CN103837325B - The apparatus and method of transmissive optical element layering phase imaging - Google Patents

The apparatus and method of transmissive optical element layering phase imaging Download PDF

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CN103837325B
CN103837325B CN201410064172.5A CN201410064172A CN103837325B CN 103837325 B CN103837325 B CN 103837325B CN 201410064172 A CN201410064172 A CN 201410064172A CN 103837325 B CN103837325 B CN 103837325B
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illu
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CN103837325A (en
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王海燕
刘诚
潘兴臣
孙美智
程君
朱健强
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Shanghai Institute of Optics and Fine Mechanics of CAS
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Abstract

A kind of apparatus and method of transmission-type element layering phase imaging, this device is by coherent source, beam expander, collecting lens, optical element to be measured, two dimension motorized precision translation stage, detector and computer composition, the Convergent Laser Beam that the quasi-parallel light that coherent source of the present invention sends is formed after collecting lens is as the illumination light of optical element to be measured, two dimension motorized precision translation stage is driven to move optical element to be measured under control of the computer, and a distance detector records the optical element to be measured diffraction pattern when diverse location after optical element to be measured, the complex amplitude transmittance function of each layer of optical element to be measured and the phase place of each layer is obtained by computer disposal. and the structure of optical element will not be caused any destruction by 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 multiple structure. The particularly apparatus and method of a kind of transmissive optical element layering phase imaging.
Background technology
Corresponding with the Typical Representative ' holography ' (holography) that employing interference technique realizes phase imaging, there is also a corresponding measuring method in non-interfering phase imaging field, be ' ptychography '. Its basic ideas were proposed by Hoppe et al. before and after 1970, progressively grow up (referring to J.R.Fienup.Phaseretrievalalgorithms:acomparison [J] by improving of Fienup et al., Appl.Opt., 1982,21 (15):
2758��2769). The method is by the object transmission light far field intensity spectrum recorded, by repeatedly iterating computing between frequency plane and object plane, using actual distribution as object of the result of calculation that restrains on object plane, thus obtaining the phase information of object.
Within 2004, JohnRodenburg proposes PtychographicIterativeEngine (PIE), (referring to J.M.RodenburgandH.M.L.Faulkner, Aphaseretrievalalgorithmforshiftingillumination [J], Appl.Phys.Lett., 2004,85 (20): 4795��4797). Sample is scanned by the diverging light that laser is formed after small holes, records a series of scattering speckle intensity I simultaneouslyn(x, y). First give object being measured one arbitrary initial guess value when carrying out phase recovery, and calculate Transmission field and its Fourier transform of this guess object, and then the amplitude of this frequency spectrum is replaced with the square root of the intensity that recorded and retains its phase invariant, remake inverse transformation and update the complex amplitude of object under test, so repeatedly by the frequency spectrum at all lighting position records by along carrying out iterating computing.
2009, Maiden etc. propose Extended-PIE (ePIE) algorithm (referring to AndrewM.MaidenandJohnM.Rodenburg, Animprovedptychographicalphaseretrievalalgorithmfordiffr activeimaging, Ultramicroscopy, 2009,109:1256��1262).EPIE is as the PIE algorithm of a kind of improvement, and on sample, illumination light gives sample and illumination light initial guess unknown respectively, in interative computation process, sample and illumination light is updated simultaneously, recovers illumination light and sample distribution simultaneously.
Summary of the invention
It is an object of the invention on the basis of ePIE algorithm, the apparatus and method of a kind 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 is formed after collecting lens is as the illumination light of optical element to be measured, two dimension motorized precision translation stage is driven to move optical element to be measured under control of the computer, and a distance detector records the optical element to be measured diffraction pattern when diverse location after optical element to be measured, the complex amplitude transmittance function of each layer of optical element to be measured and the phase place of each layer is obtained by computer disposal. and the structure of optical element will not be caused any destruction by measurement process.
The technical solution of the present invention is as follows:
A kind of device of transmissive optical element layering phase imaging, it is characterized in that: this device is made up of coherent source, beam expander, collecting lens, optical element to be measured, two dimension motorized precision translation stage, detector and computer, and the position relationship of said elements is as follows:
The light that wavelength is �� sent along coherent source becomes spherical wave after sequentially passing through beam expander, collecting lens, this spherical wave illumination optical element to be measured, described optical element to be measured is placed on two dimension motorized precision translation stage and scans line by line being perpendicular to optical path direction, the diffraction pattern distribution after optical element to be measured of the described detector record illumination light, described detector outfan is connected with the input of described computer, and the outfan of computer is connected with the control end of described two-dimentional motorized precision translation stage.
Utilizing the method that the transmissive optical element with multiple structure is realized layering phase imaging by said apparatus, it is characterized in that the method comprises the following steps:
1. being placed in by optical element to be measured on two dimension motorized precision translation stage and so as to vertical with incident beam, optical element to be measured has multiple structure, along direction of beam propagation, is defined as layer 1, layer 2, layer 3 successively ... layer N-1, layer N, and the distance between layer 1 and layer 2 is Z1, the distance between layer 2 and layer 3 is Z2, by that analogy, the distance between layer N-1 and layer N is ZN-1, last layer of optical element to be measured is Z apart from the distance of described detectorN, the distance between the focal length of layer 1 and described collecting lens (3) is Z0;
2. described computer controls described two-dimentional motorized precision translation stage makes the described optical element to be measured with multiple structure scan line by line in the plane being perpendicular to direction of beam propagation, step-length is l, must there be overlap adjacent two scanning light transmission parts, position, overlapping area is preferably 2/3rds of hot spot, the matrix that the position of the movement of optical element to be measured is arranged by p row q represents, in scanning process, when described optical element to be measured is in i row j row, the light distribution of described detector record diffraction pattern is Ii,j, wherein i is the positive integer of 1��p, and j is the positive integer of 1��q, p, and q represents total line number and total columns, the I of optical element scan matrix to be measured respectivelyi,jStore in a computer with m row n column matrix formation, after the hot spot after scanning has all recorded, obtain one group of hot spot data I1,1, I1,2,...Ii,j,..Ip,q;
3. hot spot data are utilized to carry out the step of Phase Processing:
First computer treats the transmittance function of photometry element each layer, provides a random conjecture value as initial value including amplitude transmittance and phase change amount:
obj1=obj2...=obj3=E*exp (i*rand (a, b) * 2 ��),
Wherein: E is amplitude, (a, b) for producing the random matrix of a row b row for rand, a=m+ (p-1) * l, b=n+ (q-1) * l, the wherein row, column of m, n respectively hot spot matrix, the row, column of p, q difference respectively scan matrix, l is scanning step;Illumination light along direction of beam propagation optical element ground floor (element surface) to be measured place is illu1, it is provided that a conjecture value is as initial value:
illu 1 = E 1 * exp [ - i * 2 π λ * Z 0 2 + r ( m , n ) 2 * hole ( m , n ) ,
Wherein: E1For amplitude, (m, n) for m row n column matrix, represents the distance of layer 1 each distance optical axis to r, and (m, n) for the circular hole of the scope of restriction illumination light, the wherein row, column of m, n respectively hot spot matrix for hole;
The each layer complex amplitude of optical element to be measured and illumination light update step:
(a) calculate optical element to be measured scanning position (i, j) the illuminated rear hot spot in place distribution (i=1,2 ... p, j=1,2 ... q): take obj1��obj2����objN1+ (i-1) * l row to m+ (i-1) * l row, 1+ (j-1) * l arrange n+ (j-1) * l row, be designated as obj1 i,j��obj2 i,j����objN i,j,
The Transmission field of layer 1 is Eout_1=illu1*obj1 i,j, the Transmission field of layer 1 propagates layer 2 place, the illumination light field distribution according to angular spectra theory computation layer 2 surface
illu 2 = ∫ ∫ ∞ A 1 ( α λ , β λ ) exp ( i 2 π λ 1 - α 2 - β 2 Z 1 ) exp [ i 2 π ( α λ x 2 + β λ y 2 ) ] d α λ d β λ
Wherein:For layer 1 place Transmission field angular spectrum;
The Transmission field of layer 2 is Eout_2=illu2*obj2 i,j, the Transmission field of layer 2 propagates layer 3 place, the illumination light field distribution according to angular spectra theory computation layer 3 surface
illu 3 = ∫ ∫ ∞ A 2 ( α λ , β λ ) exp ( i 2 π λ 1 - α 2 - β 2 Z 2 ) exp [ i 2 π ( α λ x 3 + β λ y 3 ) ] d α λ d β λ
Wherein:For layer 2 place Transmission field angular spectrum;
Successively computation layer 4, layer 5 ... layer N place's illumination light and Transmission field, respectively illu4��illu5����illuN, Eout_4��Eout_5����Eout_N;
COMPLEX AMPLITUDE according to angular spectra theory calculating detector place
E i , j = ∫ ∫ ∞ A N ( α λ , β λ ) exp ( i 2 π λ 1 - α 2 - β 2 Z N ) exp [ i 2 π ( α λ x ccd + β λ y ccd ) ] d α λ d β λ
Wherein:For layer N place Transmission field angular spectrum;
Calculate the COMPLEX AMPLITUDE E obtaining now detector placei,j=abs(Ei,j)exp(i��i,j), keep its phase invariant and be distributed I with described diffractional fieldi,jSquare root sqrt (Ii,j) replace its amplitude to become
E'i,j=sqrt(Ii,j)exp(i��i,j);
E' is calculated further according to angular spectra theoryi,jThe reverse layer N place exit wave function that be propagated back to is distributed an E'i,j
E ′ i , j = ∫ ∫ ∞ A CCD ( α λ , β λ ) exp ( i 2 π λ 1 - α 2 - β 2 Z N ) exp [ i 2 π ( α λ x + β λ y ) ] d α λ d β λ
Wherein,For detector place E'i,jAngular spectrum;
The knots modification �� E of exit wave function is tried to achieve by doing differencei,j=E'i,j-Eout_N; Treat photometry element layer N place complex amplitude respectivelyIt is updated by following formula with illumination light illuN, obtains newlyAnd illu'NIt is respectively as follows:
obj i , j N ′ = obj i , j N + illu N * | illu N | 2 max × βΔE i , j ,
illu ′ N = illu N + obj i , j N * | ob j i , j N | 2 max × βΔ E i , j ,
Wherein, | illuN| withIt is illu respectivelyNWithMould,WithIt is illu respectivelyNWithConjugation, �� select 0��1 constant, reflection update proportion;
WithReplace objNMiddle 1+ (i-1) * l row is to m+ (i-1) * l row, and 1+ (j-1) * l arranges the value of n+ (j-1) * l row, updates objN, the illumination light on layer N is the illumination light illu after updatingN=illu'N;
Illu is calculated according to angular spectra theoryNThe reverse layer N-1 place exit wave function that be propagated back to is distributed an E'i,j, seek the knots modification �� E of layer N-1 place exit wave functioni,j=E'i,j-Eout_N-1, it is updated obtaining obj with illumination light in the way of identical with layer N place to complex amplitudeN-1And illuN-1;
Repeat the above steps update step N-2 successively, layer N-3 ... layer 2, the sample complex amplitude at layer 1 place and illumination light distribution;
B () j=j+1, returns step (a) and continues to calculate, until j takes to q;
C () j=1, i=i+1, returns step (a) and continues to calculate, until i takes to p;
D () calculates error: error Error=��(Ii,j-Ei,j)2, and judge:
Work as error ErrorDuring close to 0, enter step (e), otherwise, return step (a);
E () terminates, finally give 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 place of optical element to be measured, namely achieve each layer imaging of optical element to be measured and phase measurement.
The technique effect of the present invention is as follows:
The significant advantage of the present invention is the apparatus and method proposing 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 is formed after collecting lens is as the illumination light of optical element to be measured, two dimension motorized precision translation stage is driven to move optical element to be measured under control of the computer, and a distance detector records the optical element to be measured diffraction pattern when diverse location after optical element to be measured, obtained the complex amplitude transmittance function of each layer of optical element to be measured and the phase place of each layer by computer disposal. And the structure of optical element will not be caused any destruction by measurement process.
The present invention is especially suitable for changing the occasion that the structure of the transmission-type element with multiple structure needs again the information every layer to separate.
Accompanying drawing explanation
Fig. 1 is the index path of the device of transmissive optical element of the present invention layering phase imaging.
Detailed description of the invention
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 the index path that Fig. 1, Fig. 1 are the devices of transmissive optical element of the present invention layering phase imaging. As seen from the figure, the device of transmissive optical element of the present invention layering phase imaging is made up of coherent source 1, beam expander 2, collecting lens 3, optical element to be measured 4, two dimension motorized precision translation stage 5, detector 6, computer 7, and the position relationship of said elements is as follows:
The light that wavelength is �� sent along coherent source 1 becomes spherical wave after sequentially passing through beam expander 2, collecting lens 3, spherical wave illumination optical element 4 to be measured, described optical element to be measured 4 is placed on two dimension motorized precision translation stage 5 and scans line by line being perpendicular to optical path direction, detector 6 records illumination light diffraction pattern distribution after optical element to be measured, detector 6 outfan is connected with the input of described computer 7, and the outfan of computer 7 is connected with the control end of described two-dimentional motorized precision translation stage 5.
The light source 1 used 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 to convert directional light to spherical wave, and the lens used by this embodiment are the biconvex lens of focal length 1535mm.
Described detector 6 is ccd detector, and resolution is 2048pixel �� 2048pixel, and each pixel length of side is 7.4 ��m, and the more high imaging of resolution is more accurate.
Described control computer 7 purpose is by accurately to control precision in electricity dynamic this embodiment of translation stage 5(of two dimension be 0.001mm) movement control the movement of optical element to be measured, it is achieved the illumination light scanning to sample.
The work process of the present embodiment is:
1. being placed in by optical element 4 to be measured on two dimension motorized precision translation stage 5 and so as to vertical with incident beam, the present embodiment optical element to be measured has three-decker, along direction of beam propagation, is defined as layer 1 successively, layer 2, distance between 3 layer 1 of layer and layer 2 are Z1, the distance between layer 2 and layer 3 is Z2, Z1=Z2=5mm, the distance Z of last layer of range finder of optical element to be measured3=77.126mm, the distance Z between the focal length of layer 1 and lens (3)0�� 15mm;
2. described computer 7 controls described two-dimentional motorized precision translation stage 5 makes the described optical element to be measured 4 with multiple structure scan line by line in the plane being perpendicular to direction of beam propagation, step-length is 0.222mm, must there be overlap adjacent two scanning light transmission parts, position, overlapping area is preferably 2/3rds of hot spot, the matrix that the position of the movement of optical element 4 to be measured is arranged by 10 row 10 represents, in scanning process, when optical element 4 to be measured is in i row j row, it is I that described detector 6 records the light distribution of diffraction patterni,j, wherein i is the positive integer of 1��10, and j is the positive integer of 1��10, Ii,jIt is stored in computer 7 with 2048 row 2048 column matrix formation, after the hot spot after scanning has all recorded, obtains one group of hot spot data I1,1, I1,2,...Ii,j,..I10,10;
3. hot spot data are utilized to carry out the step of Phase Processing:
First computer 7 treats the transmittance function of photometry element each layer, provides a random conjecture value as initial value including amplitude transmittance and phase change amount:
obj1=obj2...=obj3=E*exp (i*rand (a, b) * 2 ��),
Wherein: E is amplitude, rand (a, b) for producing the random matrix of a row b row, a=2048+ (10-1) * 30=2318, b=2048+ (10-1) * 30=2318, the illumination light along direction of beam propagation optical element ground floor (element surface) to be measured place is one conjecture value illu of offer1,illu1Closer to actual value, convergence rate is more fast, and finding the illumination light on sample here is spherical wave, therefore:
ill u 1 = E 1 * exp [ - i * 2 π λ * Z 0 2 + r ( 2048,2048 ) 2 ] * hole ( 2048,2048 ) ,
Wherein: E1For amplitude, r (2048,2048) is 2048 row 2048 column matrix, represents the distance of layer 1 each distance optical axis, and hole (2048,2048) limits the scope of illumination light;
(a) calculate optical element to be measured scanning position (i, j) the illuminated rear hot spot in place distribution (i=1,2 ... 10, j=1,2 ... 10): first take obj1��obj2��obj31+ (i-1) * 30 row to m+ (i-1) * 30 row, 1+ (j-1) * 30 row arrange to n+ (j-1) * 30, are designated as obj1 i,j��obj2 i,j��obj3 i,j,
Optical element to be measured each layer place width complex amplitude and illumination light update step:
The Transmission field of layer 1 is Eout_1=illu1*obj1 i,j, the Transmission field of layer 1 propagates layer 2 place, the illumination light field distribution according to angular spectra theory computation layer 2 surface
illu 2 = ∫ ∫ ∞ A 1 ( α λ , β λ ) exp ( i 2 π λ 1 - α 2 - β 2 Z 1 ) exp [ i 2 π ( α λ x 2 + β λ y 2 ) ] d α λ d β λ
Wherein:For layer 1 place Transmission field angular spectrum;
The Transmission field of layer 2 is Eout_2=illu2*obj2 i,j, the Transmission field of layer 2 propagates layer 3 place, the illumination light field distribution according to angular spectra theory computation layer 3 surface
illu 3 = ∫ ∫ ∞ A 2 ( α λ , β λ ) exp ( i 2 π λ 1 - α 2 - β 2 Z 2 ) exp [ i 2 π ( α λ x 3 + β λ y 3 ) ] d α λ d β λ
Wherein:For layer 2 place Transmission field angular spectrum;
The Transmission field of layer 3 is Eout_3=illu3*obj3 i,j, the Transmission field of layer 3 propagates CCD place, calculates the illumination light field distribution of CCD place according to angular spectra theory
E i , j = ∫ ∫ ∞ A N ( α λ , β λ ) exp ( i 2 π λ 1 - α 2 - β 2 Z N ) exp [ i 2 π ( α λ x ccd + β λ y ccd ) ] d α λ d β λ
Wherein:For layer 3 place Transmission field angular spectrum;
Calculate the COMPLEX AMPLITUDE E obtaining now detector placei,j=abs(Ei,j)exp(i��i,j), keep its phase invariant and be distributed I with described diffractional fieldi,jSquare root sqrt (Ii,j) replace its amplitude to become
E'i,j=sqrt(Ii,j)exp(i��i,j);
E' is calculated further according to angular spectra theoryi,jThe reverse layer N place exit wave function that be propagated back to is distributed an E'i,j
E ′ i , j = ∫ ∫ ∞ A CCD ( α λ , β λ ) exp ( i 2 π λ 1 - α 2 - β 2 Z N ) exp [ i 2 π ( α λ x + β λ y ) ] d α λ d β λ
Wherein,For detector place E'i,jAngular spectrum;
The knots modification �� E of exit wave function is tried to achieve by doing differencei,j=E'i,j-Eout_N; Treat photometry element layer 3 place complex amplitude obj respectively3 i,jWith illumination light illu3It is updated by following formula, obtains obj newly3'i,jAnd illu'3It is respectively as follows:
obj i , j N ′ = obj i , j N + illu N * | illu N | 2 max × βΔE i , j ,
illu ′ N = illu N + obj i , j N * | ob j i , j N | 2 max × βΔ E i , j ,
Wherein, illu3WithIt is illu respectively3WithMould,And obj *3* i,jIt is illu3 and obj respectively3 i,jConjugation, �� select 0��1 constant, reflection update proportion;
WithReplace obj3Middle 1+ (i-1) * 30 row is to 2048+ (i-1) * 30 row, and 1+ (j-1) * 30 row, to the value at 2048+ (j-1) * 30 row place, update obj3, the illumination light on layer 3 is the illumination light illu after updating3=illu'3;
Illu is calculated according to angular spectra theory3The reverse layer 2 place exit wave function that is propagated back to is distributed E'i,j, seek the knots modification �� E of layer 2 place exit wave functioni,j=E'i,j-Eout_2, it is updated obtaining obj with illumination light in the way of identical with layer 3 place to complex amplitude2And illu2;
Illu is calculated according to angular spectra theory2The reverse layer 1 place exit wave function that is propagated back to is distributed E'i,j, seek the knots modification �� E of layer 1 place exit wave functioni,j=E'i,j-Eout_1, it is updated obtaining obj with illumination light in the way of identical with layer 3 place to complex amplitude1And illu1;
B () j=j+1, returns step (a) and continues to calculate, until j takes to 10;
C () j=1, i=i+1, returns step (a) and continues to calculate, until i takes to 10;
D () calculates error: error Error=��(Ii,j-Ei,j)2, and judge:
Work as error ErrorDuring close to 0, enter step (e), otherwise, return step (a);
E () terminates, finally give Optical element layer 1 respectively to be measured, layer 2, layer 3 place complex amplitude amplitude transmittance function,For the phase place at each layer place of optical element to be measured, namely achieve each layer imaging of sample and phase measurement.
Experiments show that, the Convergent Laser Beam that the quasi-parallel light that coherent source is sent by the present invention is formed after collecting lens is as the illumination light of optical element to be measured, two dimension motorized precision translation stage is driven to move optical element to be measured under control of the computer, and a distance detector records the optical element to be measured diffraction pattern when diverse location after optical element to be measured, obtained the complex amplitude transmittance function of each layer of optical element to be measured and the phase place of each layer by computer disposal. And the structure of optical element will not be caused any destruction by measurement process.
The present invention is especially suitable for changing the situation that the structure of the transmission-type element with multiple structure needs again the information every layer to separate.

Claims (1)

1. the method that the transmissive optical element with multiple structure is realized layering phase imaging by the device utilizing transmissive optical element layering phase imaging, this device is made up of coherent source (1), beam expander (2), collecting lens (3), optical element to be measured (4), two dimension motorized precision translation stage (5), detector (6), computer (7), and the position relationship of said elements is as follows:
The light that wavelength is �� sent along coherent source (1) sequentially passes through beam expander (2), collecting 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 dimension motorized precision translation stage (5) and above and scans line by line being perpendicular to optical path direction, the diffraction pattern distribution after optical element to be measured of described detector (6) the record illumination light, described detector (6) outfan is connected with the input of described computer (7), the outfan of computer (7) is connected with the control end of described two-dimentional motorized precision translation stage (5), it is characterized in that the method comprises the following steps:
1. optical element to be measured (4) is placed in two dimension motorized precision translation stage (5) upper and so as to vertical with incident beam, optical element to be measured has multiple structure, along direction of beam propagation, being defined as layer 1, layer 2, layer 3 successively ... layer N-1, layer N, the distance between layer 1 and layer 2 is Z1, the distance between layer 2 and layer 3 is Z2, by that analogy, the distance between layer N-1 and layer N is ZN-1, last layer of optical element to be measured is Z apart from the distance of described detectorN, the distance between the focal length of layer 1 and described collecting lens (3) is Z0;
2. described computer (7) controls described two-dimentional motorized precision translation stage (5) makes the described optical element to be measured (4) with multiple structure scan line by line in the plane being perpendicular to direction of beam propagation, step-length is l, must there be overlap adjacent two scanning light transmission parts, position, overlapping area is 2/3rds of hot spot, the matrix that the position of the movement of optical element to be measured (4) is arranged by p row q represents, in scanning process, when described optical element to be measured (4) is in i row j row, the light distribution of described detector (6) record diffraction pattern is Ii,j, wherein i is the positive integer of 1��p, and j is the positive integer of 1��q, p, and q represents total line number and total columns, the I of optical element to be measured (4) scan matrix respectivelyi,jIt is stored in computer (7) with m row n column matrix formation, after the hot spot after scanning has all recorded, obtains one group of hot spot data I1,1, I1,2,...Ii,j,..Ip,q;
3. hot spot data are utilized to carry out the step of Phase Processing:
The transmittance function of photometry element each layer first treated by computer (7), provides a random conjecture value as initial value including amplitude transmittance and phase change amount:
obj1=obj2...=obj3=E*exp (i*rand (a, b) * 2 ��),
Wherein: E is amplitude, (a, b) for producing the random matrix of a row b row for rand, a=m+ (p-1) * l, b=n+ (q-1) * l, the wherein row, column of m, n respectively hot spot matrix, the row, column of p, q difference respectively scan matrix, l is scanning step; Illumination light along direction of beam propagation optical element layer 1 to be measured place is illu1, it is provided that a conjecture value is as initial value:
illu 1 = E 1 * exp [ - i * 2 π λ * Z 0 2 + r ( m , n ) 2 ] * h o l e ( m , n ) ,
Wherein: E1For amplitude, (m, n) for m row n column matrix, represents the distance of layer 1 each distance optical axis to r, and (m, n) for the circular hole of the scope of restriction illumination light, the wherein row, column of m, n respectively hot spot matrix for hole;
The each layer complex amplitude of optical element to be measured and illumination light update step:
(a) calculate optical element to be measured scanning position (i, j) the illuminated rear hot spot in place distribution (i=1,2 ... p, j=1,2 ... q): take obj1��obj2����objN1+ (i-1) * l row to m+ (i-1) * l row, 1+ (j-1) * l arrange n+ (j-1) * l row, be designated as obj1 i,j��obj2 i,j����objN i,j,
The Transmission field of layer 1 is Eout_1=illu1*obj1 i,j, the Transmission field of layer 1 propagates layer 2 place, the illumination light field distribution according to angular spectra theory computation layer 2 surface
illu 2 = ∫ ∫ ∞ A 1 ( α λ , β λ ) exp ( i 2 π λ 1 - α 2 - β 2 Z 1 ) exp [ i 2 π ( α λ x 2 + β λ y 2 ) ] d α λ d β λ
Wherein:For layer 1 place Transmission field angular spectrum,For spatial frequency, (x2,y2) for the coordinate of layer 2;
The Transmission field of layer 2 is Eout_2=illu2*obj2 i,j, the Transmission field of layer 2 propagates layer 3 place, the illumination light field distribution according to angular spectra theory computation layer 3 surface
illu 3 = ∫ ∫ ∞ A 2 ( α λ , β λ ) exp ( i 2 π λ 1 - α 2 - β 2 Z 2 ) exp [ i 2 π ( α λ x 3 + β λ y 3 ) ] d α λ d β λ
Wherein:For layer 2 place Transmission field angular spectrum, (x3,y3) for the coordinate of layer 3;
Successively computation layer 4, layer 5 ... layer N place's illumination light and Transmission field, respectively illu4��illu5����illuN, Eout_4��Eout_5����Eout_N;
COMPLEX AMPLITUDE according to angular spectra theory calculating detector place
E i , j = ∫ ∫ ∞ A N ( α λ , β λ ) exp ( i 2 π λ 1 - α 2 - β 2 Z N ) exp [ i 2 π ( α λ x c c d + β λ y c c d ) ] d α λ d β λ ,
Wherein:For layer N place Transmission field angular spectrum, (xccd,yccd) for the coordinate of detector;
Calculate the COMPLEX AMPLITUDE E obtaining now detector placei,j=abs (Ei,j)exp(i��i,j), keep its phase invariant and with the light distribution I of described diffraction patterni,jSquare root sqrt (Ii,j) replace its amplitude to become
E'i,j=sqrt (Ii,j)exp(i��i,j);
E' is calculated further according to angular spectra theoryi,jThe reverse layer N place exit wave function that be propagated back to is distributed an E'i,j
E ′ i , j = ∫ ∫ ∞ A C C D ( α λ , β λ ) exp ( - i 2 π λ 1 - α 2 - β 2 Z N ) exp [ i 2 π ( α λ x + β λ y ) ] d α λ d β λ ,
Wherein,For detector place E'i,jAngular spectrum, (x, y) for the coordinate of sample;
The knots modification �� E of exit wave function is tried to achieve by doing differencei,j=E'i,j-Eout_N; Treat photometry element layer N place complex amplitude respectivelyWith illumination light illuNIt is updated by following formula, obtains newlyAnd illu'NIt is respectively as follows:
obj i , j N ′ = obj i , j N + illu N * | illu N | 2 max × γΔE i , j ,
illu ′ N = illu N + obj i , j N * | obj i , j N | 2 max × γΔE i , j
Wherein, | illuN| withIt is illu respectivelyNWithMould,WithIt is illu respectivelyNWithConjugation, �� select 0��1 constant, reflection update proportion;
WithReplace objNMiddle 1+ (i-1) * l row is to m+ (i-1) * l row, and 1+ (j-1) * l arranges the value of n+ (j-1) * l row, updates objN, the illumination light on layer N is the illumination light illu after updatingN=illu'N;
Illu is calculated according to angular spectra theoryNThe reverse layer N-1 place exit wave function that be propagated back to is distributed an E'i,j, seek the knots modification �� E of layer N-1 place exit wave functioni,j=E'i,j-Eout_N-1, it is updated obtaining obj with illumination light in the way of identical with layer N place to complex amplitudeN-1And illuN-1;
Repeat the above steps update step N-2 successively, layer N-3 ... layer 2, the sample complex amplitude at layer 1 place and illumination light distribution;
B () j=j+1, returns step (a) and continues to calculate, until j takes to q;
C () j=1, i=i+1, returns step (a) and continues to calculate, until i takes to p;
D () calculates error: error Error=�� (Ii,j-Ei,j)2, and judge:
Work as error ErrorDuring close to 0, enter step (e), otherwise, return step (a);
E () terminates, finally give Respectively optical element layer 1 to be measured, layer 2 ... layer N place complex amplitude transmittance function,For the phase place at each layer place of optical element to be measured, namely achieve each layer imaging of optical element to be measured and phase measurement.
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