain its propagation vector, thus obtain rough reference light COMPLEX AMPLITUDE R (x, y);

6) by $\hat{O}(x,y)=O(x,y)/R(x,y)$ Obtain O (x, y);

7) according to automatic phase compensation method, the phase aberrated beams obtained is compensated, obtain the true phase mehtod of object light wave field.

2. the method for claim 1, wherein phase compensation method is automatically: in phase diagram, choose the region that a part of noise is little, and set up X-axis on the area, and perpendicular Y-axis; Obtain the position phase data of some along X-axis, obtain the position phase data corresponding with the upper phase amount of X-axis along Y-axis simultaneously, and perform least square method, extract position phase data; Linear fit is carried out to the position phase data extracted, obtains every fitting coefficient of X-axis and Y direction respectively, thus obtain actual phase aberrated beams expression formula, phase of ascending the throne mask; The position phase images of the phase-only pupil filter obtained and acquisition is subtracted each other, corrects a phase aberrated beams, thus obtain the position phase images of phase aberrated beams rectification.