CN111121675B - Visual field expansion method for microsphere surface microscopic interferometry - Google Patents

Visual field expansion method for microsphere surface microscopic interferometry Download PDF

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CN111121675B
CN111121675B CN201911269660.9A CN201911269660A CN111121675B CN 111121675 B CN111121675 B CN 111121675B CN 201911269660 A CN201911269660 A CN 201911269660A CN 111121675 B CN111121675 B CN 111121675B
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马骏
刘戴明
李建欣
朱日宏
魏聪
淳秋垒
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Nanjing University of Science and Technology
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    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B11/00—Measuring arrangements characterised by the use of optical techniques
    • G01B11/30—Measuring arrangements characterised by the use of optical techniques for measuring roughness or irregularity of surfaces
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
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Abstract

The invention discloses a field expansion method for microsphere surface microscopic interferometry, which comprises the steps of collecting a plurality of intensity images from an interference imaging light path polarization camera, wherein the intensity images comprise interference intensity images of test light from the outer surface of a transparent hollow microsphere and reference light from the surface of a reference mirror, and intensity images of single reference light after the microsphere is shielded. And then solving the amplitude of the test light and the phase difference between the reference light and the test light according to an intensity equation set in the four-step phase-shifting method, and combining the complex amplitude distribution of the reference light and the test light on the surface of the CCD according to a solving result. Then, according to the depth of the measured view field of the measured micro-sphere and the depth of field parameters of the micro-objective, the measured view field is divided, the self-focusing algorithm is utilized to determine the accurate focusing distance required by each divided area in the image space, each focusing distance and the complex amplitude distribution of the CCD surface are applied to an angular spectrum inverse diffraction transmission formula, so that the focusing image of each view field can be obtained, and each focusing image is overlapped so that the measurement result of the view field expansion can be obtained.

Description

Visual field expansion method for microsphere surface microscopic interferometry
Technical Field
The invention belongs to the field of optical detection, and relates to a field expansion method for microsphere surface microscopic interferometry.
Background
The surface morphology of an optical element is one of important indexes for evaluating the performance of the optical element, along with the continuous improvement of the requirements of scientific research and production and the continuous improvement of the processing level, more and more micro-elements are applied to various fields, and in a plurality of surface detection technologies for the microstructures, the micro-interference measurement technology is widely adopted by the advantages of non-contact measurement and high detection precision. However, when the high-resolution details of the surface of the object are acquired, the problem of too shallow depth of field is introduced by the high na (numerical aperture) characteristic of the microscope objective, and when the surface of the detected object has a curved feature, the characteristic inevitably greatly reduces the effective field of view of the measurement, and the measurement result in the edge area of the field of view has a defocus error, thereby reducing the measurement efficiency, so that the method for researching the solution of the problem has great significance.
In the field of view extension method of the existing microscope system, the field of view extension method can be basically divided into the following steps according to the extension principle: a deep scene extension method, a defocusing restoration method, a diffraction reconstruction method and the like. The depth of field extension method is mainly based on introducing additional devices into the system, such as a micro lens array in a light field camera and a cubic phase plate in a wavefront coding technology, and acquiring more object information by changing into an imaging process, but adding system elements introduces additional system errors. The defocusing restoration method mainly treats defocusing field information as a degraded two-dimensional signal through related knowledge in the field of image processing, constructs an image restoration model and calculates key parameters of the model for restoration, but the image restoration model is an ideal model and the restoration effect is often not accurate enough. The diffraction reconstruction method is a calculation method commonly used in the field of digital holography, can calculate complex amplitude information at other positions in space through complex amplitude information recorded on an image surface, and can better solve the problem for an interference system taking phase information as a measurement object.
In the article of scene/depth of focus extension and analysis of zoom optical system, guo tiger, et al, north cartoonish institute of china, a method for expanding a field of view by applying a wavefront coding technique to a zoom system is proposed. Although the wavefront coding technology has a significant effect on the field expansion problem, the cubic phase plate as a core element reflects an extra phase difference to the reference wavefront and the test wavefront while changing the system pupil function, which puts higher requirements on the processing precision and the placement position, and the recovery algorithm of the image also increases the complexity of the whole algorithm, so that the method is not suitable for the field expansion problem of the interferometric measurement system.
Disclosure of Invention
The invention aims to provide a field expansion method for micro-interferometry of the surface of a microsphere, aiming at the problem of small field of measurement of the spherical surface by micro-interferometry, the single measurement efficiency is improved, so that the measurement speed of a whole sample is improved, and for the microsphere with the diameter of 0.8mm, the effective measurement field can be improved from 130um to 320 um.
The technical solution for realizing the purpose of the invention is as follows: a field expansion method for microsphere surface microscopic interferometry is realized by the following steps:
step 1, collecting an interference intensity image I (x, y) of reference light and test light recorded by a polarization camera in an interference imaging light path, shielding a test light beam, and recording the intensity I of the reference light on the polarization camera0(x,y)；
Step 2, according to the interference intensity image I (x, y) and the reference light intensity image I collected in the polarization camera0(x, y) solving the phase difference distribution of the two wave surfaces by combining a four-step phase shifting method
Figure BDA0002313814150000021
And measuring the optical amplitude distribution to distribute the phase difference between the two wave surfaces
Figure BDA0002313814150000022
And the complex amplitude distribution E (x, y) of the interference light field is combined by the test light amplitude distribution;
step 3, calculating the measuring view field phi of the surface of the microsphere to be measured according to the interference intensity image I (x, y) of the collected reference light and the collected test light, and calculating the depth d of the measuring view field according to geometric conditionssDepth of field D with a microscope objectivedofFor reference, depth d of field of viewsDividing the substrate into M layers at equal intervals;
step 4, calculating the size of a conjugate image plane between each divided area on the polarization camera according to the magnification beta of the microscope objective, comparing the size of the conjugate image plane with the number of pixels of the polarization camera, and calculating the pixel effective area C of each divided image planem(x,y)；
Step 5, performing virtual lens modulation on the combined interference light field complex amplitude E (x, y) to obtain complex amplitude E '(x, y), performing inverse diffraction calculation on the E' (x, y), reconstructing complex amplitude distribution of a series of image space diffraction surfaces, extracting a series of complex amplitude distribution in each pixel effective area, and performing a focusing evaluation function M on the complex amplitude distributiondEvaluating and obtaining the accurate focusing distance dn；
Step 6, performing diffraction inversion calculation on the combined interference light field complex amplitude E (x, y) after the virtual lens is applied, wherein the diffraction distance is a focusing distance dnReconstructing a phase difference distribution phi of a series of focusing planesΔ(n)(x, y) extracting a phase difference distribution phi in each pixel effective areaΔ(m,n)(x,y)；
Step 7, phase difference distribution phi in the effective area of the superposed pixelsΔ(m,n)(x, y), completing the full-view restoration.
Compared with the prior art, the invention has the remarkable advantages that: 1. the method does not increase the complexity of the system, does not need to additionally introduce a new element, thereby avoiding further adjustment error 2, and avoids diffraction calculation among curved surfaces by introducing the virtual lens, thereby greatly reducing the calculation complexity and having high calculation speed.
Drawings
FIG. 1 is a flow chart of the field of view expansion method for microsphere surface microscopy interferometry according to the present invention.
Fig. 2 is a schematic structural diagram of a micro-interference light path for spherical surface measurement.
Fig. 3 is a schematic diagram of the divided effective areas of the pixels of the plane where the polarization camera is located, wherein the diagrams (a) to (j) respectively correspond to ten divided areas on the surface of the microsphere.
FIG. 4 is a diagram showing a focus evaluation function M in the fifth layer pixel active areadGraph as a function of diffraction distance.
Fig. 5 is a graph of the extended results of a single measurement field of view.
FIG. 6 is a comparison of the results of the microtopography measurements of a given area before and after field expansion, wherein (a) is before field expansion and (b) is after field expansion.
Fig. 7 is a schematic diagram of the height solution of the active area of each pixel.
Detailed Description
The present invention is described in further detail below with reference to the attached drawing figures.
With reference to fig. 1, a field expansion method for microsphere surface microscopic interferometry includes the following steps:
step 1, collecting an interference intensity image I (x, y) of reference light and test light recorded by a polarization camera in an interference imaging light path, shielding a test light beam, and recording the intensity I of the reference light on the polarization camera0(x,y)；
Step 2, according to the interference intensity image I (x, y) and the reference light intensity image I collected in the polarization camera0(x, y) solving the phase difference distribution of the two wave surfaces by combining a four-step phase shifting method
Figure BDA0002313814150000031
And measuring the optical amplitude distribution to distribute the phase difference between the two wave surfaces
Figure BDA0002313814150000043
And combining the test light amplitude distribution to obtain a complex amplitude distribution E (x, y) of the interference light field, which is as follows:
will polarizeThe single interference intensity image I (x, y) collected by the camera is separated into four different interference images, and the four separated interference images are different in that: the reference light and the test light in each interference pattern are additionally added with phase differences of 0, pi/2, pi and 3 pi/2 on the basis of the original phase difference, and the intensity distribution of the four interference patterns is respectively set as I01、I02、I03、I04Then, according to the four-step phase shifting method, the following expression is given:
Figure BDA0002313814150000041
in the formula IaIs the reflected light intensity from other reflecting surfaces in the interference imaging light path, I0Is the intensity of the reference light, I1Is the intensity of the test light and,
Figure BDA0002313814150000044
the above expression is a four-element equation set for the phase difference between the reference light and the test light, based on the light intensity I of the reference light collected separately0(x, y) the intensities of the four interferograms are combined to obtain
Figure BDA0002313814150000045
And I1、Ia(ii) a The complex amplitude distribution E (x, y) of the interference light field can be represented by these parameters:
Figure BDA0002313814150000042
in the formula
Figure BDA0002313814150000046
The phase factor of the reference light is cancelled by the phase factor of the virtual lens in the transmission calculation process of the complex amplitude, so that an accurate value is not substituted in the formula.
Step 3, calculating the measurement field of view phi of the surface of the microsphere to be measured according to the interference intensity pattern I (x, y) of the collected reference light and the collected test light, and obtaining the measurement field of view phiGeometric condition calculates depth d of measuring view fieldsDepth of field D with a microscope objectivedofFor reference, depth d of field of viewsAnd performing equal-interval division, wherein the number of the divided layers is M.
Step 4, calculating the size of a conjugate image plane between each divided area on the polarization camera according to the magnification beta of the microscope objective, comparing the size of the conjugate image plane with the number of pixels of the polarization camera, and calculating the pixel effective area C of each divided image planem(x,y)。
Step 5, performing virtual lens modulation on the combined interference light field complex amplitude E (x, y) to obtain complex amplitude E '(x, y), performing inverse diffraction calculation on the E' (x, y), reconstructing complex amplitude distribution of a series of image space diffraction surfaces, extracting a series of complex amplitude distribution in each pixel effective area, and performing a focusing evaluation function M on the complex amplitude distributiondEvaluating and obtaining the accurate focusing distance dm,n。
Step 6, performing diffraction inversion calculation on the combined interference light field complex amplitude E (x, y) after the virtual lens is applied, wherein the diffraction distance is a focusing distance dnReconstructing a phase difference distribution phi of a series of focusing planesΔ(n)(x, y) extracting a phase difference distribution phi in each pixel effective areaΔ(m,n)(x,y)。
Step 7, phase difference distribution phi in the effective area of the superposed pixelsΔ(m,n)(x, y), completing the full-view restoration.
With reference to the measurement light path shown in fig. 2, incident light directly strikes the center of the microsphere, and a view field angle can be calculated according to the geometric relationship, and further the depth d of the measurement view field of the microsphere to be measured in step 3 can be calculated according to the view field anglesThe formula is as follows:
Figure BDA0002313814150000051
wherein R is the radius of the outer surface of the microsphere to be measured, phi is a calculated value, beta is the vertical axis magnification ratio under the working distance, and the layering number M of the microsphere to be measured must meet the condition that the interval of each layer is smaller than D of the microobjectivedof：
ds/M＜Ddof (2)
Depth of field D of the microobjectivedofQuantitative calculations were performed by the following depth of field formula:
Figure BDA0002313814150000052
in the formula, lambda is the wavelength of the test laser, n is the refractive index of the medium, NA is the numerical aperture of the microscope objective, beta is the vertical axis magnification under the working distance, and e is the pixel size of the polarization camera.
With reference to fig. 7, in step 4, before calculating the size of the conjugate image plane, the height h of each divided field of view in the plane where the vertex of the front surface of the microsphere to be measured is located is calculated according to the projection relationshipmThe solving principle diagram shown in FIG. 7 illustrates this projection relationship, according to hmAnd the vertical axis magnification beta of the microscope objective, namely the height H of the mth layer of view field on the image surface can be calculatedm：
Hm＝β×hm (4)
With reference to the schematic diagram of the pixel effective area shown in fig. 3, bright-line areas of the pixel effective areas (g), (h), (i), (j) and the like at the rear position are narrower and narrower, which is consistent with the imaging characteristics of the actual microscope objective, so that the division result is considered to be reliable.
The specific steps of performing the inverse calculation of the diffraction of the introduced virtual lens in the step 5 are as follows:
setting the focal length f of the virtual lens as the distance d from the convergence point of the reference light and the test light to the plane of the polarization camerafThen the complex amplitude modulation factor t (x, y) of the virtual lens is:
Figure BDA0002313814150000061
the complex amplitude E' (x, y) of the interference light field after modulation by the virtual lens is then:
E′(x,y)＝E(x,y)×t(x,y) (6)
the steps of the inverse diffraction calculation are as follows:
Figure BDA0002313814150000063
wherein H (f)x,fy) Is a transfer function of the inverse diffraction process, whose form is dependent on the diffraction distance:
Figure BDA0002313814150000064
wherein j is an imaginary unit, d is an inverse diffraction distance, k is a wave number, fxAs a coordinate in the direction of the x-axis in the spectral domain, fyIs the coordinate in the direction of the y-axis in the spectral domain.
Therefore, the complex amplitude distribution E ″ (x, y) of the diffraction surface can be calculated by inputting only one distance d of the inverse diffraction, and the focus evaluation function M is applied according to the characteristicdObtaining each pixel effective area CmAccurate focus distance d within (x, y)m,nIn FIG. 4, the evaluation function M is plotted by taking the fifth pixel effective area as an exampledAccording to the variation curve of the diffraction distance, the diffraction distance corresponding to the maximum point is the accurate focusing distance d5,n。
The phase difference distribution phi of the focusing plane in the step 6Δ(n)(x, y) is calculated by an active four-step phase shifting method, and the complex amplitude E' (x, y) of the transmission object after being modulated by the virtual lens is written as follows:
Figure BDA0002313814150000071
in pair type
Figure BDA0002313814150000075
Complex amplitude E after active phase shifting1'(x,y)、E2'(x,y)、E3' (x, y) are as follows:
Figure BDA0002313814150000072
Figure BDA0002313814150000073
Figure BDA0002313814150000074
d for each actively phase-shifted complex amplitudenDistance inverse diffraction transmission, converting the complex amplitude distribution after transmission into light intensity distribution, and calculating d by applying four-step phase-shifting algorithm againnPhase difference distribution phi on planeΔ(n)(x, y) similarly denoted by dm,nCalculating the phase difference distribution phi of each pixel effective area for the reverse diffraction distanceΔ(m,n)(x,y)。
The microspheres to be detected are transparent hollow microspheres.
In step 7, the actual result of the superposition process is shown in fig. 5.
According to the graph shown in fig. 6, the microstructure on the surface of the same microsphere is obtained by comparing the microstructure before and after the visual field restoration, the highest measurement height of the microstructure before the restoration is only 150nm due to the defocusing problem, and the measurement result can reach 350nm after the expansion method is applied, so that the effectiveness of the visual field expansion method is proved.
In summary, the present invention determines the focus distance of each region on the microsphere surface by the diffraction inverse calculation and the layered auto-focusing method, and performs layered recovery on the full field of view based on the focus distance to obtain accurate focused phase information in the full field of view. Compared with other field expansion methods, the method shortens the calculation time, avoids introducing unnecessary elements and improves the detection efficiency.

Claims (7)

1. A field expansion method for microsphere surface microscopic interferometry is characterized by comprising the following implementation steps:
step 1, collecting the record of a polarization camera in an interference imaging light pathThe interference intensity pattern I (x, y) of the reference light and the test light, the test light beam is shielded, and the intensity I of the reference light on the polarization camera is recorded0(x,y)；
Step 2, according to the interference intensity image I (x, y) and the reference light intensity image I collected in the polarization camera0(x, y) solving the phase difference distribution of the two wave surfaces by combining a four-step phase shifting method
Figure FDA0003104515440000011
And measuring the light amplitude distribution to distribute the phase difference between the two wave surfaces
Figure FDA0003104515440000012
And the complex amplitude distribution E (x, y) of the interference light field is combined by the test light amplitude distribution;
step 3, calculating the measuring view field phi of the surface of the microsphere to be measured according to the interference intensity image I (x, y) of the collected reference light and the collected test light, and calculating the depth d of the measuring view field according to geometric conditionssDepth of field D with a microscope objectivedofFor reference, depth d of field of viewsDividing the substrate into M layers at equal intervals;
step 4, calculating the size of a conjugate image plane between each divided area on the polarization camera according to the magnification beta of the microscope objective, comparing the size of the conjugate image plane with the number of pixels of the polarization camera, and calculating the pixel effective area C of each divided image planem(x,y)；
Step 5, performing virtual lens modulation on the combined interference light field complex amplitude E (x, y) to obtain complex amplitude E '(x, y), performing inverse diffraction calculation on the E' (x, y), reconstructing complex amplitude distribution of a series of image space diffraction surfaces, extracting a series of complex amplitude distribution in each pixel effective area, and performing a focusing evaluation function M on the complex amplitude distributiondEvaluating and obtaining the accurate focusing distance dm,n；
Step 6, performing diffraction inversion calculation on the combined interference light field complex amplitude E (x, y) after the virtual lens is applied, wherein the diffraction distance is a focusing distance dm,nReconstructing a phase difference distribution phi of a series of focusing planesΔ(n)(x, y) extracting respective pixel significanceDistribution of phase difference phi in zoneΔ(m,n)(x,y)；
Step 7, phase difference distribution phi in the effective area of the superposed pixelsΔ(m,n)(x, y), completing the full-view restoration.
2. The field of view expansion method for microsphere surface microscopy interferometry according to claim 1, wherein: in the step 2, four different interferograms are separated from a single interference intensity pattern I (x, y) acquired by the polarization camera, and the four separated interferograms are different in that: the reference light and the test light in each interferogram additionally increase the phase difference of 0, pi/2, pi and 3 pi/2 on the basis of the original phase difference, and the intensity distribution of the four interferograms is respectively set as I01、I02、I03、I04Then, according to the four-step phase shifting method, the following expression is given:
Figure FDA0003104515440000021
in the formula IaIs the reflected light intensity from other reflecting surfaces in the interference imaging light path, I0Is the intensity of the reference light, I1Is the intensity of the test light and,
Figure FDA0003104515440000022
the expression is a quaternary equation set for the phase difference between the reference light and the test light, and is based on the light intensity I of the reference light collected separately0(x, y) the intensities of the four interferograms are combined to obtain
Figure FDA0003104515440000023
And I1、Ia(ii) a The complex amplitude distribution E (x, y) of the interference light field can be represented by these parameters:
Figure FDA0003104515440000024
in the formula
Figure FDA0003104515440000025
The phase factor of the reference light is cancelled by the phase factor of the virtual lens during the transmission calculation of the complex amplitude, so that the exact value is not substituted in the formula.
3. The field of view expansion method for microsphere surface microscopy interferometry according to claim 1, wherein: the depth d of the field of view is measured by the microspheres to be measured in the step 3sQuantitative calculations were performed by the following formula:
Figure FDA0003104515440000026
wherein R is the radius of the outer surface of the microsphere to be measured, phi is a calculated value, beta is the vertical axis magnification under a working distance, and the layering number M of the microsphere to be measured must meet the condition that the interval of each layer is smaller than D of the microobjectivedof：
ds/M＜Ddof
Depth of field D of the microobjectivedofQuantitative calculations were performed by the following depth of field formula:
Figure FDA0003104515440000027
in the formula, lambda is the wavelength of the test laser, n is the refractive index of the medium, NA is the numerical aperture of the microscope objective, beta is the vertical axis magnification under the working distance, and e is the pixel size of the polarization camera.
4. The field of view expansion method for microsphere surface microscopy interferometry according to claim 1, wherein: in the step 4, before calculating the size of the conjugate image plane, firstly, the height h of each divided view field in the plane where the vertex of the front surface of the microsphere to be measured is located is calculated according to the projection relationmAccording to hmAnd the vertical axis of the microscope objectiveThe magnification factor beta is used for calculating the height H of the mth layer of view field on the image planem：
Hm＝β×hm。
5. The field of view expansion method for microsphere surface microscopy interferometry according to claim 1, wherein the step 5 comprises the following specific steps:
setting the focal length f of the virtual lens as the distance d from the convergence point of the reference light and the test light to the plane of the polarization camerafThen the complex amplitude modulation factor t (x, y) of the virtual lens is:
Figure FDA0003104515440000031
the complex amplitude E' (x, y) of the interference light field after modulation by the virtual lens is then:
E'(x,y)＝E(x,y)×t(x,y)
the steps of the inverse diffraction calculation are as follows:
Figure FDA0003104515440000032
wherein H (f)x,fy) Is a transfer function of the inverse diffraction process, whose form is dependent on the diffraction distance:
Figure FDA0003104515440000033
wherein j is an imaginary unit, d is an inverse diffraction distance, k is a wave number, fxAs a coordinate in the direction of the x-axis in the spectral domain, fyIs the coordinate in the direction of the y-axis in the frequency spectrum domain;
therefore, the complex amplitude distribution E ″ (x, y) of the diffraction surface can be calculated by inputting only one distance d of the inverse diffraction, and the focus evaluation function M is applied according to the characteristicdObtaining each pixel effective area CmExact focus within (x, y)From dm,n。
6. The field of view expansion method for microsphere surface microscopy interferometry according to claim 1, wherein: the phase difference distribution phi of the focusing plane in the step 6Δ(n)(x, y) is calculated by an active four-step phase shifting method, and the complex amplitude E' (x, y) of the transmission object after being modulated by the virtual lens is written as follows:
Figure FDA0003104515440000041
in pair type
Figure FDA0003104515440000042
Complex amplitude E after active phase shifting1'(x,y)、E2'(x,y)、E3' (x, y) are as follows:
Figure FDA0003104515440000043
Figure FDA0003104515440000044
Figure FDA0003104515440000045
d for each actively phase-shifted complex amplitudenDistance inverse diffraction transmission, converting the complex amplitude distribution after transmission into light intensity distribution, and calculating d by applying four-step phase-shifting algorithm againm,nPhase difference distribution phi on planeΔ(n)(x, y) similarly denoted by dm,nCalculating the phase difference distribution phi of each pixel effective area for the reverse diffraction distanceΔ(m,n)(x,y)。
7. The field of view expansion method for microsphere surface microscopy interferometry according to claim 1, wherein: the microspheres to be detected are transparent hollow microspheres.
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