CN103837325A - Device and method for transmission type optical element layering phase position imaging - Google Patents

Abstract

The invention discloses a device and method for transmission type optical element layering phase position imaging. The device is composed of a coherent light source, a beam expander, a convergent lens, a to-be-tested optical element, a two-dimensional electric transversely-moving table, a detector and a computer. A convergent spherical wave formed in the mode that quasi-parallel light emitted by the coherent light source passes through the convergent lens serves as illumination light of the to-be-tested optical element, the two-dimensional electric transversely-moving table is driven under control of the computer to move the to-be-tested optical element, diffraction spots generated when the to-be-tested optical element is at different positions are recorded through the detector at the position a certain distance behind the to-be-tested optical element, and complex-amplitude transmission rate functions of layers of the to-be-tested optical element and phase positions of the layers of the to-be-tested optical element are obtained through processing of the computer. The structure of the optical element can not be damaged in the measurement process.

Description

The apparatus and method of transmissive optical element layering phase imaging

Technical field

The present invention relates to the optical element of sandwich construction.Particularly a kind of apparatus and method of transmissive optical element layering phase imaging.

Background technology

The Typical Representative ' holography ' of realizing phase imaging with employing interference technique is (holography) corresponding, also has a corresponding measuring method in non-interferometric phase imaging field, is ' ptychography '.Its basic ideas were proposed by people such as Hoppe before and after 1970, by the people such as Fienup improve progressively grow up (referring to J.R.Fienup.Phase retrieval algorithms:a comparison[J], Appl.Opt., 1982,21 (15):

2758～2769）。The method is to use recorded object transmitted light far field intensity spectrum, by repeatedly iterating computing between frequency plane and object plane, and the actual distribution using the result of calculation restraining on object plane as object, thus obtain the phase information of object.

Within 2004, John Rodenburg proposes Ptychographic Iterative Engine (PIE), (referring to J.M.Rodenburg and H.M.L.Faulkner, A phase retrieval algorithm for shifting illumination[J], Appl.Phys.Lett., 2004,85 (20): 4795～4797).The diverging light that laser forms after small holes scans sample, records a series of scattering spot intensity I simultaneously _n(x, y).While carrying out phase bit recovery, first give one of object being measured initial guess value arbitrarily, and calculate this guess transmission light field of object and its Fourier transform, and then use the square root of be recorded to intensity to replace the amplitude of this frequency spectrum and retain its phase invariant, remake inverse transformation and upgrade the complex amplitude of object under test, so repeatedly by the frequency spectrum at all lighting positions records by along iterating computing.

2009, Maiden etc. have proposed Extended-PIE (ePIE) algorithm (referring to Andrew M.Maiden and John M.Rodenburg, An improved ptychographical phase retrieval algorithm for diffractive imaging, Ultramicroscopy, 2009,109:1256～1262).EPIE is as the improved PIE algorithm of one, on sample, gives respectively sample and illumination light initial guess illumination light the unknown in the situation that, in interative computation process, sample and illumination light upgraded simultaneously, recovers illumination light and sample distribution simultaneously.

Summary of the invention

The object of the invention is on the basis of ePIE algorithm, a kind of apparatus and method of transmissive optical element layering phase imaging are proposed, the Convergent Laser Beam that the quasi-parallel light that coherent source of the present invention sends forms after convergent lens is as the illumination light of optical element to be measured, under the control of computing machine, drive two-dimentional motorized precision translation stage to move optical element to be measured, and the diffraction pattern of optical element to be measured when the diverse location recorded with detector in a distance after optical element to be measured, process and obtain the complex amplitude transmittance function of each layer of optical element to be measured and the phase place of each layer by computing machine.And can not cause any destruction to the structure of optical element in measuring process.

Technical solution of the present invention is as follows:

A device for transmissive optical element layering phase imaging, its feature is: this device is made up of coherent source, beam expander, convergent lens, optical element to be measured, two-dimentional motorized precision translation stage, detector and computing machine, and the position relationship of said elements is as follows:

The wavelength sending along coherent source is that the light of λ becomes spherical wave successively after beam expander, convergent lens, this spherical wave illumination optical element to be measured, described optical element to be measured is placed on two-dimentional motorized precision translation stage and is scanning line by line perpendicular to optical path direction, described detector records the diffraction pattern of illumination light after optical element to be measured and distributes, described detector output terminal is connected with the input end of described computing machine, and the output terminal of computing machine is connected with the control end of described two-dimentional motorized precision translation stage.

Utilize said apparatus to realize the method for layering phase imaging to having the transmissive optical element of sandwich construction, its feature is that the method comprises the following steps:

1. optical element to be measured be placed on two-dimentional motorized precision translation stage and make it vertical with incident beam, optical element to be measured has sandwich construction, along direction of beam propagation, is defined as successively layer 1, layer 2, layer 3 ... layer N-1, layer N, the distance between layer 1 and layer 2 is Z ₁, the distance between layer 2 and layer 3 is Z ₂, by that analogy, the distance between layer N-1 and layer N is Z _n-1, the last one deck of optical element to be measured is Z apart from the distance of described detector _n, the distance between layer 1 and the focal length of described convergent lens (3) is Z ₀;

2. the two-dimentional motorized precision translation stage described in described computer control scans line by line the described optical element to be measured with sandwich construction in the plane perpendicular to direction of beam propagation, step-length is l, light transmission part, adjacent two scanning position places must have overlapping, overlapping area is preferably 2/3rds of hot spot, the position of the movement of optical element to be measured is by the matrix representation of the capable q row of p, in scanning process, when described optical element to be measured is during in the capable j row of i, the light distribution that described detector records diffraction pattern is I _i,j, the positive integer that wherein i is 1～p, the positive integer that j is 1～q, p, q represents respectively total line number and total columns of optical element scan matrix to be measured, I _i,jbe stored in computing machine with the capable n column matrix of m form, the hot spot after scanning obtains one group of hot spot data I after all having recorded _1,1, I _1,2... I _i,j..I _p,q;

3. utilize hot spot data to carry out the step of Phase Processing:

First computing machine treats the transmittance function of the every one deck of photometry element, comprises that amplitude transmittance and phase change amount provide a random conjecture value as initial value:

obj ¹=obj ²...=obj ³=E*exp(i*rand(a,b)*2π)，

Wherein: E is amplitude, rand (a, b) is for producing the stochastic matrix of the capable b row of a, a=m+ (p-1) * l, b=n+ (q-1) * l, wherein m, n are respectively the row, column of hot spot matrix, p, q are respectively respectively the row, column of scan matrix, and l is scanning step; The illumination light of locating along direction of beam propagation optical element ground floor to be measured (element surface) is illu ₁, provide a conjecture value as initial value:

${\mathrm{illu}}_1=E_1*\exp [-i*\frac{2\mathrm{\π}}{\mathrm{\λ}}*\sqrt{Z_0^2+r{(m,n)}^2}*\mathrm{hole}(m,n),$

Wherein: E ₁for amplitude, r (m, n) is the capable n column matrix of m, and the each point of presentation layer 1 is apart from the distance of optical axis, and hole (m, n) is the circular hole of the scope of restriction illumination light, and wherein m, n are respectively the row, column of hot spot matrix;

Each layer of complex amplitude of optical element to be measured and illumination light step of updating are:

(a) calculate optical element to be measured scanning position (i, j) locate illuminated rear hot spot distribute (i=1,2 ... p, j=1,2 ... q): get obj ¹, obj ²obj ⁿ1+ (i-1) * l capable capable to m+ (i-1) * l, 1+ (j-1) * l is listed as n+ (j-1) * l row, is designated as obj ¹ _i,j, obj ² _i,jobj ⁿ _i,j,

The transmission light field of layer 1 is E _{out_1}=illu ₁* obj ¹ _i,j, the transmission light field of layer 1 propagates into layer 2 place, according to the illumination light field distribution on angular spectra theory computation layer 2 surfaces

${\mathrm{illu}}_2=\underset{\&infin;}{\&Integral;\&Integral;}{A}_1(\frac{\mathrm{\&alpha;}}{\mathrm{\&lambda;}},\frac{\mathrm{\&beta;}}{\mathrm{\&lambda;}})\exp \left(\mathrm{<figure-callout\; id="2"\; label="i"\; filenames="HDA0000469389120000011.png"\; state="\{\{state\}\}">i</figure-callout>}\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}\sqrt{1-{\mathrm{\&alpha;}}^2-{\mathrm{\&beta;}}^2}{Z}_1\right)\exp \left[i2\mathrm{\&pi;}(\frac{\mathrm{\&alpha;}}{\mathrm{\&lambda;}}{x}_2+\frac{\mathrm{\&beta;}}{\mathrm{\&lambda;}}{y}_2)\right]d\frac{\mathrm{\&alpha;}}{\mathrm{\&lambda;}}d\frac{\mathrm{\&beta;}}{\mathrm{\&lambda;}}$

Wherein: for layer 1 transmitted light rink corner, place spectrum;

The transmission light field of layer 2 is E _{out_2}=illu ₂* obj ² _i,j, the transmission light field of layer 2 propagates into layer 3 place, according to the illumination light field distribution on angular spectra theory computation layer 3 surfaces

${\mathrm{illu}}_3=\underset{\&infin;}{\&Integral;\&Integral;}{A}_2(\frac{\mathrm{\&alpha;}}{\mathrm{\&lambda;}},\frac{\mathrm{\&beta;}}{\mathrm{\&lambda;}})\exp \left(\mathrm{<figure-callout\; id="2"\; label="i"\; filenames="HDA0000469389120000011.png"\; state="\{\{state\}\}">i</figure-callout>}\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}\sqrt{1-{\mathrm{\&alpha;}}^2-{\mathrm{\&beta;}}^2}{Z}_2\right)\exp \left[i2\mathrm{\&pi;}(\frac{\mathrm{\&alpha;}}{\mathrm{\&lambda;}}{x}_3+\frac{\mathrm{\&beta;}}{\mathrm{\&lambda;}}{y}_3)\right]d\frac{\mathrm{\&alpha;}}{\mathrm{\&lambda;}}d\frac{\mathrm{\&beta;}}{\mathrm{\&lambda;}}$

Wherein:

for layer 2 transmitted light rink corner, place spectrum;

Computation layer 4, layer 5 successively ... layer N place illumination light and transmission light field, be respectively illu ₄, illu ₅illu _n, E _{out_4}, E _{out_5}e _{out_N};

According to the COMPLEX AMPLITUDE at angular spectra theory calculating detector place

$E_{i,j}=\underset{\&infin;}{\&Integral;\&Integral;}{A}_N(\frac{\mathrm{\&alpha;}}{\mathrm{\&lambda;}},\frac{\mathrm{\&beta;}}{\mathrm{\&lambda;}})\exp \left(\mathrm{<figure-callout\; id="2"\; label="i"\; filenames="HDA0000469389120000011.png"\; state="\{\{state\}\}">i</figure-callout>}\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}\sqrt{1-{\mathrm{\&alpha;}}^2-{\mathrm{\&beta;}}^2}{Z}_N\right)\exp \left[i2\mathrm{\&pi;}(\frac{\mathrm{\&alpha;}}{\mathrm{\&lambda;}}{x}_{\mathrm{ccd}}+\frac{\mathrm{\&beta;}}{\mathrm{\&lambda;}}{y}_{\mathrm{ccd}})\right]d\frac{\mathrm{\&alpha;}}{\mathrm{\&lambda;}}d\frac{\mathrm{\&beta;}}{\mathrm{\&lambda;}}$

Wherein: for transmitted light rink corner, layer N place spectrum;

Calculate the now COMPLEX AMPLITUDE E at detector place _i,j=abs (E _i,j) exp (i φ _i,j), keep its phase invariant also with described diffractional field distribution I _i,jsquare root sqrt (I _i,j) replace its amplitude to become

E' _i,j=sqrt(I _i,j)exp(iφ _i,j)；

Calculate E' according to angular spectra theory again _i,jthe reverse layer N place outgoing wave function distribution E' that be propagated back to _i,j

${E^{\&prime;}}_{i,j}=\underset{\&infin;}{\&Integral;\&Integral;}{A}_{\mathrm{CCD}}(\frac{\mathrm{\&alpha;}}{\mathrm{\&lambda;}},\frac{\mathrm{\&beta;}}{\mathrm{\&lambda;}})\exp \left(\mathrm{<figure-callout\; id="2"\; label="i"\; filenames="HDA0000469389120000011.png"\; state="\{\{state\}\}">i</figure-callout>}\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}\sqrt{1-{\mathrm{\&alpha;}}^2-{\mathrm{\&beta;}}^2}{Z}_N\right)\exp \left[\mathrm{<figure-callout\; id="2"\; label="i"\; filenames="HDA0000469389120000011.png"\; state="\{\{state\}\}">i</figure-callout>}2\mathrm{\&pi;}(\frac{\mathrm{\&alpha;}}{\mathrm{\&lambda;}}x+\frac{\mathrm{\&beta;}}{\mathrm{\&lambda;}}y)\right]d\frac{\mathrm{\&alpha;}}{\mathrm{\&lambda;}}d\frac{\mathrm{\&beta;}}{\mathrm{\&lambda;}}$

Wherein,

for the E' of detector place _i,jangular spectrum;

By makeing the poor change amount Δ E that tries to achieve outgoing wave function _i,j=E' _i,j-E _{out_N}; Treat respectively photometry element layer N place complex amplitude

illuN upgrades by following formula with illumination light, obtains newly

and illu' _nbe respectively:

${\mathrm{obj}}_{i,j}^{N^{\&prime;}}={\mathrm{obj}}_{i,j}^N+\frac{{\mathrm{illu}}_N^{*}}{|{\mathrm{illu}}_N{{|}^2}_{\max }}\&times;{\mathrm{\&beta;\&Delta;E}}_{i,j},$

${{\mathrm{illu}}^{\&prime;}}_N={\mathrm{illu}}_N+\frac{{\mathrm{obj}}_{i,j}^{N*}}{{{\left|\mathrm{ob}{j}_{i,j}^N\right|}^2}_{\max }}\&times;\mathrm{\&beta;\&Delta;}{E}_{i,j},$

Wherein, | illu _n| and

respectively illu _nwith

mould,

with respectively illu _nwith

conjugation, β selects 0～1 constant, proportion is upgraded in reflection;

With

replace obj ⁿmiddle 1+ (i-1) * l is capable capable to m+ (i-1) * l, and 1+ (j-1) * l is listed as the value of n+ (j-1) * l row, upgrades obj ⁿ, the illumination light on layer N is to upgrade illumination light illu afterwards _n=illu' _n;

Calculate illu according to angular spectra theory _nthe reverse layer N-1 place outgoing wave function distribution E' that be propagated back to _i,j, ask the change amount Δ E of layer N-1 place outgoing wave function _i,j=E' _i,j-E _{out_N-1}, complex amplitude and illumination light are upgraded and obtain obj in the mode identical with layer N place ^n-1and illu _n-1;

Repeat above-mentioned steps upgrade successively a layer N-2, layer N-3 ... sample complex amplitude and the illumination light at layer 2, layer 1 place distribute;

(b) j=j+1, returns to step (a) and continues to calculate, until j is taken to q;

(c) j=1, i=i+1, returns to step (a) and continues to calculate, until i is taken to p;

(d) error of calculation: error E _rror=∑ (I _i,j-E _i,j) ², and judge:

Work as error E _rrorapproach at 0 o'clock, enter step (e), otherwise, step (a) returned to;

(e) finish, finally obtain

be respectively optical element layer 1 to be measured, layer 2 ... layer N place complex amplitude amplitude transmittance function, for the phase place at each layer of place of optical element to be measured, each layer of imaging of optical element to be measured and phase measurement are realized.

Technique effect of the present invention is as follows:

The significant advantage of the present invention is the apparatus and method that proposed a kind of transmissive optical element layering phase imaging, the Convergent Laser Beam that the quasi-parallel light that coherent source of the present invention sends forms after convergent lens is as the illumination light of optical element to be measured, under the control of computing machine, drive two-dimentional motorized precision translation stage to move optical element to be measured, and after optical element to be measured, the diffraction pattern of optical element to be measured when the diverse location recorded with detector in a distance, processed and obtained the complex amplitude transmittance function of each layer of optical element to be measured and the phase place of each layer by computing machine.And can not cause any destruction to the structure of optical element in measuring process.

The structure that the present invention is specially adapted to change the transmission-type element with sandwich construction needs again the information separated of every layer occasion out.

Accompanying drawing explanation

Fig. 1 is the index path of the device of transmissive optical element layering phase imaging of the present invention.

Embodiment

Below in conjunction with embodiment and accompanying drawing, the invention will be further described, but should not limit the scope of the invention with this.

Embodiment:

First refer to Fig. 1, Fig. 1 is the index path of the device of transmissive optical element layering phase imaging of the present invention.As seen from the figure, the device of transmissive optical element layering phase imaging of the present invention is made up of coherent source 1, beam expander 2, convergent lens 3, optical element to be measured 4, two-dimentional motorized precision translation stage 5, detector 6, computing machine 7, and the position relationship of said elements is as follows:

The wavelength sending along coherent source 1 is that the light of λ becomes spherical wave successively after beam expander 2, convergent lens 3, spherical wave illumination optical element 4 to be measured, described optical element to be measured 4 is placed on two-dimentional motorized precision translation stage 5 and is scanning line by line perpendicular to optical path direction, detector 6 records the diffraction pattern of illumination light after optical element to be measured and distributes, detector 6 output terminals are connected with the input end of described computing machine 7, and the output terminal of computing machine 7 is connected with the control end of described two-dimentional motorized precision translation stage 5.

The light source 1 using in the embodiment of the present invention is He-Ne solid state laser, and optical maser wavelength is 632.8nm.

In the embodiment of the present invention, the movement matrix of optical element to be measured is 10 row × 10 row, and moving step length is 0.222mm(30 pixel), optical element to be measured has three-decker.

Described lens 3 are in order to convert directional light to spherical wave, and this embodiment lens used are the biconvex lens of focal length 1535mm.

Described detector 6 is for being ccd detector, and resolution is 2048pixel × 2048pixel, and each pixel length of side is 7.4 μ m, and the higher imaging of resolution is more accurate.

Described control computing machine 7 objects are for to control precision in moving this embodiment of translation stage 5(of electricity two dimension be 0.001mm by accurate) movement control the movement of optical element to be measured, realize the scanning of illumination light to sample.

The course of work of the present embodiment is:

1. optical element 4 to be measured be placed on two-dimentional motorized precision translation stage 5 and make it vertical with incident beam, the present embodiment optical element to be measured has three-decker, and along direction of beam propagation, the distance being defined as successively between layer 1, layer 2,3 layer 1, layer and layer 2 is Z ₁, the distance between layer 2 and layer 3 is Z ₂, Z ₁=Z ₂=5mm, the distance Z of the last one deck range finder of optical element to be measured ₃=77.126mm, the distance Z between layer 1 and the focal length of lens (3) ₀≈ 15mm;

2. the described described two-dimentional motorized precision translation stage 5 of computing machine 7 control scans line by line the described optical element to be measured 4 with sandwich construction in the plane perpendicular to direction of beam propagation, step-length is 0.222mm, light transmission part, adjacent two scanning position places must have overlapping, overlapping area is preferably 2/3rds of hot spot, the matrix representation that the position of the movement of optical element 4 to be measured is listed as by 10 row 10, in scanning process, when optical element 4 to be measured is during in the capable j row of i, the light distribution that described detector 6 records diffraction pattern is I _i,j, the positive integer that wherein i is 1～10, the positive integer that j is 1～10, I _i,jbe stored in computing machine 7 with 2048 row 2048 column matrix forms, the hot spot after scanning obtains one group of hot spot data I after all having recorded _1,1, I _1,2... I _i,j..I _10,10;

3. utilize hot spot data to carry out the step of Phase Processing:

First computing machine 7 treats the transmittance function of the every one deck of photometry element, comprises that amplitude transmittance and phase change amount provide a random conjecture value as initial value:

obj ¹=obj ²...=obj ³=E*exp(i*rand(a,b)*2π)，

Wherein: E is amplitude, rand (a, b) for producing the stochastic matrix of the capable b row of a, a=2048+ (10-1) * 30=2318, b=2048+ (10-1) * 30=2318, the illumination light of locating along direction of beam propagation optical element ground floor to be measured (element surface) is for providing a conjecture value illu ₁, illu ₁more approach actual value, speed of convergence is faster, and finding the illumination light on sample is here spherical wave, therefore:

$\mathrm{ill}{u}_1=E_1*\exp [-i*\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}*\sqrt{Z_0^2+{r\left(\mathrm{2048,2048}\right)}^2}]*\mathrm{hole}\left(\mathrm{2048,2048}\right),$

Wherein: E ₁for amplitude, r (2048,2048) is 2048 row 2048 column matrix, and the each point of presentation layer 1 is apart from the distance of optical axis, and hole (2048,2048) limits the scope of illumination light;

(a) calculate optical element to be measured scanning position (i, j) locate illuminated rear hot spot distribute (i=1,2 ... 10, j=1,2 ... 10): first get obj ¹, obj ², obj ³1+ (i-1) * 30 row to m+ (i-1) * 30 row, 1+ (j-1) * 30 row are listed as to n+ (j-1) * 30, are designated as obj ¹ _i,j, obj ² _i,j, obj ³ _i,j,

Each layer of place's width complex amplitude of optical element to be measured and illumination light step of updating are:

The transmission light field of layer 1 is E _{out_1}=illu ₁* obj ¹ _i,j, the transmission light field of layer 1 propagates into layer 2 place, according to the illumination light field distribution on angular spectra theory computation layer 2 surfaces

${\mathrm{<figure-callout\; id="2"\; label="illu"\; filenames="HDA0000469389120000011.png"\; state="\{\{state\}\}">illu</figure-callout>}}_2=\underset{\&infin;}{\&Integral;\&Integral;}{A}_1(\frac{\mathrm{\&alpha;}}{\mathrm{\&lambda;}},\frac{\mathrm{\&beta;}}{\mathrm{\&lambda;}})\exp \left(\mathrm{<figure-callout\; id="2"\; label="i"\; filenames="HDA0000469389120000011.png"\; state="\{\{state\}\}">i</figure-callout>}\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}\sqrt{1-{\mathrm{\&alpha;}}^2-{\mathrm{\&beta;}}^2}{Z}_1\right)\exp \left[\mathrm{<figure-callout\; id="2"\; label="i"\; filenames="HDA0000469389120000011.png"\; state="\{\{state\}\}">i</figure-callout>}2\mathrm{\&pi;}(\frac{\mathrm{\&alpha;}}{\mathrm{\&lambda;}}{x}_2+\frac{\mathrm{\&beta;}}{\mathrm{\&lambda;}}{y}_2)\right]d\frac{\mathrm{\&alpha;}}{\mathrm{\&lambda;}}d\frac{\mathrm{\&beta;}}{\mathrm{\&lambda;}}$

Wherein: for layer 1 transmitted light rink corner, place spectrum;

The transmission light field of layer 2 is E _{out_2}=illu ₂* obj ² _i,j, the transmission light field of layer 2 propagates into layer 3 place, according to the illumination light field distribution on angular spectra theory computation layer 3 surfaces

${\mathrm{<figure-callout\; id="3"\; label="illu"\; filenames="HDA0000469389120000011.png"\; state="\{\{state\}\}">illu</figure-callout>}}_3=\underset{\&infin;}{\&Integral;\&Integral;}{A}_2(\frac{\mathrm{\&alpha;}}{\mathrm{\&lambda;}},\frac{\mathrm{\&beta;}}{\mathrm{\&lambda;}})\exp \left(\mathrm{<figure-callout\; id="2"\; label="i"\; filenames="HDA0000469389120000011.png"\; state="\{\{state\}\}">i</figure-callout>}\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}\sqrt{1-{\mathrm{\&alpha;}}^2-{\mathrm{\&beta;}}^2}{Z}_2\right)\exp \left[\mathrm{<figure-callout\; id="2"\; label="i"\; filenames="HDA0000469389120000011.png"\; state="\{\{state\}\}">i</figure-callout>}2\mathrm{\&pi;}(\frac{\mathrm{\&alpha;}}{\mathrm{\&lambda;}}{x}_3+\frac{\mathrm{\&beta;}}{\mathrm{\&lambda;}}{y}_3)\right]d\frac{\mathrm{\&alpha;}}{\mathrm{\&lambda;}}d\frac{\mathrm{\&beta;}}{\mathrm{\&lambda;}}$

Wherein:

for layer 2 transmitted light rink corner, place spectrum;

The transmission light field of layer 3 is E _{out_3}=illu ₃* obj ³ _i,j, the transmission light field of layer 3 propagates into CCD place, calculates the illumination light field distribution of CCD place according to angular spectra theory

$E_{i,j}=\underset{\&infin;}{\&Integral;\&Integral;}{A}_N(\frac{\mathrm{\&alpha;}}{\mathrm{\&lambda;}},\frac{\mathrm{\&beta;}}{\mathrm{\&lambda;}})\exp \left(\mathrm{<figure-callout\; id="2"\; label="i"\; filenames="HDA0000469389120000011.png"\; state="\{\{state\}\}">i</figure-callout>}\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}\sqrt{1-{\mathrm{\&alpha;}}^2-{\mathrm{\&beta;}}^2}{Z}_N\right)\exp \left[\mathrm{<figure-callout\; id="2"\; label="i"\; filenames="HDA0000469389120000011.png"\; state="\{\{state\}\}">i</figure-callout>}2\mathrm{\&pi;}(\frac{\mathrm{\&alpha;}}{\mathrm{\&lambda;}}{x}_{\mathrm{ccd}}+\frac{\mathrm{\&beta;}}{\mathrm{\&lambda;}}{y}_{\mathrm{ccd}})\right]d\frac{\mathrm{\&alpha;}}{\mathrm{\&lambda;}}d\frac{\mathrm{\&beta;}}{\mathrm{\&lambda;}}$

Wherein:

for layer 3 transmitted light rink corner, place spectrum;

Calculate the now COMPLEX AMPLITUDE E at detector place _i,j=abs (E _i,j) exp (i φ _i,j), keep its phase invariant also with described diffractional field distribution I _i,jsquare root sqrt (I _i,j) replace its amplitude to become

E' _i,j=sqrt(I _i,j)exp(iφ _i,j)；

Calculate E' according to angular spectra theory again _i,jthe reverse layer N place outgoing wave function distribution E' that be propagated back to _i,j

${E^{\&prime;}}_{i,j}=\underset{\&infin;}{\&Integral;\&Integral;}{A}_{\mathrm{CCD}}(\frac{\mathrm{\&alpha;}}{\mathrm{\&lambda;}},\frac{\mathrm{\&beta;}}{\mathrm{\&lambda;}})\exp \left(\mathrm{<figure-callout\; id="2"\; label="i"\; filenames="HDA0000469389120000011.png"\; state="\{\{state\}\}">i</figure-callout>}\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}\sqrt{1-{\mathrm{\&alpha;}}^2-{\mathrm{\&beta;}}^2}{Z}_N\right)\exp \left[\mathrm{<figure-callout\; id="2"\; label="i"\; filenames="HDA0000469389120000011.png"\; state="\{\{state\}\}">i</figure-callout>}2\mathrm{\&pi;}(\frac{\mathrm{\&alpha;}}{\mathrm{\&lambda;}}x+\frac{\mathrm{\&beta;}}{\mathrm{\&lambda;}}y)\right]d\frac{\mathrm{\&alpha;}}{\mathrm{\&lambda;}}d\frac{\mathrm{\&beta;}}{\mathrm{\&lambda;}}$

Wherein, for the E' of detector place _i,jangular spectrum;

By makeing the poor change amount Δ E that tries to achieve outgoing wave function _i,j=E' _i,j-E _{out_N}; Treat respectively the photometry element layer 3 complex amplitude obj of place ³ _i,jwith illumination light illu ₃upgrade by following formula, obtain obj newly ³' _i,jand illu' ₃be respectively:

${\mathrm{obj}}_{i,j}^{N^{\&prime;}}={\mathrm{obj}}_{i,j}^N+\frac{{\mathrm{illu}}_N^{*}}{|{\mathrm{illu}}_N{{|}^2}_{\max }}\&times;{\mathrm{\&beta;\&Delta;E}}_{i,j},$

${{\mathrm{illu}}^{\&prime;}}_N={\mathrm{illu}}_N+\frac{{\mathrm{obj}}_{i,j}^{N*}}{{{\left|\mathrm{ob}{j}_{i,j}^N\right|}^2}_{\max }}\&times;\mathrm{\&beta;\&Delta;}{E}_{i,j},$

Wherein, illu ₃with

respectively illu ₃with mould,

and obj * ^3* _i,jrespectively illu3 and obj ³ _i,jconjugation, β selects 0～1 constant, proportion is upgraded in reflection;

With

replace obj ³middle 1+ (i-1) * 30 row are to 2048+ (i-1) * 30 row, and 1+ (j-1) * 30 row, to the value at 2048+ (j-1) * 30 row places, upgrade obj ³, the illumination light on layer 3 is the illumination light illu after upgrading ₃=illu' ₃;

Calculate illu according to angular spectra theory ₃the reverse layer 2 place's outgoing wave function distribution E' that are propagated back to _i,j, ask layer 2 place's outgoing wave function change amount Δ E _i,j=E' _i,j-E _{out_2}, complex amplitude is upgraded and obtains obj in the mode identical with layer 3 place with illumination light ²and illu ₂;

Calculate illu according to angular spectra theory ₂the reverse layer 1 place's outgoing wave function distribution E' that be propagated back to _i,j, ask layer 1 place's outgoing wave function change amount Δ E _i,j=E' _i,j-E _{out_1}, complex amplitude is upgraded and obtains obj in the mode identical with layer 3 place with illumination light ¹and illu ₁;

(b) j=j+1, returns to step (a) and continues to calculate, until j is taken to 10;

(c) j=1, i=i+1, returns to step (a) and continues to calculate, until i is taken to 10;

(d) error of calculation: error E _rror=∑ (I _i,j-E _i,j) ², and judge:

Work as error E _rrorapproach at 0 o'clock, enter step (e), otherwise, step (a) returned to;

(e) finish, finally obtain

be respectively optical element layer 1 to be measured, layer 2, layer 3 place's complex amplitude amplitude transmittance function,

for the phase place at each layer of place of optical element to be measured, each layer of imaging of sample and phase measurement are realized.

Experiment shows, the Convergent Laser Beam that the quasi-parallel light that the present invention sends coherent source forms after convergent lens is as the illumination light of optical element to be measured, under the control of computing machine, drive two-dimentional motorized precision translation stage to move optical element to be measured, and after optical element to be measured, the diffraction pattern of optical element to be measured when the diverse location recorded with detector in a distance, processed and obtained the complex amplitude transmittance function of each layer of optical element to be measured and the phase place of each layer by computing machine.And can not cause any destruction to the structure of optical element in measuring process.

The structure that the present invention is specially adapted to change the transmission-type element with sandwich construction needs again the information separated of every layer situation out.

Claims (2)

1. the device of a transmissive optical element layering phase imaging, it is characterized in that: this device is made up of coherent source (1), beam expander (2), convergent lens (3), optical element to be measured (4), two-dimentional motorized precision translation stage (5), detector (6), computing machine (7), and the position relationship of said elements is as follows:

The light that the wavelength sending along coherent source (1) is λ passes through beam expander (2) successively, convergent lens becomes spherical wave after (3), spherical wave illumination optical element to be measured (4), described optical element to be measured (4) is placed in two-dimentional motorized precision translation stage (5) above and is scanning line by line perpendicular to optical path direction, described detector (6) records the diffraction pattern of illumination light after optical element to be measured and distributes, described detector (6) output terminal is connected with the input end of described computing machine (7), the output terminal of computing machine (7) is connected with the control end of described two-dimentional motorized precision translation stage (5).

2. utilize device described in claim 1 to realize the method for layering phase imaging to thering is the transmissive optical element of sandwich construction, it is characterized in that the method comprises the following steps:

1. optical element to be measured (4) is placed in to two-dimentional motorized precision translation stage (5) and goes up and make it vertical with incident beam, optical element to be measured has sandwich construction, along direction of beam propagation, be defined as successively layer 1, layer 2, layer 3 ... layer N-1, layer N, the distance between layer 1 and layer 2 is Z ₁, the distance between layer 2 and layer 3 is Z ₂, by that analogy, the distance between layer N-1 and layer N is Z _n-1, the last one deck of optical element to be measured is Z apart from the distance of described detector _n, the distance between layer 1 and the focal length of described convergent lens (3) is Z ₀;

2. the described described two-dimentional motorized precision translation stage (5) of computing machine (7) control scans line by line the described optical element to be measured (4) with sandwich construction in the plane perpendicular to direction of beam propagation, step-length is l, light transmission part, adjacent two scanning position places must have overlapping, overlapping area is preferably 2/3rds of hot spot, the position of the movement of optical element to be measured (4) is by the matrix representation of the capable q row of p, in scanning process, when described optical element to be measured (4) is during in the capable j row of i, the light distribution that described detector (6) records diffraction pattern is I _i,j, the positive integer that wherein i is 1～p, the positive integer that j is 1～q, p, q represents respectively total line number and total columns of optical element to be measured (4) scan matrix, I _i,jbe stored in computing machine (7) with the capable n column matrix of m form, the hot spot after scanning obtains one group of hot spot data I after all having recorded _1,1, I _1,2... I _i,j..I _p,q,

3. utilize hot spot data to carry out the step of Phase Processing:

Computing machine (7) is first treated the transmittance function of the every one deck of photometry element, comprises that amplitude transmittance and phase change amount provide a random conjecture value as initial value:

obj ¹=obj ²...=obj ³=E*exp(i*rand(a,b)*2π)，

Wherein: E is amplitude, rand (a, b) is for producing the stochastic matrix of the capable b row of a, a=m+ (p-1) * l, b=n+ (q-1) * l, wherein m, n are respectively the row, column of hot spot matrix, p, q are respectively respectively the row, column of scan matrix, and l is scanning step; The illumination light of locating along direction of beam propagation optical element ground floor to be measured (element surface) is illu ₁, provide a conjecture value as initial value:

${\mathrm{illu}}_1=E_1*\exp [-i*\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}*\sqrt{Z_0^2+{r(m,n)}^2}]*\mathrm{hole}(m,n)$

Wherein: E ₁for amplitude, r (m, n) is the capable n column matrix of m, and the each point of presentation layer 1 is apart from the distance of optical axis, and hole (m, n) is the circular hole of the scope of restriction illumination light, and wherein m, n are respectively the row, column of hot spot matrix;

Each layer of complex amplitude of optical element to be measured and illumination light step of updating are:

(a) calculate optical element to be measured scanning position (i, j) locate illuminated rear hot spot distribute (i=1,2 ... p, j=1,2 ... q): get obj ¹, obj ²obj ⁿ1+ (i-1) * l capable capable to m+ (i-1) * l, 1+ (j-1) * l is listed as n+ (j-1) * l row, is designated as obj ¹ _i,j, obj ² _i,jobj ⁿ _i,j,

The transmission light field of layer 1 is E _{out_1}=illu ₁* obj ¹ _i,j, the transmission light field of layer 1 propagates into layer 2 place, according to the illumination light field distribution on angular spectra theory computation layer 2 surfaces

${\mathrm{illu}}_2=\underset{\&infin;}{\&Integral;\&Integral;}{A}_1(\frac{\mathrm{\&alpha;}}{\mathrm{\&lambda;}},\frac{\mathrm{\&beta;}}{\mathrm{\&lambda;}})\exp \left(i\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}\sqrt{1-{\mathrm{\&alpha;}}^2-{\mathrm{\&beta;}}^2}{Z}_1\right)\exp \left[i2\mathrm{\&pi;}(\frac{\mathrm{\&alpha;}}{\mathrm{\&lambda;}}{x}_2+\frac{\mathrm{\&beta;}}{\mathrm{\&lambda;}}{y}_2)\right]d\frac{\mathrm{\&alpha;}}{\mathrm{\&lambda;}}d\frac{\mathrm{\&beta;}}{\mathrm{\&lambda;}}$

Wherein:

for layer 1 transmitted light rink corner, place spectrum;

The transmission light field of layer 2 is E _{out_2}=illu ₂* obj ² _i,j, the transmission light field of layer 2 propagates into layer 3 place, according to the illumination light field distribution on angular spectra theory computation layer 3 surfaces

${\mathrm{illu}}_3=\underset{\&infin;}{\&Integral;\&Integral;}{A}_2(\frac{\mathrm{\&alpha;}}{\mathrm{\&lambda;}},\frac{\mathrm{\&beta;}}{\mathrm{\&lambda;}})\exp \left(i\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}\sqrt{1-{\mathrm{\&alpha;}}^2-{\mathrm{\&beta;}}^2}{Z}_2\right)\exp \left[i2\mathrm{\&pi;}(\frac{\mathrm{\&alpha;}}{\mathrm{\&lambda;}}{x}_3+\frac{\mathrm{\&beta;}}{\mathrm{\&lambda;}}{y}_3)\right]d\frac{\mathrm{\&alpha;}}{\mathrm{\&lambda;}}d\frac{\mathrm{\&beta;}}{\mathrm{\&lambda;}}$

Wherein:

for layer 2 transmitted light rink corner, place spectrum;

Computation layer 4, layer 5 successively ... layer N place illumination light and transmission light field, be respectively illu ₄, illu ₅illu _n, E _{out_4}, E _{out_5}e _{out_N};

According to the COMPLEX AMPLITUDE at angular spectra theory calculating detector place

$E_{i,j}=\underset{\&infin;}{\&Integral;\&Integral;}{A}_N(\frac{\mathrm{\&alpha;}}{\mathrm{\&lambda;}},\frac{\mathrm{\&beta;}}{\mathrm{\&lambda;}})\exp \left(i\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}\sqrt{1-{\mathrm{\&alpha;}}^2-{\mathrm{\&beta;}}^2}{Z}_N\right)\exp \left[i2\mathrm{\&pi;}(\frac{\mathrm{\&alpha;}}{\mathrm{\&lambda;}}{x}_{\mathrm{ccd}}+\frac{\mathrm{\&beta;}}{\mathrm{\&lambda;}}{y}_{\mathrm{ccd}})\right]d\frac{\mathrm{\&alpha;}}{\mathrm{\&lambda;}}d\frac{\mathrm{\&beta;}}{\mathrm{\&lambda;}}$

Wherein:

for transmitted light rink corner, layer N place spectrum;

Calculate the now COMPLEX AMPLITUDE E at detector place _i,j=abs (E _i,j) exp (i φ _i,j), keep its phase invariant also with described diffractional field distribution I _i,jsquare root sqrt (I _i,j) replace its amplitude to become

E' _i,j=sqrt(I _i,j)exp(iφ _i,j)；

Calculate E' according to angular spectra theory again _{i, j}the reverse layer N place outgoing wave function distribution E' that be propagated back to _{i, j}

${E^{\&prime;}}_{i,j}=\underset{\&infin;}{\&Integral;\&Integral;}{A}_{\mathrm{CCD}}(\frac{\mathrm{\&alpha;}}{\mathrm{\&lambda;}},\frac{\mathrm{\&beta;}}{\mathrm{\&lambda;}})\exp \left(i\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}\sqrt{1-{\mathrm{\&alpha;}}^2-{\mathrm{\&beta;}}^2}{Z}_N\right)\exp \left[i2\mathrm{\&pi;}(\frac{\mathrm{\&alpha;}}{\mathrm{\&lambda;}}x+\frac{\mathrm{\&beta;}}{\mathrm{\&lambda;}}y)\right]d\frac{\mathrm{\&alpha;}}{\mathrm{\&lambda;}}d\frac{\mathrm{\&beta;}}{\mathrm{\&lambda;}}$

Wherein,

for the E' of detector place _i,jangular spectrum;

By makeing the poor change amount Δ E that tries to achieve outgoing wave function _i,j=E' _i,j-E _{out_N}; Treat respectively photometry element layer N place complex amplitude

with illumination light illu _nupgrade by following formula, obtain newly

' and illu' _nbe respectively:

${\mathrm{obj}}_{i,j}^{N^{\&prime;}}={\mathrm{obj}}_{i,j}^N+\frac{{\mathrm{illu}}_N^{*}}{|{\mathrm{illu}}_N{{|}^2}_{\max }}\&times;{\mathrm{\&beta;\&Delta;E}}_{i,j},$

${{\mathrm{illu}}^{\&prime;}}_N={\mathrm{illu}}_N+\frac{{\mathrm{obj}}_{i,j}^{N*}}{{{\left|\mathrm{ob}{j}_{i,j}^N\right|}^2}_{\max }}\&times;\mathrm{\&beta;\&Delta;}{E}_{i,j},$

Wherein, | illu _n| and

be respectively illuN and

mould,

with

respectively illu _nwith

conjugation, β selects 0～1 constant, proportion is upgraded in reflection;

With replace obj ⁿmiddle 1+ (i-1) * l is capable capable to m+ (i-1) * l, and 1+ (j-1) * l is listed as the value of n+ (j-1) * l row, upgrades obj ⁿ, the illumination light on layer N is to upgrade illumination light illu afterwards _n=illu' _n;

Calculate illu according to angular spectra theory _nthe reverse layer N-1 place outgoing wave function distribution E' that be propagated back to _i,j, ask the change amount Δ E of layer N-1 place outgoing wave function _i,j=E' _i,j-E _{out_N-1}, complex amplitude and illumination light are upgraded and obtain obj in the mode identical with layer N place ^n-1and illu _n-1;

Repeat above-mentioned steps upgrade successively a layer N-2, layer N-3 ... sample complex amplitude and the illumination light at layer 2, layer 1 place distribute;

(b) j=j+1, returns to step (a) and continues to calculate, until j is taken to q;

(c) j=1, i=i+1, returns to step (a) and continues to calculate, until i is taken to p;

(d) error of calculation: error E _rror=∑ (I _i,j-E _i,j) ², and judge:

Work as error E _rrorapproach at 0 o'clock, enter step (e), otherwise, step (a) returned to;

(e) finish, finally obtain

be respectively optical element layer to be measured 1 layer 2 ... layer N place complex amplitude amplitude transmittance function,

for the phase place at each layer of place of optical element to be measured, each layer of imaging of optical element to be measured and phase measurement are realized.

Images