A precise grating displacement measurement method based on vortex light excitation

Abstract

A kind of vortex light excitation precision grating measuring device, the present application carries topological charge vortex light beam as the excitation light source of grating, and displacement measurement is carried out using the interference of ±m order diffracted vortex light beam.Vortex light excitation precision grating measuring method and device, the displacement to be measured moves p / m corresponding interference petal pattern rotates a circle 2π, then the displacement to be measured corresponding to interference pattern rotation 1 ° is p / 360m.Compared with the precision measurement grating method using traditional light source excitation, grating interference sensing signal itself realizes higher optical subdivision multiple.Meanwhile, the electronic subdivision method of grating interference sensing signal changes from phase interpolation to circumference angle subdivision, circumference has 360 ° natural reference, avoids the influence of grating interference sensing signal quality on the effectiveness of phase interpolation subdivision, improves the resolution and precision of precision grating measurement in principle.

Description

Technical Field

[0001] This invention relates to the field of precision measurement technology, and in particular to a method and apparatus for measuring the displacement of a precision grating using vortex optical excitation. Background Technology

[0002] Precision displacement measurement technology, as a leading technological foundation for precision engineering and cutting-edge scientific development, has always been a research hotspot and a strategic high ground pursued and competed for by countries around the world. Among them, precision grating displacement sensing technology and devices, as one of the most promising cross-scale nanometer measurement technologies, are core basic functional components that determine the accuracy of high-end equipment, and their application scenarios have expanded from CNC machine tool modification to semiconductor manufacturing equipment.

[0003] The measurement resolution of a precision grating displacement measuring device is determined by both the grating pitch and the subdivision magnification (electronic subdivision, optical subdivision). However, the following problems currently exist in precision grating displacement measurement:

[0004] 1) The continuous reduction of grating pitch. By manufacturing smaller grating pitches, the measurement resolution can be improved. However, grating manufacturing needs to take into account both the grating pitch scale and the grating size. The manufacturing of small-pitch, large-format gratings is highly dependent on the precision of manufacturing equipment, the control of process parameters, and the guarantee of environmental conditions. It requires huge capital investment, long-term accumulation of process experience, and fundamental breakthroughs and developments in manufacturing processes.

[0005] 2) Implementation of electronic subdivision methods. By subdividing the grating sensing signal through interpolation, such as arctangent subdivision or phase-locked loop subdivision, the measurement resolution is improved. The higher the electronic subdivision magnification, the lower the dynamic response speed of the measuring device. Furthermore, subdivision error must be considered; otherwise, simply increasing the subdivision magnification is meaningless.

[0006] 3) Design of Optical Subdivision Structure. Existing methods achieve optical frequency doubling of the grating sensing signal and improve measurement resolution by selecting higher-order diffraction beams or increasing the diffraction order. In principle, optical frequency doubling does not affect the dynamic response characteristics of the measurement device; however, both increasing the diffraction order and increasing the diffraction number are accompanied by a significant decrease in beam energy, thus affecting signal strength and signal-to-noise ratio. In practical grating measurement device designs, second or fourth harmonics are generally chosen. There is an urgent need to invent new optical frequency doubling methods to improve the optical subdivision magnification of precision grating measurement devices. Summary of the Invention

[0007] To overcome the shortcomings of the prior art, this invention provides a precision grating displacement measurement device and method excited by a vortex beam. Compared with precision measurement grating methods using traditional light source excitation, the grating interference sensing signal itself achieves a higher optical subdivision factor based on the helical phase characteristics of the vortex beam. Simultaneously, the electronic subdivision method for the grating interference sensing signal changes from phase interpolation to circumferential angle subdivision. The circumference has a natural 360° reference, avoiding the influence of the grating interference sensing signal quality on the effectiveness of phase interpolation subdivision, thus fundamentally improving the resolution and accuracy of precision grating measurement.

[0008] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0009] A precision grating measurement device excited by a vortex beam includes a laser, a phase modulation device at the laser's exit, a reflector in front of the phase modulation device, a grating on the left side of the reflector, and two reflectors and three polarizing beam splitters. The two reflectors are a first reflector and a second reflector, positioned vertically opposite each other. The three polarizing beam splitters are a first polarizing beam splitter, a second polarizing beam splitter, and a third polarizing beam splitter. The first and second polarizing beam splitters are on one optical path, and the first and third polarizing beam splitters are on another optical path, arranged at right angles. A first quarter-wave plate is positioned between the first and second polarizing beam splitters, and a second quarter-wave plate is positioned between the first and third polarizing beam splitters. A first photodetector and a second photodetector are positioned on either side of the second polarizing beam splitter, and a third photodetector and a fourth photodetector are positioned on either side of the third polarizing beam splitter.

[0010] Furthermore, the phase modulation device is a spiral phase plate or a spatial light modulator.

[0011] Furthermore, a Dove prism is placed between the grating and the second reflecting mirror.

[0012] A method for precision grating measurement excited by a vortex beam includes the following steps.

[0013] Step 1): The laser emitted from the laser is converted into a vortex beam by a phase modulation device; the vortex beam is reflected by a mirror and hits the grating and diffracts, producing +m and -m order diffracted light; the laser emitted from the laser is converted into a Laguerre-Gaussian vortex beam carrying orbital angular momentum by a spatial light modulator, the characteristics of which are mainly characterized by the radial index n and the azimuth index l.

[0014] Step 2): The +m diffracted light enters the first polarization beam splitter after being reflected by the first reflecting mirror, and the -m diffracted light first passes through the Dowell prism and carries the opposite topological charge, and then enters the first polarization beam splitter through the second reflecting mirror.

[0015] Step 3): The first polarizing beam splitter splits the light into two beams. In one optical path, the +m order S beam and the -1 order P beam pass through the first quarter wave plate, and in the other optical path, the +m order P beam and the -1 order S beam pass through the second quarter wave plate.

[0016] Step 4): The two beams enter the second polarizing beam splitter and the third polarizing beam splitter again, and are split into two beams once more, forming circularly polarized light and interfering with each other, ultimately producing four coherent patterns.

[0017] Step 5): When the grating moves, the ±m-order diffracted light generates a phase difference Δφ. At this time, the phase change caused by the measured displacement corresponds to the rotation angle of the equally distributed interference pattern, and the rotation direction corresponds to the measured displacement direction. The measured grating displacement can be demodulated from the rotation angle information of the interference pattern.

[0018] Furthermore, the expressions for the vortex light fields with topological charge numbers (i.e., azimuth index) of l and -l are simplified as follows:

[0019] E l (r,θ)=R l (r)exp(ilθ) (1)

[0020] E -l (r,θ)=R l (r)exp(-ilθ) (2)

[0021] The amplitude of the electric field produced by the coherence of the two is:

[0022] E l (r,θ)+E -l (r,θ)=2R l (r)cos(lθ) (3)

[0023] When the grating moves, due to the Doppler frequency shift effect of the diffracted light, the +m and -m order diffracted light of the grating will produce a phase difference Δφ, the expression of which is:

[0024]

[0025] In the formula, x represents the displacement of the grating, and p represents the grating pitch. The above formula shows that the grating displacement x can be solved by the phase difference Δφ between the +m and -m order diffracted beams. At this point, the electric field amplitude generated by the coherence of the two diffracted beams is:

[0026]

[0027] As can be seen from formula (5), the phase change Δφ caused by the measured displacement x corresponds to the rotation angle of the equally distributed interference pattern, and the rotation direction corresponds to the direction of the measured displacement. In the precision grating measurement method excited by vortex light, the measured displacement movement p / m corresponds to the interference petal pattern rotating 2π times, so the measured displacement corresponding to the interference pattern rotating 1° is p / 360m.

[0028] Compared with the prior art, the beneficial effects of the present invention are:

[0029] 1) This invention adds a phase modulation device, such as a spiral phase plate or a spatial light modulator, to the optical path emitted from a laser source to synthesize a vortex beam with topological charge, thereby using the vortex beam to excite the grating.

[0030] 2) Vortex beams, carrying topological charges, can produce coherent patterns with unique intensity distributions when coherent. This characteristic can be used to transform the electronic subdivision processing method for grating interference signals from phase interpolation to circular angle subdivision. Moreover, the circumference has a natural 360° reference, avoiding the influence of interference signal quality on the effectiveness of phase interpolation subdivision, thus fundamentally improving the resolution and accuracy of grating measurements. Attached Figure Description

[0031] Figure 1 A front view of the precision grating measurement device excited by a vortex beam, as shown in the embodiment.

[0032] Figure 2 The image represents the coherent pattern generated by the vortex beam used in the embodiment, where l = 10 and n = 0.

[0033] Figure 3 The image represents the coherent pattern generated by the vortex beam used in the embodiment, where l = 0 and n = 3.

[0034] Figure 4 The image shows the coherent pattern generated by the vortex beam used in the embodiment, where l = 10 and n = 3.

[0035] The following labels are used in the diagram: Laser 1; Phase modulation device 2; Mirror 3; Grating 4; Dowell prism 5; First mirror 6; Second mirror 7; First polarizing beam splitter 8; First quarter wave plate 9; Second quarter wave plate 10; Second polarizing beam splitter 11; Third polarizing beam splitter 12; First photodetector 13; Third photodetector 14; Second photodetector 15; Fourth photodetector 16. Detailed Implementation

[0036] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0037] Example, refer to Figure 1 and Figure 2 A precision grating measurement device excited by a vortex beam includes a laser 1, a phase modulation device 2 at the exit of the laser 1, a reflector 3 directly in front of the phase modulation device 2, a grating 4 on the left side of the reflector 3, and two reflectors and three polarizing beam splitters. The two reflectors are a first reflector 6 and a second reflector 7, positioned vertically opposite each other. The three polarizing beam splitters are a first polarizing beam splitter 8, a second polarizing beam splitter 11, and a third polarizing beam splitter 12. The polarizing beam splitter 11 is on one optical path, while the first polarizing beam splitter 8 and the third polarizing beam splitter 12 are on another optical path. The three polarizing beam splitters are arranged at right angles. A first quarter-wave plate 9 is disposed between the first polarizing beam splitter 8 and the second polarizing beam splitter 11, and a second quarter-wave plate 10 is disposed between the first polarizing beam splitter 8 and the third polarizing beam splitter 12. A first photodetector 13 and a second photodetector 15 are disposed on both sides of the second polarizing beam splitter 11, and a third photodetector 14 and a fourth photodetector 16 are disposed on both sides of the third polarizing beam splitter 12.

[0038] Preferably, the phase modulation device 2 is a spiral phase plate or a spatial light modulator.

[0039] Preferably, a Dove prism 5 is disposed between the grating 4 and the second reflector 7.

[0040] A method for precision grating measurement excited by a vortex beam includes the following steps.

[0041] Step 1): The laser emitted from laser 1 is converted into a vortex beam by phase modulation device 2; the vortex beam is reflected by mirror 3 and hits grating 4 and diffracts, producing +m and -m order diffracted light.

[0042] The laser emitted by laser 1 is converted into a Laguerre-Gaussian vortex beam carrying orbital angular momentum by spatial light modulator 2. Its characteristics are mainly characterized by the radial index n and the azimuth index l.

[0043] Step 2): The +m diffracted light enters the first polarization beam splitter 8 after being reflected by the first reflecting mirror 6. The -m diffracted light first passes through the Dowell prism 5 and carries the opposite topological charge, and then enters the first polarization beam splitter 8 through the second reflecting mirror 7.

[0044] Step 3): The first polarizing beam splitter splits the light into two beams. In one optical path, the +m order S beam and the -1 order P beam pass through the first quarter wave plate 9. In the other optical path, the +m order P beam and the -1 order S beam pass through the second quarter wave plate 10.

[0045] Step 4): The two beams re-enter the second polarizing beam splitter 11 and the third polarizing beam splitter 12, respectively, and are split into two beams again, forming circularly polarized light and interfering with each other, ultimately producing four coherent patterns.

[0046] Step 5) When the grating moves, the ±m-order diffracted light generates a phase difference Δφ. At this time, the phase change caused by the measured displacement corresponds to the rotation angle of the equally distributed interference pattern, and the rotation direction corresponds to the measured displacement direction. Therefore, the measured grating displacement can be demodulated from the rotation angle information of the interference pattern.

[0047] When the radial exponent n and the azimuth exponent l have different values, the interference patterns of the conjugate vortex beams of ±m-order diffraction are shown in the attached figure. Figure 2 As shown, by using a 360° natural circumference reference, the rotation center of each interference fringe and interference pattern can be located through image processing fitting, enabling high-resolution precision measurement of the interference pattern rotation angle and the corresponding measured displacement. In the interference pattern, the finer and more uniformly and clearly the interference fringes are distributed, the better the signal processing accuracy and measurement resolution are improved.

[0048] Furthermore, the expressions for the vortex light fields with topological charge numbers (i.e., azimuth index) of l and -l are simplified as follows:

[0049] E l (r,θ)=R l (r)exp(ilθ) (1)

[0050] E -l (r,θ)=R l (r)exp(-ilθ) (2)

[0051] The amplitude of the electric field produced by the coherence of the two is:

[0052] E l (r,θ)+E -l (r,θ)=2R l (r)cos(lθ) (3)

[0053] When the grating moves, due to the Doppler frequency shift effect of the diffracted light, the +m and -m order diffracted light of the grating will produce a phase difference Δφ, the expression of which is:

[0054]

[0055] In the formula, x represents the displacement of the grating, and p represents the grating pitch. The above formula shows that the grating displacement x can be solved by the phase difference Δφ between the +m and -m order diffracted beams. At this point, the electric field amplitude generated by the coherence of the two diffracted beams is:

[0056]

[0057] As can be seen from formula (5), the phase change Δφ caused by the measured displacement x corresponds to the rotation angle of the equally distributed interference pattern, and the rotation direction corresponds to the direction of the measured displacement. In the precision grating measurement method and device excited by vortex light, the measured displacement movement p / m corresponds to the interference petal pattern rotating 2π times, so the measured displacement corresponding to the interference pattern rotating 1° is p / 360m.

[0058] The above description is merely a preferred embodiment of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention. All components not explicitly stated in this embodiment can be implemented using existing technology.

Claims

1. A method for measuring a precision grating excited by vortex light, the method being based on a precision grating measuring device excited by vortex light, the measuring device comprising a laser (1), a phase modulation device (2) disposed at the exit of the laser (1), a reflector (3) disposed directly in front of the phase modulation device (2), a grating (4) disposed to the left of the reflector (3), and further comprising two reflectors and three polarizing beam splitters, wherein, The two reflectors are a first reflector (6) and a second reflector (7), which are arranged vertically opposite each other. The three polarizing beam splitters are a first polarizing beam splitter (8), a second polarizing beam splitter (11), and a third polarizing beam splitter (12). The first polarizing beam splitter (8) and the second polarizing beam splitter (11) are on one optical path, and the first polarizing beam splitter (8) and the third polarizing beam splitter (12) are on another optical path. The optical prisms are arranged at right angles. A first quarter-wave plate (9) is disposed between the first polarizing beam splitter (8) and the second polarizing beam splitter (11), and a second quarter-wave plate (10) is disposed between the first polarizing beam splitter (8) and the third polarizing beam splitter (12). A first photodetector (13) and a second photodetector (15) are disposed on both sides of the second polarizing beam splitter (11), and a third photodetector (14) and a fourth photodetector (16) are disposed on both sides of the third polarizing beam splitter (12). A Dove prism (5) is disposed between the grating (4) and the second reflecting mirror (7); The measurement method is characterized by comprising the following steps: Step 1): The laser emitted from the laser (1) is converted into a vortex beam by the phase modulation device (2); the vortex beam is reflected by the mirror (3) and hits the grating (4) and diffracts, producing +m and -m order diffracted light; the laser emitted from the laser (1) is converted into a Laguerre-Gaussian vortex beam carrying orbital angular momentum by the spatial light modulator (2), and the characteristics of the vortex beam are mainly characterized by the radial index n and the azimuth index l; Step 2): The +m diffracted light enters the first polarization beam splitter (8) after being reflected by the first reflecting mirror (6), and the -m diffracted light first passes through the Dowell prism (5) and then carries the opposite topological charge, and then enters the first polarization beam splitter (8) through the second reflecting mirror (7). Step 3): The first polarizing beam splitter splits the light into two beams. In one optical path, the +m order S beam and the -1 order P beam pass through the first 1 / 4 wave plate (9), and in the other optical path, the +m order P beam and the -1 order S beam pass through the second 1 / 4 wave plate (10). Step 4): The two beams enter the second polarizing beam splitter (11) and the third polarizing beam splitter (12) again, and are split into two beams again, forming circularly polarized light and interfering with each other, ultimately producing four coherent patterns. Step 5): When the grating moves, the ±m-order diffracted light generates a phase difference Δφ. At this time, the phase change caused by the measured displacement corresponds to the rotation angle of the equally distributed interference pattern, and the rotation direction corresponds to the measured displacement direction. The measured grating displacement can be demodulated from the rotation angle information of the interference pattern. Step 5) specifically refers to: The expressions for the vortex light fields with azimuth indices l and -l are simplified as follows: From l (r,θ)=R l (r)exp(ilθ)(1) From -l (r,θ)=R l (r)exp(-ilθ)(2) The amplitude of the electric field produced by the coherence of the two is: E l (r,θ)+E -l (r,θ)=2R l (r)cos(lθ)(3) When the grating moves, due to the Doppler frequency shift effect of the diffracted light, the +m and -m order diffracted light of the grating will produce a phase difference Δφ, the expression of which is:

2. In the formula, x is the displacement of the grating, and p is the grating pitch; the above formula shows that the grating displacement x can be solved by the phase difference Δφ between the +m and -m order diffracted beams; at this time, the electric field amplitude generated by the coherence of the two diffracted beams is:

3. The phase change Δφ caused by the measured displacement x corresponds to the rotation angle of the equally distributed interference pattern, and the rotation direction corresponds to the direction of the measured displacement. In the precision grating measurement method excited by vortex light, the measured displacement movement p / m corresponds to one rotation of the interference petal pattern, and the measured displacement corresponding to 1° rotation of the interference pattern is p / 360m.

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