CN115585894A - Wavefront detection method for realizing extremely small four-wavefront transverse shear rate based on 4f system - Google Patents
Wavefront detection method for realizing extremely small four-wavefront transverse shear rate based on 4f system Download PDFInfo
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Abstract
The invention discloses a wavefront detection method for realizing extremely small transverse shear rate of four wavefronts based on a 4f system. The invention comprises a 4f system composed of two groups of aplanatic optical systems, a random coding mixed grating composed of an amplitude grating and a phase grating is arranged on an object plane, and the mixed grating is directly imaged on an image plane of a CCD photosensitive surface through the 4f system. The invention can realize that the shear rate of the four-wave front can reach minimum and high-precision detection is realized; by adjusting the wavefront of different positions behind the mixed grating to be positioned on the front focal plane of the 4f system, 4f imaging of interference wavefronts with different shearing amounts behind the grating can be realized, so that the variable shearing rate is realized, and the balance of high precision and high sensitivity is realized; the imaging method can also solve the defect that the CCD camera photosensitive surface is limited by similar protective glass and other physical structures and cannot be controlled to realize smaller shear rate, particularly for expensive and special cameras, image intensifiers and the like.
Description
Technical Field
The invention relates to a wavefront detection method for realizing extremely small transverse shear rate of four wavefronts based on a 4f system, and mainly relates to the field of optical wavefront detection and quantitative phase detection.
Background
The method for detecting the wave front of the common path by utilizing the four-wave front transverse shearing interference method generated by the random coding mixed grating consisting of the amplitude grating and the phase grating can be used for detecting the wave front of the common path, an additional reference light path is not needed, the anti-interference capability is strong, the shock insulation effect is good, the stability is high, and the high-precision wave front detection can be realized in the field and workshop environment. However, because the shear rate of the four-wavefront lateral shearing interference is related to the distance between the mixed grating and the CCD photosensitive surface, sometimes the CCD camera photosensitive surface is limited by similar protective glass and other physical structures, and it is impossible to control and realize a small shear rate, and it is difficult to realize the balance between high precision and high sensitivity. Especially for some very expensive and special cameras, image intensifiers and the like, the structures of the photosensitive surface and the protective glass are more complicated, and the realization of wavefront detection in a reasonable imaging mode is urgently needed. And in combination with a 4f system would solve this troublesome problem.
The 4f system is an optical information processing system that is often used to perform image operations, filtering, and transmission. The principle of image transmission by the 4f optical system is as follows: when the object to be measured is located on the input plane, the image is exactly located on the detection plane, wherein the input plane, i.e. the object plane and the detection plane image plane, are respectively connected with the Fourier lens group L 1 、L 2 Coincide. Thus, the invention provides a wavefront detection method for realizing extremely small transverse shear rate of four wavefronts based on a 4f system. And a random coding mixed grating consisting of an amplitude grating and a phase grating is arranged on the object plane, and the mixed grating is directly imaged on an image plane of the CCD photosensitive surface through a 4f system. Because the shearing rate is related to the distance between the mixed grating and the CCD photosensitive surface, the invention has the technical characteristics that the four-wave front shearing rate can be extremely low, and high-precision detection is realized; the wave front at the position behind the mixed grating is adjusted to be positioned on the front focal plane of the 4f system, so that the balance of high precision and high sensitivity is realized; the imaging method can also solve the defect that the CCD camera photosensitive surface is limited by similar protective glass and other physical structures and cannot be controlled to realize smaller shear rate, and the imaging method is particularly significant for expensive and special cameras, image intensifiers and the like and is used for realizing high-precision wavefront detection.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and realize a wavefront detection method with extremely small four-wavefront transverse shear rate based on a 4f system.
The wavefront detection system for realizing the minimum transverse shear rate of the four-wave front based on a 4f system comprises a laser beam S1, a collimation beam expander S2, a random coding mixed grating S3, a spherical aberration elimination lens group S4 and S6 and a CCD camera S7; wherein the collimating beam expander S2, the random coding mixed grating S3, the aplanatic lens groups S4 and S6 and the CCD camera S7 are arranged in sequence; the aplanatic lens groups S4 and S6 are respectively a first aplanatic lens S4 and a second aplanatic lens S6. Wherein, the target collection interference wavefront formed by the random coding mixed grating S3 is positioned at the front focal plane position of the first spherical aberration elimination lens S4; the first spherical aberration eliminating lens S4 and the second spherical aberration eliminating lens S6 are lenses with the same parameters, have the same focal length f, and the distance between the two is twice of the focal length f; wherein S5 is a middle frequency spectrum plane of the 4f wavefront detection system; where the CCD camera S7 is located at the back focal plane position of the 4f imaging system.
The method for realizing the wavefront detection with extremely small transverse shear rate of four wavefronts based on the 4f system comprises the following specific implementation steps:
adjusting the relative position and the angle posture of an incident laser beam S1 and a collimation beam expanding lens S2, so that the incident laser beam S1 passes through the collimation beam expanding lens S2 to generate a collimated beam with a larger aperture.
And (2) adjusting the position posture of the random coding mixed grating S3, so that the incident laser beam S1 passes through the grating to generate four-wave front transverse shear stripes.
And (3) adjusting a first spherical aberration eliminating mirror S4 and a second spherical aberration eliminating mirror S6 in the 4f imaging system to enable the transverse shearing wavefront to be located at the front focal plane position of the first spherical aberration eliminating mirror S4, setting the distance between the object plane and the rear end face of the random coding mixed grating S3 according to the shearing amount required by the four-wavefront transverse shearing interference system, taking the object plane position as the front focal plane position of the 4f imaging system, and adjusting the distance between the first spherical aberration eliminating mirror S4 and the second spherical aberration eliminating mirror S6 to be 2f.
And (4) adjusting the position of the CCD camera S7 on the back focal plane of the 4f imaging system to realize object image conjugation, and acquiring an interference imaging image formed after the interference fringes are imaged by the 4f imaging system.
And (5) demodulating the current four-wavefront transverse shearing interference imaging image through a demodulation algorithm of software, thereby obtaining a detection result of the wavefront to be detected.
The demodulation algorithm of the software is the existing algorithm and is the prior patent technical scheme of the inventor.
Step (6) of collecting ideal wavefront W 0 The light beam is incident to a four-wave front transverse shearing interference system based on a 4f system to form an interference image after being imaged, and a system error W is obtained as shown in figure 2 S (ii) a Then obtaining the measured distorted wavefront W t The distorted wavefront W t The wavefront after passing through the detection system is (W) t +W S ) Using a stored subtraction to obtain: (W) t +W S )-W S ＝W t And removing system errors to obtain accurate to-be-detected distorted wavefront.
And the mixed grating is imaged on a photosensitive surface of the image surface CCD camera by using a 4f imaging system, so that object image conjugation is realized. The transmittance equation after quantization coding of the random coding mixed grating S3 is as follows:
d is the grating pitch of the grating, N and M are the number of grids and the subdivision number of the quantization coding grids respectively, four wave front beams with certain transverse shearing quantity are generated after the wave front E (x, y) to be detected passes through the grating, interference wave front E (x, y) is generated by superposition of the four wave front beams, and the shearing quantity of the interference wave front is determined by the distance between the interference wave front E (x, y) and the rear end face of the grating. Since the interference wavefront E (x, y) is located at the front focal plane position of the 4f imaging system, the spectral equation of the focal plane is:
the frequency spectrum position is on the middle focal plane, and the image at the position of the back focal plane is as follows:
wherein E (x ', y') represents an image plane interferogram distribution function; (x ', y') represents image plane coordinates; f (F) x ,f y ) Represents a spectral distribution function, (f) x ,f y ) Representing the spectral coordinates. Therefore, the 4f imaging system used by the detection system is equivalent to performing Fourier transform twice on an interference wavefront (object plane), and an interference image with the magnification of-1 is formed at the position of an image plane, so that the system can acquire interferograms with different shearing amounts.
The invention has the following beneficial effects:
in the conventional transverse shearing interference, the mixed grating is directly arranged in front of a CCD camera, and the shearing rate of the system is related to the distance between the mixed grating and a CCD photosensitive surface. The invention can realize the extremely small four-wave front shear rate so as to achieve high-precision detection; 4f imaging of interference wavefront at different distances behind the grating can be realized by adjusting the position of the mixed grating in front of the 4f system, so that the variable shear rate is realized, and the balance of high precision and high sensitivity is realized; the imaging method can also solve the defect that the CCD camera photosensitive surface is limited by similar protective glass and other physical structures and cannot be controlled to realize smaller shear rate, and has important significance for realizing high-precision wavefront detection by using the invention especially for expensive and special cameras, image intensifiers and the like.
Drawings
FIG. 1 is a layout diagram of a wavefront sensing method based on a 4f system to achieve extremely small lateral shear rate of four wavefronts;
FIG. 2 is a schematic diagram of a method for eliminating system aberration of a 4f optical lens group in wavefront measurement;
FIG. 3 is a flow chart of wavefront sensing with minimal lateral shear rate of the four-wavefront using a 4f system;
FIG. 4 is an interferogram acquired by wavefront sensing with minimal four-wavefront lateral shear rate using a 4f system;
FIG. 5 is a diagram of the results of wavefront measurements with a 4f based system to achieve very low lateral shear rate of the four wavefronts with systematic errors removed, where (a) is a three-dimensional diagram and (b) is a two-dimensional diagram;
FIG. 6 is a systematic error map for four wavefront lateral shear wavefront sensing based on a 4f system using a standard light source, where (a) is a three-dimensional map and (b) is a two-dimensional map;
Detailed Description
The invention is further illustrated by the following examples in conjunction with the drawings.
As shown in fig. 1, a wavefront detection system based on a 4f system and capable of realizing a minimum four-wavefront transverse shear rate comprises a laser beam S1, a collimating beam expander S2, a random coding mixed grating S3, degaussing lens groups S4 and S6, and a CCD camera S7; wherein the collimating beam expander S2, the random coding mixed grating S3, the aplanatic lens groups S4 and S6 and the CCD camera S7 are arranged in sequence; the aplanatic lens groups S4 and S6 are respectively a first aplanatic lens S4 and a second aplanatic lens S6. Wherein, the target collection interference wavefront formed by the random coding mixed grating S3 is positioned at the front focal plane position of the first spherical aberration elimination lens S4; the first spherical aberration eliminating lens S4 and the second spherical aberration eliminating lens S6 are lenses with the same parameters, have the same focal length f, and the distance between the two is twice of the focal length f; wherein S5 is a middle frequency spectrum plane of the 4f wavefront detection system; where the CCD camera S7 is located at the back focal plane position of the 4f imaging system.
The method for realizing the wavefront detection with extremely small transverse shear rate of four wavefronts based on the 4f system comprises the following specific implementation steps:
adjusting the relative position and the angle posture of an incident laser beam S1 and a collimation beam expanding lens S2, so that the incident laser beam S1 passes through the collimation beam expanding lens S2 to generate a collimated beam with a larger aperture.
And (2) adjusting the position posture of the random coding mixed grating S3, so that the incident laser beam S1 passes through the grating to generate four-wave front transverse shear stripes.
And (3) adjusting a first spherical aberration eliminating mirror S4 and a second spherical aberration eliminating mirror S6 in the 4f imaging system to enable the transverse shearing wavefront to be located at the front focal plane position of the first spherical aberration eliminating mirror S4, setting the distance between the object plane and the rear end face of the random coding mixed grating S3 according to the shearing amount required by the four-wavefront transverse shearing interference system, taking the object plane position as the front focal plane position of the 4f imaging system, and adjusting the distance between the first spherical aberration eliminating mirror S4 and the second spherical aberration eliminating mirror S6 to be 2f.
And (4) adjusting the position of the CCD camera S7 on the back focal plane of the 4f imaging system to realize object image conjugation, and acquiring an interference imaging image formed after the interference fringes are imaged by the 4f imaging system.
And (5) demodulating the current four-wavefront transverse shearing interference imaging image through a demodulation algorithm of software, thereby obtaining a detection result of the wavefront to be detected.
The demodulation algorithm of the software is the existing algorithm and is the prior patent technical scheme of the inventor.
Step (6) of collecting ideal wavefront W 0 The light beam is incident to a four-wave front transverse shearing interference system based on a 4f system to form an interference image after being imaged, and a system error W is obtained as shown in figure 2 S (ii) a Then obtaining the measured distorted wavefront W t The distorted wavefront W t The wavefront after passing through the detection system is (W) t +W S ) Using the stored subtraction to yield: (W) t +W S )-W S ＝W t And removing system errors to obtain accurate to-be-detected distorted wavefront.
And imaging the mixed grating on the image surface CCD camera photosensitive surface by using a 4f imaging system to realize object image conjugation. The transmittance equation after quantization coding of the random coding mixed grating S3 is as follows:
d is the grating pitch of the grating, N and M are the number of grids and the subdivision number of the quantization coding grids respectively, four wave front beams with certain transverse shearing quantity are generated after the wave front E (x, y) to be detected passes through the grating, interference wave front E (x, y) is generated by superposition of the four wave front beams, and the shearing quantity of the interference wave front is determined by the distance between the interference wave front E (x, y) and the rear end face of the grating. Since the interference wavefront E (x, y) is located at the front focal plane position of the 4f imaging system, the spectral equation of the focal plane is:
the frequency spectrum position is on the middle focal plane, and the image at the position of the back focal plane is as follows:
therefore, the 4f imaging system used by the detection system equivalently performs Fourier transform twice on interference wavefront (object plane) and forms an interference image with the magnification of-1 at the position of the image plane, so that the system can acquire interference images with different shearing quantities.
Example 1:
examples of applications of the invention to wavefront sensing are described below:
as shown in fig. 1, a wavefront measurement optical path layout diagram for implementing wavefront measurement with extremely small four-wavefront lateral shear rate based on a 4f system is shown, and a measurement object of the system is a distorted wavefront introduced by a laser beam after being collimated and expanded. A light beam S1 incident from a helium-neon laser light source passes through a collimation beam expander S2 to generate a large-caliber collimation wavefront, and wavefront distortion is introduced by a system. The four-wave front transverse shearing interference wavefront generated after the wavefront to be detected passes through the random coding mixed grating S3 is positioned at the front focus of the 4f system, the four-wave front transverse shearing interference wavefront passes through the 4f system consisting of the spherical aberration eliminating lens groups S4 and S6 and then is imaged on a CCD camera S7 positioned on a back focus plane, and the S5 position is a middle frequency spectrum plane of the 4f system.
FIG. 3 is a flow chart of a method for realizing wavefront measurement with a minimum four-wavefront transverse shear rate by using a 4f system, wherein the equal height and the same axis of a light path are firstly adjusted, a laser of a light source input system and a collimation beam expander are adjusted to generate collimated light beams, a grating and the subsequent 4f system are adjusted, and an interference pattern is acquired by a CCD camera. The system firstly collects the system wavefront without introduced distortion, then collects the wavefront containing the distortion to be measured, and subtracts the system wavefront from the wavefront to obtain the distortion information to be measured. FIG. 4 is a diagram of a 4f system acquisition to obtain a wavefront interferogram produced by a randomly coded hybrid grating.
Fig. 5 (a) is a three-dimensional diagram of a wavefront obtained by demodulation; in FIG. 5, (b) is a two-dimensional graph having a PV value of 0.04. Lambda. And an RMS value of 0.01. Lambda. Fig. 6 is a systematic error diagram for implementing four-wavefront lateral shear wavefront measurement based on a 4f system using a standard light source, wherein (a) in fig. 6 is a three-dimensional diagram, and (b) in fig. 6 is a two-dimensional diagram, with a PV value of 0.19 λ and an RMS value of 0.04 λ. Meanwhile, the system is used for repeatability verification, the wavefront is collected once every 10 minutes for a certain wavefront, the system collects 10 wavefronts, and repeatability calculation is carried out, wherein repeatability deviation is shown in table 1, the maximum and minimum deviation of 10 PV values is 0.02 lambda, and the maximum and minimum deviation of RMS is 0.01 lambda.
Table 1: deviation of repeatability
| Measuring | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Mean value of | Maximum and minimum deviation |
| PV(λ) | 0.84 | 0.84 | 0.83 | 0.84 | 0.84 | 0.83 | 0.83 | 0.85 | 0.84 | 0.84 | 0.84 | 0.02 |
| RMS(λ) | 0.16 | 0.16 | 0.16 | 0.16 | 0.15 | 0.16 | 0.16 | 0.16 | 0.16 | 0.16 | 0.16 | 0.01 |
In the conventional transverse shearing interference, the mixed grating is directly arranged in front of the CCD camera, the shearing amount of the system is related to the distance l between the mixed grating and the photosensitive surface of the CCD camera, the smaller the shearing amount is, the larger the detection dynamic range of the system is, and the shearing amount s can be expressed as:
wherein lambda is the central wavelength of the light source, and d is the grating pitch. Under the limitation of a mechanical structure and the influence of protective glass in front of a photosensitive surface of a camera, the minimum l value can reach about 2.2mm, and when lambda is 632.8nm and d is 30 mu m, the minimum shear quantity s is 0.0656mm, but the shear quantity of a 4f imaging system can get rid of the limitation of the protective glass and the mechanical structure, and the shear quantity s can reach below 0.01mm, so that the dynamic range of system detection is improved.
Claims (5)
1. The wavefront detection system for realizing the minimum transverse shear rate of the four-wavefront based on a 4f system is characterized by comprising a laser beam S1, a collimating beam expander S2, a random coding mixed grating S3, spherical aberration elimination lens groups S4 and S6 and a CCD camera S7; wherein the collimating beam expander S2, the random coding mixed grating S3, the aplanatic lens groups S4 and S6 and the CCD camera S7 are arranged in sequence; the aplanatic lens groups S4 and S6 are respectively a first aplanatic lens S4 and a second aplanatic lens S6; wherein, the target collection interference wavefront formed by the random coding mixed grating S3 is positioned at the front focal plane position of the first spherical aberration elimination lens S4; the first spherical aberration eliminating lens S4 and the second spherical aberration eliminating lens S6 are lenses with the same parameters, have the same focal length f, and the distance between the two is twice of the focal length f; wherein S5 is a middle frequency spectrum plane of the 4f wavefront detection system; where the CCD camera S7 is located at the back focal plane position of the 4f imaging system.
2. The wavefront detection method for realizing the extremely small transverse shear rate of the four wavefronts based on the 4f system is characterized by comprising the following steps of:
adjusting the relative position and the angle posture of an incident laser beam S1 and a collimation beam expanding lens S2 to enable the incident laser beam S1 to generate a collimated beam with a larger aperture after passing through the collimation beam expanding lens S2;
adjusting the position posture of a random coding mixed grating S3 to enable an incident laser beam S1 to generate four-wave front transverse shear stripes after passing through the grating;
step (3) adjusting a first spherical aberration eliminating mirror S4 and a second spherical aberration eliminating mirror S6 in a 4f imaging system to enable transverse shearing wavefronts to be located at the front focal plane position of the first spherical aberration eliminating mirror S4, setting the distance between an object plane and the rear end face of the random coding mixed grating S3 according to the shearing quantity required by a four-wavefront transverse shearing interference system, taking the object plane position as the front focal plane position of the 4f imaging system, and adjusting the distance between the first spherical aberration eliminating mirror S4 and the second spherical aberration eliminating mirror S6 to be 2f;
adjusting the position of a CCD camera S7 on a back focal plane of a 4f imaging system to realize object image conjugation, and acquiring an interference imaging image formed after interference fringes are imaged by the 4f imaging system;
demodulating the current four-wavefront transverse shear interference imaging image by using a demodulation algorithm of software so as to obtain a detection result of the wavefront to be detected;
step (6) of collecting ideal wavefront W 0 The light beam is incident to a four-wave front transverse shearing interference system based on a 4f system to form an interference imaging image after being imaged, and a system error W is obtained S (ii) a Then obtaining the measured distorted wavefront W t The distorted wavefront W t The wavefront after passing through the detection system is (W) t +W S ) Using a stored subtraction to obtain: (W) t +W S )-W S ＝W t And removing system errors to obtain accurate to-be-detected distorted wavefront.
3. The wavefront detection method based on the 4f system to realize the minimum transverse shear rate of the four wavefronts according to claim 2, wherein the 4f imaging system is used to image the mixed grating on the image plane CCD camera photosensitive plane to realize the object-image conjugation; the transmittance equation after quantization coding of the random coding mixed grating S3 is as follows:
d is the grating pitch of the grating, N and M are respectively the grid number and the subdivision number of the quantization coding grid, four wave front beams with certain transverse shearing amount are generated after the wave front E (x, y) to be detected passes through the grating, interference wave front E (x, y) is generated by superposition of the four wave front beams, and the shearing amount of the interference wave front is determined by the distance between the interference wave front E (x, y) and the rear end face of the grating; since the interference wavefront E (x, y) is located at the front focal plane position of the 4f imaging system, the spectral equation of the focal plane is:
the frequency spectrum position is on the middle focal plane, and the image at the position of the back focal plane is as follows:
wherein E (x ', y') represents an image plane interferogram distribution function; (x ', y') represents image plane coordinates; f (F) x ,f y ) Represents a spectral distribution function, (f) x ,f y ) Representing spectral coordinates; therefore, the 4f imaging system used by the detection system equivalently performs Fourier transform on the interference wavefront twice, and an interference image with the magnification of-1 is formed at the image surface position, so that the system can acquire interferograms with different shearing amounts.
4. The wavefront detection method based on the 4f system to realize the minimum transverse shear rate of the four wavefronts according to claim 2 or 3, wherein the method adjusts the wavefront after the mixed grating to be located on the front focal plane of the 4f system, so that the shear rate is minimum, and high-precision detection is achieved; meanwhile, the shear rate can be changed by adjusting the front focal plane of the 4f system of the wave fronts at different positions behind the mixed grating, so that the balance of high precision and high sensitivity is realized; and finally, the defects that the photosensitive surface of the CCD camera is limited by protective glass and other physical structures and cannot be controlled to realize smaller shear rate are overcome through the aplanatic lens groups S4 and S6.
5. The wavefront sensing method of claim 1 with minimal four-wavefront lateral shear rate based on a 4f system; characterized in that the method is applicable to different laser wavelengths.
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