CN112219096B - Method and system for measuring optical shear of birefringent device beyond diffraction limit - Google Patents
Method and system for measuring optical shear of birefringent device beyond diffraction limit Download PDFInfo
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- 238000000034 method Methods 0.000 title claims abstract description 19
- 230000003287 optical effect Effects 0.000 title abstract description 25
- 230000010287 polarization Effects 0.000 claims abstract description 71
- 238000006073 displacement reaction Methods 0.000 claims abstract description 31
- 238000009826 distribution Methods 0.000 claims abstract description 26
- 238000004458 analytical method Methods 0.000 claims abstract description 15
- 238000010008 shearing Methods 0.000 claims abstract description 8
- 238000003384 imaging method Methods 0.000 claims description 12
- 238000000926 separation method Methods 0.000 claims description 7
- 238000005286 illumination Methods 0.000 abstract description 11
- 238000010586 diagram Methods 0.000 description 14
- 238000005259 measurement Methods 0.000 description 5
- 230000000694 effects Effects 0.000 description 4
- 239000013078 crystal Substances 0.000 description 3
- 230000004807 localization Effects 0.000 description 3
- 238000001152 differential interference contrast microscopy Methods 0.000 description 2
- 238000012512 characterization method Methods 0.000 description 1
- 238000007405 data analysis Methods 0.000 description 1
- 230000003111 delayed effect Effects 0.000 description 1
- 238000002060 fluorescence correlation spectroscopy Methods 0.000 description 1
- 230000001902 propagating effect Effects 0.000 description 1
- 238000012876 topography Methods 0.000 description 1
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
- G01J9/00—Measuring optical phase difference; Determining degree of coherence; Measuring optical wavelength
- G01J9/02—Measuring optical phase difference; Determining degree of coherence; Measuring optical wavelength by interferometric methods
- G01J9/0215—Measuring optical phase difference; Determining degree of coherence; Measuring optical wavelength by interferometric methods by shearing interferometric methods
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Abstract
Methods and systems for directly measuring the optical shear angle and lateral displacement of a light beam passing through a birefringent device (212) having a resolution exceeding the diffraction limit. A system for measuring shear angle comprises an illumination module (310), a polarization control unit (209) or a polarizer (309), the birefringent means (212), a lens module (215) and a data acquisition module (218) for recording a light intensity distribution. When using the polarization control unit (209), the polarization of the input light beam (201) from the illumination module (310) is controlled such that two spots (206, 207) with orthogonal polarizations can be recorded separately at different frames. When using a polarizer (309), with mixed polarization of the input beam (201) from the illumination module (310), the polarizer (309) is placed in front of the data acquisition module (218) to record two spots (206, 207) with orthogonal polarization at different frames, respectively. Positioning analysis is then applied to determine the central position of the two spots (206, 207) with perpendicular polarization and to calculate the value of the shear angle/displacement between the transverse shear beams. The method can solve the problem that the shearing angle/displacement exceeds the light diffraction limit.
Description
Technical Field
The present disclosure relates to optical characterization of the optical shear of a birefringent device.
Background
Birefringent crystals or prisms may be used to split incident light into two orthogonally polarized beams that are displaced in different directions or laterally. Fig. 1 shows a schematic view of such a device. In fig. 1A, an input ray 101 is incident on a birefringent device 102 and split into two beams (104 and 105) at a shear plane 103, 104 and 105 having orthogonal polarizations (P + and P -) with a shear angle epsilon. In fig. 1B, an input ray 106 is incident on a birefringent device 107 and split into two parallel rays (109 and 110) at a shear plane 108, 109 and 110 having orthogonal polarizations (P + and P -) with a lateral shear displacement S. An example of such a device is a Nomarski (Nomarski) prism, which consists of two birefringent crystal wedge mirrors aligned with different optical axes. Nomads prism is a key component of Differential Interference Contrast (DIC) microscopy. For prisms used in DIC microscopes, the shear angle is typically about 10 -5 rad or even less. While this shear angle is critical to the spatial resolution, contrast and depth of DIC microscopes, commercial manufacturers typically do not provide any such information. Increased interest in label-free bioimaging and surface topography has driven the development of quantitative DIC microscopy, which requires accurate determination of the beam-shearing parameters of the prism. However, only indirect methods, such as using calibrated samples or standard wedges, bifocal fluorescence correlation spectroscopy, spatial interference and delayed derivatives, are currently proposed and demonstrated. These measurements require complex setup and data analysis.
Consider a collimated monochromatic light beam (e.g., a laser) of wavelength λ and diameter D passing through a birefringent prism. The output is two orthogonally polarized beams propagating along directions separated by a small angle epsilon. Limited by diffraction effects of the light, the shear angle must be greater than the diffraction angle of the beam, i.eSo that the sheared light beam can be spatially resolved. This condition suggests that if it is desired to directly measure the separation of scattered beams with small shear angles, a sufficiently large incident beam is required (i.e). For example, in a typical configuration where λ=400 nm and the shear angle ε=10 μrad (μrad=10 -6 rad), the required beam size should be greater than or equal to 5cm. However, most birefringent devices are much smaller than 5cm in size, which has hampered the development of direct methods in this field.
For measuring lateral displacement, if the displacement S is less than or equal to the diffraction limitWhere n is the refractive index, it is not possible to use the direct method.
In the present invention, by applying a localization analysis to reconsider a direct spatial measurement of the optical shear of the birefringent device, it is possible to accurately determine the centroid of each of the two light waves beyond the diffraction limit. The novelty lies inMomentum and polarization do not overlap in joint space.
Disclosure of Invention
Methods and systems are described for directly measuring the optical shear angle and lateral displacement of a light beam passing through a birefringent device having a resolution exceeding the diffraction limit. The system for measuring the shear angle comprises an illumination module, a polarization control unit or polarizer, said birefringent means, a lens module, and a data acquisition module for recording the light intensity distribution. The system for measuring shear displacement comprises an illumination module, a polarization control unit or polarizer, said birefringent means, an imaging module, and a data acquisition module for recording the light intensity distribution. When using a polarization control unit, the polarization of the input beam from the illumination module is controlled such that two spots with orthogonal polarizations can be recorded separately at different frames. When using a polarizer, with mixed polarization of the input beam from the illumination module, the polarizer is placed in front of the data acquisition module to record two spots of orthogonal polarization at different frames, respectively. Then, a positioning analysis is applied to determine the center position of the two spots with perpendicular polarization, and the value of the shear angle/displacement between the transverse shear beams is calculated. The method can solve the problem that the shearing angle/displacement exceeds the optical diffraction limit.
Drawings
Fig. 1 shows a schematic diagram of the optical shearing effect of two different birefringent devices. Fig. 1A shows the shearing angle effect of light passing through one type of birefringent device. Fig. 1B shows the shear displacement effect of light passing through another type of birefringent device.
Fig. 2A is a schematic diagram of an optical setup for measuring the shear angle of a birefringent device using a Polarization Control Unit (PCU). Fig. 2B shows a block diagram of a corresponding system for measuring the shear angle of a birefringent device using a Polarization Control Unit (PCU).
Fig. 3A is a schematic diagram of an optical setup for measuring the shear angle of a birefringent device using a polarizer. Fig. 3B shows a block diagram of a corresponding system for measuring the shear angle of a birefringent device using a polarizer.
Fig. 4A is a schematic diagram of an optical setup for measuring the shear displacement of a birefringent device using a Polarization Control Unit (PCU). Fig. 4B shows a block diagram of a corresponding system for measuring the shear displacement of a birefringent device using a Polarization Control Unit (PCU).
Fig. 5A is a schematic diagram of an optical setup for measuring the shear displacement of a birefringent device using a polarizer. Fig. 5B shows a block diagram of a corresponding system for measuring the shear displacement of a birefringent device using a polarizer.
Fig. 6 shows the intensity distribution collected by the data acquisition module and the results of the localization analysis. Fig. 6A shows the intensity distribution of two overlapping spots with mixed polarizations P + and P -. Fig. 6B shows the intensity distribution of a spot with polarization P +. Fig. 6C shows the intensity distribution of a spot with polarization P -.
Fig. 7 is a block diagram illustrating the procedure of a method of measuring shear angle and displacement of a birefringent device.
Detailed Description
A first optical setup for directly measuring the shear angle of a birefringent device is shown in fig. 2A. The beam 201 of diameter D is incident into a birefringent means that spatially shears the output beam 203 having polarization P + behind the shearing plane 202 by an angle epsilon with respect to the output beam 204 having polarization P -. Polarization P + and polarization P - are orthogonal to each other. A Polarization Control Unit (PCU) 209 is used to control the polarization state of the input beam 201 and to vary the intensity contributions to the P + and P – components of the output sheared beam. A lens 205 with a focal length f is used to focus the two sheared beams 203 and 204 into two spots 206 and 207 whose centers are separated by a in the focal plane, which is the fourier transform of the two beams in momentum space. The intensity distribution I (x, y) of the spot is collected by the recording means 208 at the focal plane. The centroid spacing between the two spots 206 and 207 is estimated as
The spot size of each beam in the focal plane is estimated as
Using conventional direct measurement, the necessary condition for resolving the two spots 206 and 207 in the image is Δ > d, i.eIn this system, the PCU 209 may be used to control the input beam polarization so that the intensity distribution of each spot can be collected separately at different camera frames to avoid spot overlap. The above operation is realized by the following steps: 1) At p=p +, an image showing P + polarized spot I + (x, y) is taken; 2) At p=p -, an image with a P - polarized spot I - (x, y) is taken.
Depending on the polarization state, the PCU includes different optical components. 1) In the case of unpolarized incident light, the PCU consists of a switchable polarizing filter for selecting either P + or P –. 2) In the case of polarized incident light, the PCU may be a half-wave plate or a combination of half-wave plates and quarter-wave plates for selecting P + or P-. Depending on the type of birefringent crystal used, the polarization components P + and P-are either linearly or circularly orthogonal to each other.
Fig. 2B shows a block diagram of a corresponding system for measuring the shear angle of a birefringent device in a first optical setting. To achieve the functionality of fig. 1A, the system consists of an illumination module 210 that emits a light beam, a PCU 209, a birefringent device 212, a lens module 215, and a data acquisition module 218.
Fig. 3A shows a second optical setup for directly measuring the shear angle of a birefringent device. Unlike the first optical arrangement in fig. 2A, a polarizer 309 is placed in front of the light intensity distribution recording device 208. In this arrangement, the incident beam includes a mixed polarization of both P + and P –, and the polarizer 309 in this arrangement allows only one polarization to pass through and be collected at 208. By switching the bypass of polarizer 309, intensities I + (x, y) and I - (x, y) at different data frames can be collected separately without overlapping.
Fig. 3B shows a block diagram of a corresponding system for measuring the shear angle of a birefringent device in a second optical setting. To achieve the functionality of fig. 3A, the system consists of an illumination module 310 that emits a light beam, a birefringent device 212, a lens module 215, a switchable polarizer 309 and a data acquisition module 218.
Fig. 4A shows a first optical setup for directly measuring the shear displacement of a birefringent device. The beam 401 is focused on a shear plane 402 where two output orthogonal polarization components 403 and 404 are laterally offset by a displacement S. The shear plane is then imaged by the imaging system 405 at a magnification M onto the light intensity distribution recording device 208. Finally, 208 collects two spots 406 and 407. The PCU 209 is used to control the polarization state of the incident beam so that I + (x, y) and I - (x, y) can be acquired at different data frames, respectively.
Fig. 4B shows a block diagram of a corresponding system for measuring the shear displacement of a birefringent device in a first optical setting. To achieve the functionality of fig. 4A, the system consists of an illumination module 410 that emits a focused beam of light, a PCU 209, a birefringent device 412, an imaging module 415, and a data acquisition module 218.
Fig. 5A shows a second optical setup for directly measuring the shear displacement of a birefringent device. A switchable polarizer 309 is placed in front of the light intensity distribution recording device 208. In this arrangement, the incident beam comprises mixed polarization states, i.e., P + and P-, the polarizer 309 in this arrangement allows only one polarization to pass and is collected at 208, such that the intensity distributions I + (x, y) and I - (x, y) are recorded separately at 208 at different data frames.
Fig. 5B shows a block diagram of a corresponding system for measuring the shear displacement of a birefringent device in a second optical setup. To achieve the functionality of fig. 5A, the system consists of an illumination module 510 that emits a focused beam of light with mixed polarization, a birefringent device 412, an imaging module 415, a polarizer 309, and a data acquisition module 218.
To illustrate the positioning analysis in this method without loss of generality, FIG. 6 shows that the optical shear of the birefringent device (FIG. 1A or FIG. 1B) is less than or equal toIs an example of (a). Three types of results collected by the data acquisition module 218 are presented: 1) FIG. 6A, intensity distribution 601I +(x,y)+I- (x, y); 2) FIG. 6B, intensity distribution 602I + (x, y); 3) Fig. 6C, intensity distribution 604I - (x, y). Clearly, the interval Δ cannot be resolved in fig. 6A. By the localization analysis, the position (x +,y+) of the centroid 603 of the spot 602 corresponding to the intensity distribution I + (x, y) and the position (x -,y-) of the centroid 605 of the spot 604 corresponding to the intensity distribution I - (x, y) are determined, respectively. The interval between these two positions can then be calculated as
The corresponding shear angle is determined by equation (1). The positioning accuracy is estimated as
Where σ is the standard deviation of the single spot intensity distribution, a is the pixel size of the data acquisition module, N is the number of photons collected, and b is the background noise. Since there is in principle no limit to the photon budget, N is limited only by the camera sensor saturation. Thus, considering system disturbances from the environment, such as mechanical vibrations and temperature fluctuations, it is possible to actually achieve nanometer positioning accuracy beyond the diffraction limit.
In order to measure the shear angle of the birefringent device in fig. 2 and 3, equation (1) is applied to obtain the value of the shear angle
The shear angle measurement accuracy or resolution is given by
For the typical configuration of f=10 cm in fig. 2 and 3, the nano-positioning accuracy is such that the shear angle measurement accuracy reaches 10 -8 rad.
To measure the shear displacement of the birefringent device of fig. 4 and 5, the shear displacement is determined by:
Fig. 7 summarizes the method and process of measuring and determining the shear angle epsilon and the shear displacement S. The type of birefringent device is checked beginning at step 701. If the task is to measure the shear angle epsilon, go to step 702 and use the settings in fig. 2 or fig. 3. In step 703, frame 1 with I + (x, y) and frame 2 with I - (x, y) are taken and the center positions (x +,y+) and (x -,y-) of frame 1 and frame 2 are obtained using a positioning analysis. In step 704, the separation distance between the two centers is obtained In step 705, a value of the shear angle is obtainedWhere f is the focal length of the lens system in fig. 2 and 3. If the task is to measure the shear displacement S, then go from 701 to step 706 and use the setup in FIG. 4 or FIG. 5. In step 707, frame 1 with I + (x, y) and frame 2 with I - (x, y) are taken, and the center positions (x +,y+) and (x -,y-) of frame 1 and frame 2 are obtained using a positioning analysis. In step 708, the separation distance between the two centers is obtainedIn step 709, a value of the shear displacement is obtainedHere, M is the lateral image magnification of the imaging module in fig. 4 and 5.
Claims (25)
1. A method for measuring a shear angle of a birefringent device, comprising:
Projecting a light beam on the birefringent means;
Dividing two orthogonal polarized output beams behind the birefringent device, the two orthogonal polarized output beams entering two different directions at a shearing angle, the two orthogonal polarized output beams being a first polarized beam and a second polarized beam;
focusing the two orthogonally polarized output beams using a lens system;
Placing a light intensity distribution recording device behind the lens system at a position where the light beam is focused;
recording a first frame in the light intensity distribution recording means using the first polarized light beam;
determining a first center position of the light intensity distribution in the first frame using a positioning analysis;
recording a second frame in the recording device using the second polarized light beam;
determining a second center position of the light intensity distribution in the second frame using a positioning analysis;
Calculating a separation distance between the first center position and the second center position; and
The shearing angle is calculated from the separation distance and the focal length of the lens system.
2. The method of claim 1, wherein the two orthogonal polarizations are two orthogonal linear polarizations or two orthogonal circular polarizations, depending on the type of the birefringent device.
3. The method of claim 1, wherein the lens system is a single lens system or a combined multi-lens system.
4. A first system for measuring a shear angle of a birefringent device, comprising:
a light irradiation module outputting a light beam;
A polarization control unit;
the birefringent means;
A lens module; and
A data acquisition module placed at a position where two light beams exceeding a diffraction limit resolution are focused and a spot center positioning analysis method,
The polarization control unit is used for controlling the polarization of the input light beam, so that the polarization of the output light beam from the light irradiation module can be switched between two orthogonal polarizations at different data frames, and therefore positioning accuracy exceeding diffraction limit resolution is achieved.
5. The first system of claim 4, wherein the polarization control unit is a polarizer in the case where the light beam is unpolarized, or the polarization control unit is a half-wave plate, or a combination of a half-wave plate and a quarter-wave plate, or other polarization unit.
6. The first system of claim 4, wherein the two orthogonal polarizations are two orthogonal linear polarizations or two orthogonal circular polarizations, depending on the type of the birefringent means.
7. The first system of claim 4, wherein the lens module is a single lens system or a combined multi-lens system.
8. The first system of claim 4, wherein the data acquisition module is a CCD camera or a CMOS camera.
9. A second system for measuring a shear angle of a birefringent device, comprising:
a light irradiation module outputting a light beam;
the birefringent means;
a lens module;
a switchable polarizing filter; and
A data acquisition module disposed at a position where two light beams exceeding a diffraction limit resolution are focused and a spot center positioning analysis method,
The switchable polarizing filter is used to select one of two orthogonally polarized light components passing through the filter at different data frames to achieve positioning accuracy beyond diffraction limited resolution.
10. The second system of claim 9, wherein the switchable polarizing filter is a linear polarizer or a circular polarizing filter, depending on the type of two orthogonal polarizations.
11. The second system of claim 9, wherein the two orthogonally polarized light components are two orthogonally linearly polarized lights or two orthogonally circularly polarized lights, depending on the type of the birefringent means.
12. The second system of claim 9, wherein the lens module is a single lens system or a combined multi-lens system.
13. The second system of claim 9, wherein the data acquisition module is a CCD camera or a CMOS camera.
14. A method for measuring the shear displacement S of a birefringent device, comprising:
projecting a beam focused on a shear plane of the birefringent device;
Splitting two orthogonally polarized output beams at the shear plane, the two orthogonally polarized output beams having a lateral shear displacement S, the two orthogonally polarized output beams being a first polarized beam and a second polarized beam;
Imaging the shear plane to a light intensity distribution recording means at an image magnification M using an imaging system;
Recording a first frame in the recording device using the first polarized light beam;
determining a first center position of the light intensity distribution in the first frame using a positioning analysis;
recording a second frame in the recording device using the second polarized light beam;
determining a second center position of the light intensity distribution in the second frame using a positioning analysis;
calculating a separation distance delta between the first central position and the second central position; and
The shear displacement S is calculated from the measured separation distance delta divided by the imaging magnification M, i.e. s=delta/M.
15. The method of claim 14, wherein the two orthogonal polarizations are two orthogonal linear polarizations or two orthogonal circular polarizations, depending on the type of the birefringent device.
16. A first system for measuring the shear displacement S of a birefringent device, comprising:
a light irradiation module outputting a focused light beam;
A polarization control unit;
The birefringent means having an s-shear plane when the input beam is focused;
An imaging module; and
The polarization control unit is used for controlling the polarization of an input light beam, so that the polarization of an output light beam from the irradiation module can be switched between two orthogonal polarizations at different data frames, and the positioning precision exceeding the diffraction limit resolution is realized.
17. The first system of claim 16, wherein the polarization control unit is a polarizer in the case that the input beam is unpolarized, or the polarization control unit is a half-wave plate, or a combination of a half-wave plate and a quarter-wave plate, or other polarization unit.
18. The first system of claim 16, wherein the two orthogonal polarizations are two orthogonal linear polarizations or two orthogonal circular polarizations, depending on the type of the birefringent means.
19. The first system of claim 16, wherein the imaging module is a single lens system or a multi-lens system.
20. The first system of claim 16, wherein the data acquisition module is a CCD camera or a CMOS camera.
21. A second system for measuring the shear displacement S of a birefringent device, comprising:
a light irradiation module outputting a focused light beam;
the birefringent means having an s-shear plane when the light beam is focused;
A switchable polarizing filter;
An imaging module; and
A data acquisition module and a spot centering analysis method placed at a position forming an image of the shear plane beyond the diffraction limited resolution, the switchable polarizing filter being used to select one of two orthogonal polarized light components passing through the filter at different data frames, thereby achieving positioning accuracy beyond the diffraction limited resolution.
22. The second system of claim 21, wherein the switchable polarizing filter is a linear polarizer or a circular polarizing filter, depending on the type of two orthogonal polarizations.
23. The second system of claim 21, wherein the two orthogonally polarized light components are two orthogonally linearly polarized lights or two orthogonally circularly polarized lights, depending on the type of the birefringent means.
24. The second system of claim 21, wherein the imaging module is a single lens system or a multi-lens system.
25. The second system of claim 21, wherein the data acquisition module is a CCD camera or a CMOS camera.
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| CN1786662A (en) * | 2005-12-21 | 2006-06-14 | 哈尔滨工业大学 | Double hole type measural apparatus for scattering angle of laser beam |
| CN201096526Y (en) * | 2007-08-22 | 2008-08-06 | 中国科学院上海光学精密机械研究所 | Phase-shifting lateral shearing interferometer |
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| JP2010002846A (en) * | 2008-06-23 | 2010-01-07 | Univ Nagoya | Multiple image polarization element group |
| TWM381175U (en) * | 2009-12-22 | 2010-05-21 | Li-Yu Lin | Improved ceramic radiator structure |
| CN102981268B (en) * | 2012-11-23 | 2014-11-05 | 西安交通大学 | Birefringent crystal beam splitter with adjustable lateral shearing quantity |
| CN103424195A (en) * | 2013-08-09 | 2013-12-04 | 中国科学院上海光学精密机械研究所 | Phase-shifting shearing interferometer by rotating crystal plate |
| CN103424196B (en) * | 2013-08-09 | 2015-10-28 | 中国科学院上海光学精密机械研究所 | Two flat-plate polarizing phase shift shearing interferometer |
| EP3055729A1 (en) * | 2013-10-07 | 2016-08-17 | Ramot at Tel-Aviv University Ltd. | Polarization-independent differential interference contrast optical arrangement |
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| CN1786662A (en) * | 2005-12-21 | 2006-06-14 | 哈尔滨工业大学 | Double hole type measural apparatus for scattering angle of laser beam |
| CN201096526Y (en) * | 2007-08-22 | 2008-08-06 | 中国科学院上海光学精密机械研究所 | Phase-shifting lateral shearing interferometer |
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