Self-correction calculation device and method for nanoscale infinitesimal displacement based on polarization image

Abstract

The invention discloses a self-correction calculation device and method for nanoscale infinitesimal displacement based on a polarization image, and relates to the technical field of optical interference precision metrology, and the device comprises a laser, a half-wave plate, a collimation system, a beam expander, a beam splitter, a wire grid polarizer, a movable reflection element, a quarter-wave plate and a polarization camera. Two circularly polarized light in the clockwise direction and the anticlockwise direction are obtained through light path design, different polarized light intensity information is obtained at the same time through single exposure by combining a polarization camera lens formed by a micro-polaroid array, the process of introducing phase shift for multiple times and shooting for multiple times is replaced with single exposure of a polarization camera, operation is easy, the device is simplified, and the cost is reduced. Data acquisition is free from interference of time factors; and only three groups of data are needed for phase calculation during displacement calculation, four phase calculation results can be obtained by measuring data for a single time, abnormal values are eliminated through self-checking, a mean value is solved, and checking of the data acquisition process and phase correction can be completed.

Description

Technical Field

[0001] This invention relates to the field of optical interferometry precision measurement technology, and in particular to a self-calibrating calculation device and method for nanoscale micro-displacements based on polarization images. Background Technology

[0002] Optical methods for measuring minute displacements generally convert the displacement of the object under test into an optical path difference. Then, by detecting the changes in the brightness of interference fringes (phase change) caused by the change in optical path difference, the displacement is deduced. In other words, the measurement of displacement is transformed into a measurement of phase. There are two traditional methods for obtaining phase change information: one is the "fringe counting" method, which converts the measurement of phase into counting the changes in fringe intensity. The accuracy of this method depends on the accuracy of the count of fringe intensity, and since the fringe count is generally an integer, it can only be estimated by one bit at most. Therefore, the highest accuracy of displacement measurement is only one order of magnitude lower than the wavelength of light, that is, tens of nanometers, and cannot achieve the measurement of nanometer-scale displacements. The second method is multi-step phase shifting technology. By actively introducing multiple known and precisely controlled phase modulations, and acquiring the interferograms of each phase shift for numerical calculation, the phase containing information about the object's surface height or displacement can be accurately calculated from the interference light intensity. While this method can accurately acquire phase information of the light field, its theoretical accuracy depends solely on the accuracy of the interferogram acquisition, enabling measurements of nanometer-level displacements. However, traditional multi-step phase-shifting techniques typically utilize spatial light modulators or precise displacement devices to control the phase shift, requiring multiple introductions of phase shifts and subsequent measurements to obtain phase information. This results in complex optical paths and low measurement efficiency. Furthermore, the data is susceptible to time-related factors due to the varying acquisition times of different phase shift values, leading to poor anti-interference capabilities. Additionally, traditional multi-step phase-shifting algorithms utilize all light intensity information to calculate the phase; a problem with any particular intensity information renders the phase calculation impossible, resulting in low error tolerance. In summary, both methods have their advantages but also significant limitations, such as low measurement accuracy, low error tolerance, complex and cumbersome equipment and operation, low measurement efficiency, and poor anti-interference capabilities. Summary of the Invention

[0003] To address the above problems, this invention proposes a self-correcting calculation device and method for nanoscale micro-displacement based on polarization images. It introduces phase shift through polarization technology: the phase difference changes after a clockwise and a counterclockwise circularly polarized light beam passes through a linear polarizer. Combined with a polarization camera using a lens composed of a micro-polarizer array, it achieves simultaneous acquisition of different polarization intensity information in a single exposure. This single exposure with a polarization camera replaces the process of multiple exposures with phase shifts, simplifying operation and streamlining the device. Since different polarization intensity data are acquired simultaneously, data acquisition is not affected by time factors. Furthermore, the use of a single-optical-path system based on a Fizeau interferometer further simplifies the optical path, and the high overlap of the two optical paths significantly improves resistance to vibration and other interference.

[0004] On the one hand, a self-correcting computing device for nanoscale micro-displacement based on polarization images includes a laser, a half-wave plate, a collimation system, a beam expander, a beam splitter, a wire grid polarizer, a movable reflective element, a quarter-wave plate, a polarization camera, and a displacement calculation module.

[0005] The laser emits horizontally polarized light, which is modulated into linearly polarized light oriented at 45° by a half-wave plate. After collimation by a collimating system, it is filtered and expanded by a beam expander to obtain expanded beam light. Rays perpendicular to the transmission axis of the linear grating polarizer are reflected by the polarizer to a beam splitter. Rays parallel to the transmission axis of the polarizer pass through the polarizer, are reflected by a movable reflective element, and then pass through the polarizer again to enter the beam splitter, where they are combined with the reflected light from the polarizer to form a combined beam. The combined beam is then split by a quarter-wave plate, converting it into two beams, one clockwise and one counterclockwise. After the circularly polarized beam enters the polarization camera, the polarization intensity is obtained. The displacement calculation module calculates the displacement of the movable reflective element based on the two sets of polarization intensities before and after displacement. The transmission axis of the linear grating polarizer is at 45° to the polarization direction of the linearly polarized light modulated by the half-wave plate. The polarization directions of the linear polarizers in the polarization unit of the polarization camera are 0°, 45°, 90° and 135°, respectively, and the interference intensity distribution of the four polarized lights after passing through the four linear polarizers is obtained. The movable reflective element reflects the incident light and performs nanometer-level displacement.

[0006] Preferably, the beam expander includes a microscope objective, a pinhole, and a lens connected in sequence. The microscope objective focuses the light onto the pinhole, which filters the light. The lens then converges the filtered divergent light into parallel light.

[0007] Preferably, the beam splitter is a beam splitter prism.

[0008] Preferably, the collimation system is a dual-plane mirror collimation system.

[0009] Preferably, the movable reflective element includes a plane mirror and a stepper motor; the stepper motor drives the plane mirror to perform nanometer-level displacement; the plane mirror reflects the incident light.

[0010] Preferably, the displacement calculation module calculates the displacement of the movable reflective element based on two sets of polarized light intensities before and after the displacement, as follows:

[0011] Three non-repeating polarized light intensities from the four polarized light intensities before displacement of the movable reflective element and the corresponding three polarized light intensities after displacement are selected. The phase change caused by the object displacement is calculated by solving the polarization light intensity equations simultaneously. The displacement value is calculated based on the relationship between the phase change and the displacement. A total of four displacement values ​​are obtained.

[0012] Calculate the average of the four displacement values. If the ratio of each displacement value to the average is less than a preset ratio threshold, the average is taken as the final displacement measurement result; otherwise, the displacement value with the largest deviation from the average is taken as the final displacement measurement result.

[0013] Preferably, the preset ratio threshold is 8%.

[0014] Preferably, the formulas for the four polarization light intensities before the displacement are as follows:

[0015] ;

[0016] in, , , and These represent the polarized light intensities corresponding to the filters at 0°, 45°, 90°, and 135° before displacement, respectively. Represents the amplitude constant of light; This indicates the phase of the reference light, i.e., the light reflected by the linear grid polarizer; This indicates the phase of the measured light, i.e., the light passing through the linear grid polarizer.

[0017] On the other hand, the self-correction calculation method based on nanoscale micro-displacements of polarization images includes the following steps:

[0018] S1, start the laser, and the displacement calculation module obtains the intensity of the polarized light before displacement;

[0019] S2, Move the movable reflective element, and the displacement calculation module obtains the intensity of the polarized light after displacement;

[0020] S3, the displacement calculation module calculates the displacement of the movable reflective element based on the polarized light intensity before and after the displacement.

[0021] Compared with the prior art, the present invention has the following beneficial effects:

[0022] (1) Based on the traditional multi-step phase shift technology, this invention introduces phase shift through polarization technology: the phase difference between a clockwise and a counterclockwise circularly polarized light beam changes after passing through a linear polarizer. Combined with a polarization camera lens composed of a micro-polarizer array, it achieves simultaneous acquisition of different polarization light intensity information in a single exposure. The process of multiple phase shifts and multiple shots is replaced by a single exposure of the polarization camera. The operation is simple and the device is streamlined. Since the data of different polarization light intensities are acquired simultaneously, the data acquisition is not affected by time factors.

[0023] (2) The present invention adopts a single optical path system based on Fizeau interferometer, which makes the optical path more concise and the two optical paths highly overlapped, greatly improving the ability to resist vibration and other interference;

[0024] (3) This invention requires only three sets of data to calculate the phase, and four phase calculation results can be obtained from a single measurement (single image), while traditional multi-step phase shift technology requires four sets of phase shift data to calculate the phase; by self-checking and removing outliers and calculating the average, the process of collecting data and the correction of the phase can be completed, thereby correcting the displacement measurement results. The data is more accurate and the measurement efficiency is higher. Attached Figure Description

[0025] The present invention will now be described in further detail with reference to the accompanying drawings;

[0026] Figure 1 This is a schematic diagram of the optical path of the self-calibrating computing device for nanoscale micro-displacement based on polarization images according to an embodiment of the present invention.

[0027] Figure 2 This is a flowchart of a self-calibration calculation method for nanoscale micro-displacement based on polarization images, according to an embodiment of the present invention.

[0028] Figure 3 This is a schematic diagram of the polarization array of the polarization camera in the self-calibration computing device for nanoscale micro-displacement based on polarization images according to an embodiment of the present invention; wherein, (a) represents the polarization array structure of the polarization camera; and (b) represents the polarization direction of four adjacent polarization units forming a 2×2 "superpixel" structure.

[0029] Figure 4 This is a schematic diagram showing the polarization angle relationship between vertically polarized light, horizontally polarized light, and a linear polarizer in the self-correction calculation method for nanoscale micro-displacement based on polarization images according to an embodiment of the present invention; wherein, (a) represents the propagation direction of vertically polarized light A (yellow) and horizontally polarized light B (blue), QW is a quarter-wave plate, and P is a polarizer; (b) represents the angle between the projection directions of the polarizer;

[0030] Reference numerals: 1. Laser; 2. Half-wave plate; 3. Plane mirror group; 4. Microscope objective; 5. Pinhole; 6. Lens; 7. Beam splitter prism; 8. Grid polarizer; 9. Plane mirror; 10. Stepper motor; 11. Quarter-wave plate; 12. Polarizing camera. Detailed Implementation

[0031] The present invention will be further described below through specific embodiments.

[0032] like Figure 1As shown, the self-correcting computing device for nanoscale micro-displacement based on polarization images includes: a laser 1, a half-wave plate 2, a plane mirror group 3, a microscope objective 4 (MO), a pinhole 5, a lens 6 (L), a beam splitter 7 (BS), a wire grid polarizer 8 (WGP), a plane mirror 9, a stepper motor 10, a quarter-wave plate 11 (QWP), and a polarization camera 12 (P-Cam).

[0033] The optical path system of the self-calibrating computing device for nanometer-scale micro-displacement based on polarization images is as follows:

[0034] In this embodiment, laser 1 is a He-Ne laser. The horizontally polarized light emitted by the He-Ne laser first passes through a half-wave plate 2, which modulates the original horizontally polarized light into linearly polarized light oriented at 45°. After being collimated by a plane mirror group 3, the linearly polarized light is filtered and expanded by a beam expander composed of a microscope objective 4, a pinhole 5, and a lens 6. Subsequently, it passes through a beam splitter (beam splitter prism 7) and then through a linear grating polarizer 8. The transmission direction of the linear grating polarizer 8 is at 45° to the polarization direction of the linearly polarized light. After transmission through the linear grating polarizer 8, the light is split into two beams with mutually perpendicular polarization directions. The P-polarized light, whose polarization direction is perpendicular to the transmission direction of the linear grating polarizer 8, is reflected back and used as a reference beam. The S-polarized light, whose polarization direction is parallel to the transmission direction of the linear grating polarizer 8, passes through the linear grating polarizer 8 and is then reflected by a plane mirror 9. The displacement of the plane mirror 9 is precisely controlled by a stepper motor 10. The reflected P-polarized light and the transmitted S-polarized light are recombined by a beam splitter (beam splitter prism 7) and then transmitted through a wire grid polarizer 8 to be converted into left and right circularly polarized beams. An interferogram is acquired using a polarization camera. By utilizing interferograms with different polarization directions (0°, 45°, 90°, and 135°), and employing a self-calibration calculation method based on the polarization image for nanoscale micro-displacement, the phase can be obtained non-invasively, thus enabling the measurement of minute displacements.

[0035] The plane mirror group 3, composed of two plane mirrors, can achieve a precise collimation effect. It should be noted that, in addition to the plane mirror group 3 composed of two plane mirrors, other collimation systems, such as single plane mirrors, can also be used to collimate linearly polarized light. The specific settings are determined according to the needs, and this embodiment does not impose any restrictions.

[0036] The flowchart of the method for measuring minute displacements is as follows: Figure 2 As shown. First, turn on laser 1 and polarization camera 12. The reference light and object light interfere with each other. Polarization camera 12 collects the interference intensity information of the two beams before the object under test is displaced. The polarization array in front of polarization camera 12 is shown in the figure. Figure 3 As shown, the polarization directions of four adjacent polarization units are 0°, 45°, 90° and 135° respectively, forming a 2×2 "superpixel" structure.

[0037] When two mutually perpendicular circularly polarized beams pass through a polarization angle of... After applying a linear polarizer, the intensity distribution of the two-light interference pattern is as follows:

[0038] ;

[0039] The polarization angles of light A and B with the linear polarizer are as follows: Figure 4 As shown, and These represent the phases of the two beams of light. This represents the phase difference between the two beams.

[0040] Therefore, the polarization intensity information obtained by the four arrays of polarization camera 12 The corresponding phase shifts are respectively .

[0041] ;

[0042] Compared to the traditional four-step phase-shifting algorithm, this method does not require four types of polarization intensity information to calculate the phase; instead, any three of these four types are sufficient. Therefore, there are four calculation combinations, meaning that four sets of data can be calculated from a single image. The specific calculation process is as follows:

[0043] The calculation combinations are as follows: 0°, 45°, 90°; 0°, 90°, 135°; 0°, 45°, 135°; 45°, 90°, 135°. Calculate the displacement data for each of the four combinations:

[0044] Group 1: Light intensity information at 0°, 45°, and 90°:

[0045] Solving the three equations simultaneously, we get:

[0046] ;

[0047] We can obtain:

[0048] ;

[0049] Take another picture after the object has shifted, and obtain... Let the phase change caused by the displacement of the object be... We can obtain:

[0050] ;

[0051] According to the trigonometric function relations, we can obtain... , represented as:

[0052] ;

[0053] Then, based on the relationship between phase change and displacement ,in, Given the wave number, a small displacement can be obtained. , represented as:

[0054] ;

[0055] The second group: Taking the light intensity information at 0°, 90°, and 135°, we can obtain:

[0056] ;

[0057] The third group: Taking the light intensity information at 0°, 45°, and 135°, we can obtain:

[0058] ;

[0059] Group 4: Taking the light intensity information at 45°, 90°, and 135°, we can obtain:

[0060] ;

[0061] After collecting the data, four displacements are calculated using four combinations. The average of the four displacements is then calculated, and the difference between each of the four displacements and the average is calculated. If the ratio of each of the four differences to the average is less than 8%, it proves that the four displacement data are correct, and the average is taken as the final displacement measurement result. Conversely, if any data has a deviation greater than 8%, it proves that a certain polarization intensity information is incorrect. According to the formula, one of the four displacement data must have been unaffected by this incorrect polarization intensity information during the calculation process. Therefore, the displacement data that was not affected, which is the data with the largest deviation from the average, is identified and taken as the final displacement measurement result.

[0062] In summary, this embodiment, based on traditional multi-step phase-shifting technology, introduces phase shift through polarization technology: the phase difference changes when two mutually perpendicular circularly polarized lights pass through a linear polarizer. Combined with a polarization camera using a lens composed of a micro-polarizer array, it achieves simultaneous acquisition of different polarized light intensity information in a single exposure. Furthermore, this algorithm can calculate four sets of phase data from a single image, achieving accurate phase calculation and enabling the measurement of nanometer-scale displacements. Compared to traditional techniques, this solution replaces multiple phase-shifting and multiple shooting processes with a single exposure using a polarization camera, simplifying operation and reducing device complexity. Since different polarized light intensity data are acquired simultaneously, data acquisition is not affected by time factors. Moreover, unlike traditional multi-step phase-shifting techniques that use four sets of phase shift data to calculate the phase, this method only requires three sets of data. A single measurement yields four phase calculation results. Through self-checking to remove outliers and averaging, the data acquisition process can be verified and the phase corrected, thereby correcting the displacement measurement results. This results in more accurate data and higher measurement efficiency. This embodiment employs a single-optical-path system based on a Fizeau interferometer, resulting in a more streamlined optical path and high overlap between the two optical paths, significantly improving resistance to vibration and other interference. In summary, compared to traditional solutions, the self-calibrating computational device for nanoscale micro-displacements based on polarization images in this embodiment offers higher accuracy, higher measurement efficiency, stronger anti-interference capabilities, and is more streamlined and easier to operate. The micro-displacement calculation method in this embodiment boasts higher efficiency and a higher fault tolerance. It overcomes the shortcomings of traditional methods, such as low accuracy, complex devices, and poor anti-interference capabilities, meeting the needs of cutting-edge fields such as microelectromechanical systems (MEMS) deformation detection and gravitational wave interferometers.

[0063] The above are merely specific embodiments of the present invention, but the design concept of the present invention is not limited thereto. Any non-substantial modifications made to the present invention using this concept shall be considered as infringing upon the protection scope of the present invention.

Claims

1. A self-calibrating computing device for nanoscale micro-displacement based on polarization images, characterized in that, It includes lasers, half-wave plates, collimation systems, beam expanders, beam splitters, wire grid polarizers, movable reflective elements, quarter-wave plates, polarization cameras, and displacement calculation modules; The laser emits horizontally polarized light, which is modulated into linearly polarized light oriented at 45° by a half-wave plate. After collimation by a collimating system, it is filtered and expanded by a beam expander to obtain expanded beam light. Rays perpendicular to the transmission axis of the linear grating polarizer are reflected by the polarizer to a beam splitter. Rays parallel to the transmission axis of the polarizer pass through the polarizer, are reflected by a movable reflective element, and then pass through the polarizer again to enter the beam splitter, where they are combined with the reflected light from the polarizer to form a combined beam. The combined beam is then split by a quarter-wave plate, converting it into two beams, one clockwise and one counterclockwise. After the circularly polarized beam enters the polarization camera, the polarization intensity is obtained. The displacement calculation module calculates the displacement of the movable reflective element based on the two sets of polarization intensities before and after displacement. The transmission axis of the linear grating polarizer is at 45° to the polarization direction of the linearly polarized light modulated by the half-wave plate. The polarization directions of the linear polarizers in the polarization unit of the polarization camera are 0°, 45°, 90° and 135°, respectively, and the interference intensity distribution of the four polarized lights after passing through the four linear polarizers is obtained. The movable reflective element reflects the incident light and performs nanometer-level displacement.

2. The self-calibration calculation device for nanoscale micro-displacement based on polarization images according to claim 1, characterized in that, The beam expander includes a microscope objective, a pinhole, and a lens connected in sequence. The microscope objective focuses the light onto the pinhole, which filters the light. The lens then converges the filtered divergent light into parallel light.

3. The self-calibration calculation device for nanoscale micro-displacement based on polarization images according to claim 1, characterized in that, The beam splitter is a beam splitter prism.

4. The self-calibration calculation device for nanoscale micro-displacement based on polarization images according to claim 1, characterized in that, The collimation system is a dual-plane mirror collimation system.

5. The self-correcting calculation device for nanoscale micro-displacement based on polarization images according to claim 1, characterized in that, The movable reflective element includes a plane mirror and a stepper motor; the stepper motor drives the plane mirror to perform nanometer-level displacement; the plane mirror reflects the incident light.

6. The self-calibration calculation device for nanoscale micro-displacement based on polarization images according to claim 1, characterized in that, The displacement calculation module calculates the displacement of the movable reflective element based on two sets of polarized light intensities before and after the displacement, as detailed below: Three non-repeating polarized light intensities from the four polarized light intensities before displacement of the movable reflective element and the corresponding three polarized light intensities after displacement are selected. The phase change caused by the object displacement is calculated by solving the polarization light intensity equations simultaneously. The displacement value is calculated based on the relationship between the phase change and the displacement. A total of four displacement values ​​are obtained. Calculate the average of the four displacement values. If the ratio of each displacement value to the average is less than a preset ratio threshold, the average is taken as the final displacement measurement result; otherwise, the displacement value with the largest deviation from the average is taken as the final displacement measurement result.

7. The self-correcting calculation device for nanoscale micro-displacement based on polarization images according to claim 6, characterized in that, The preset ratio threshold is 8%.

8. The self-calibration calculation device for nanoscale micro-displacement based on polarization images according to claim 6, characterized in that, The formulas for the four polarization light intensities before the displacement are: ； in, , , and These represent the polarized light intensities corresponding to the filters at 0°, 45°, 90°, and 135° before displacement, respectively. Represents the amplitude constant of light; This indicates the phase of the reference light, i.e., the light reflected by the linear grid polarizer; This indicates the phase of the measured light, i.e., the light passing through the linear grid polarizer.

9. A self-calibration calculation method for nanoscale micro-displacements based on polarization images, characterized in that, The self-calibrating computing device based on nanoscale micro-displacement of polarization image according to any one of claims 1-8 includes the following steps: S1, start the laser, and the displacement calculation module obtains the intensity of the polarized light before displacement; S2, Move the movable reflective element, and the displacement calculation module obtains the intensity of the polarized light after displacement; S3, the displacement calculation module calculates the displacement of the movable reflective element based on the polarized light intensity before and after the displacement.

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