CN113670456B - A Wavefront Restoration Method Using a Hartmann Wavefront Sensor with Adjustable Spatial Resolution - Google Patents

Abstract

A Hartmann wavefront sensor with adjustable spatial resolution and a wavefront restoration method belong to the field of photoelectric detection, and include an industrial computer; a focal length conversion device and a photoelectric detection device connected to the industrial computer; The direction is parallel to the normal direction of the measured beam; the wavefront dividing device is arranged between the focal length conversion device and the photoelectric detection device, and the receiving surface of the photoelectric detection device is located at the focal plane of the wavefront dividing device; the focal length conversion device collects the detected The light beam is focused on the receiving surface of the photoelectric detection device through the wavefront dividing device, and at the same time, array spot information is formed on the receiving surface of the photoelectric detection device, and the array spot information is recorded by the industrial computer and the wavefront restoration information is calculated. The invention can adjust the spatial resolution according to the actual detection requirement of the measured beam, further improve the detection performance of the wavefront sensor, improve the measurement accuracy under the condition of large dynamic range detection requirement, and provide a strong guarantee for high-precision wavefront detection.

Description

A wavefront complex using a Hartmann wavefront sensor with adjustable spatial resolution original method

technical field

The invention belongs to the technical field of photoelectric detection, and in particular relates to a Hartmann wavefront sensor with adjustable spatial resolution and a wavefront recovery method.

Background technique

The Hartmann wavefront sensor has the advantages of compact structure, strong anti-interference ability, and high utilization rate of light energy. It has been widely used in adaptive optics, optical detection, photoelectric detection and other fields.

The Chinese patent publication number CN1245904 discloses a classic structural form of the Hartmann wavefront sensor, which uses optical elements such as microlens arrays to spatially divide the wavefront of the incident light wave and divide the wavefront into multiple sub-regions. Finally, focus the beam of each sub-area on the receiving surface of the photodetector, and form a series of array spots on the receiving surface. Finally, by analyzing and processing the change information of the centroid of the array spot, combined with the corresponding recovery algorithm, Obtain the wavefront information of the measured beam. Because the wavefront sensor with this structure has the advantage of calibrating the system error, it is favored in practical engineering applications. Under the premise of large dynamic range requirements, how to improve the detection accuracy of Hartmann wavefront sensors has become a research hotspot.

The main factors affecting the detection accuracy of the Hartmann wavefront sensor are: information extraction, restoration algorithm, and structural form. In terms of information extraction, the accurate extraction of the spot centroid change information is the guarantee for the realization of high-precision wavefront restoration. Therefore, the accuracy of the wavefront detection can be improved by improving the accuracy of the centroid calculation. Method” (Li Jing, Gong Yan, etc. [J]. China Laser, 2014, 41(3)). In terms of wavefront recovery, the wavefront information of the measured beam can be accurately reconstructed according to the information provided by the centroid calculation. Therefore, by improving and optimizing the wavefront recovery algorithm, the accuracy can be effectively improved. For example, the Chinese Patent Publication No. CN102749143A discloses A wavefront reconstruction method to improve the measurement accuracy of the Shack-Hartmann wavefront sensor. In terms of structural form, the number of sub-regions divided by the wavefront can be increased by improving the spatial resolution to improve the accuracy of wavefront detection. Although the accuracy of wavefront reconstruction can be further improved by optimizing information extraction methods and wavefront reconstruction algorithms, spatial resolution is always a prerequisite for wavefront detection. When using the pattern method to restore the wavefront, it is impossible to decide how many orders of Zernike polynomials can be used to restore the measured wavefront, whether in terms of information extraction or wavefront restoration. The adoption of a sufficient order is the guarantee that the measured wavefront can be recovered in good condition. For example, when the measured beam contains 35th-order high-order aberrations, and the spatial resolution is only 2×2, under the condition of such spatial resolution, only low-order aberration components can be restored (the first 7th order) , cannot reflect the high-order term of the 35th order. Under such conditions, neither the information extraction nor the wavefront restoration algorithm can improve the accuracy, but only improve the spatial resolution. When the spatial resolution is increased to 10×10, it can restore the 65th-order aberrations. Under the premise of such spatial resolution, it is more meaningful to use the means of optimizing information extraction and the method of wavefront reconstruction algorithm.

However, there is currently a lack of a method that can effectively adjust the spatial resolution of the wavefront sensor. Therefore, it is urgent to develop a Hartmann wavefront that can further improve the accuracy of wavefront detection under the condition of a large dynamic range. sensor.

SUMMARY OF THE INVENTION

In order to solve the problem of how to improve the detection accuracy of the Hartmann wavefront sensor under the condition of large dynamic range, the present invention provides a Hartmann wavefront sensor with adjustable spatial resolution and a wavefront recovery method.

The technical scheme adopted by the present invention for solving the technical problem is as follows:

A Hartmann wavefront sensor with adjustable spatial resolution of the present invention includes:

industrial computer;

A focal length conversion device and a photoelectric detection device connected with the industrial computer, the optical axis direction of the focal length conversion device is parallel to the normal direction of the measured beam;

a wavefront dividing device arranged between the focal length conversion device and the photoelectric detection device, the receiving surface of the photoelectric detection device is located at the focal plane of the wavefront dividing device;

The focal length conversion device collects the detected light beam, focuses it on the receiving surface of the photoelectric detection device through the wavefront dividing device, and forms array spot information on the receiving surface of the photoelectric detection device, records the array spot information through the industrial computer and calculates the wavefront recovery. information.

Further, the focal length conversion device includes: a conjugate compensation device connected with the industrial computer, a first focal length free conversion device and a second focal length free conversion device installed on the conjugate compensation device; behind the first focal length free transformation device; the conjugate compensation device drives the first focal length free transformation device and the second focal length free transformation device to move along the optical axis direction.

Further, the focal length f _{1 of the first focal length free transformation device and the focal length f 2 of} the second focal length free transformation device satisfy:

(1) The optical interval L=f ₁ +f ₂ between the first focal length free transformation device and the second focal length free transformation device;

(2) The required magnification of the focal length conversion device 1 is β=f ₂ /f ₁ ;

(3) f ₁ =L/(1+β), f ₂ =βL/(1+β).

Further, the first focal length free transforming device and the second focal length free transforming device constitute a magnification transforming optical system, and the structural form of the magnification transforming optical system is a Kepler telescopic structure or a Galilean telescopic structure.

Further, when conjugate detection is required, the magnification conversion optical system selects a Kepler telephoto structure, the first focal length free conversion device and the second focal length free conversion device are both positive lenses, and the focal lengths f ₁ and f ₂ are both positive lenses. greater than zero; when there is no special requirement, the magnification conversion optical system adopts the Galilean telephoto structure, the first focal length free transforming device and the second focal length free transforming device are both positive lenses, the focal length f ₁ is less than zero, and the focal length f ₂ is greater than zero .

Further, the first focal length free transformation device adopts a liquid crystal spatial light modulator, a digital micromirror, a deformable mirror or a zoom optical lens group; the second focal length free transformation device adopts a liquid crystal spatial light modulator, a digital micromirror, a deformation mirror or zoom optics.

Further, the first focal length free transformation device and the second focal length free transformation device both use a liquid crystal spatial light modulator to realize focal length transformation, and the detected light beam is a rectangular square spot with a size of D=2mm×2mm; the first focal length The phase diagram of the free transformation device and the second focal length free transformation device satisfies the formula (1):

表示空间光调制器要生成的面型，x，y分别为坐标值；将f₁、f₂分别带入到公式(1)中，获得第一焦距自由变换装置与第二焦距自由变换装置所需要产生的面型。Among them, λ represents the wavelength of the measured beam, f represents the focal length of the focal length conversion device,

Represents the surface shape to be generated by the spatial light modulator, x and y are the coordinate values respectively; bring f ₁ and f ₂ into formula (1) respectively, to obtain the first focal length free transformation device and the second focal length free transformation device. The face shape that needs to be produced.

The wavefront restoration method realized by adopting a Hartmann wavefront sensor with adjustable spatial resolution of the present invention includes the following steps:

(1) The measured beam forms a converging beam through the first focal length free transforming device and converges at the focal point of the first focal length free transforming device, forms a diverging beam when it continues to transmit forward through the focus, and transmits to the second focal length free transforming device, After being collimated by the second focal length free transformation device, it enters the wavefront dividing device and is divided into a plurality of sub-regions, and an array light spot is formed at the receiving surface of the photoelectric detection device;

(2) Adjust the interval between the focal length conversion device and the wavefront dividing device by driving the conjugate compensation device through the industrial computer;

( ₃ ) The photoelectric detection device transmits the array light spot data at the receiving surface to the industrial computer, and records and stores the array light spot data through the industrial computer _; The corresponding surface shape is calculated by the gray-scale weighting method, and the centroid of the light spot is calculated according to formula (2), and the wavefront slope information is calculated according to the centroid offset information and formula (3), and the restoration method based on the pattern method is used to restore wavefront information, and control the first focal length free transformation device and the second focal length free transformation device to generate corresponding surface shapes, so as to realize the focal length transformation of the first focal length free transformation device and the second focal length free transformation device;

Among them, I _ij represents the light intensity of the (i, j)th pixel on the receiving surface of the photodetector, x _ij , y _ij represent the coordinates of the (i, j) th pixel, respectively, x _c , y _c represent the reference beam, respectively The centroid position of the light spot is formed at the sub-aperture;

表示微积分。Among them, L _k (x, y) represents the k-th Legendre polynomial, l represents the number of Legendre polynomial terms used in wavefront restoration; f represents the focal length of the focal length conversion device; a _k represents the k-th Legendre polynomial coefficients ; g _x (i) represents the slope in the X direction, g _y (i) represents the slope in the Y direction, s represents the number of sub-apertures, Δx represents the centroid offset in the X direction, Δy represents the centroid offset in the Y direction,

Represents calculus.

Further, in step (2), the moving direction of the conjugate compensation device is parallel to the transmission direction of the optical axis, and the adjustment amount is the focal length f ₂ of the second focal length free conversion device before zooming and the second focal length free after zooming. The difference between the focal length f ₂ ˊ of the conversion device is f ₂ ˊ-f ₂ ; when the difference is positive, it is adjusted in the opposite direction to the transmission direction of the optical axis, so that the conjugate compensation device is far away from the wavefront dividing device; When it is negative, it is adjusted in the same direction as the transmission direction of the optical axis, so that the conjugate compensation device is close to the wavefront division device.

Further, in step (3), adopt the restoration method based on the pattern method to restore the wavefront information, and the calculation process of the pattern method wavefront slope information is as follows:

G=L·A (4)

Among them, the column vector G is the wavefront slope information of the M sub-apertures in the X and Y directions; L is the reconstruction matrix when the wavefront is reconstructed by the mode method; A is the mode coefficient;

Using the least squares fitting method, the minimum norm solution is obtained:

A=L ⁺ ·G (5)

Among them, L ⁺ is the generalized inverse matrix of matrix L, and the coefficients are brought into formula (6) to obtain the wavefront slope φ(x, y):

where a _k represents the coefficient of the k-th Legendre polynomial.

The beneficial effects of the present invention are:

Although the accuracy of wavefront reconstruction can be further improved by optimizing information extraction methods and wavefront reconstruction algorithms, spatial resolution is always a prerequisite for wavefront detection. For example: when the number of sub-apertures of the wavefront dividing device 4 is 2x2, when the mode method is used to restore the wavefront, it can only restore the low-order aberration (first 5th-order aberration) components, but cannot detect high-order aberrations. For the first-order aberration components, it is difficult to detect the high-order aberration components even if the technical approach of optimizing the information extraction method and the wavefront reconstruction algorithm is adopted at this time. At this time, when the number of sub-apertures of the wavefront dividing device 4 is 9×9, more detailed information about the incident wavefront can be obtained at this time, and the aberration order that can be restored will be increased to 65th order, and the reconstructed wave The front type is more realistic. It can be seen that the expected effect of improving the reconstruction accuracy can be achieved only by optimizing the information extraction method and the wavefront reconstruction algorithm on the premise that the spatial resolution meets the requirements. In addition, when the wavefront detection of beams with different apertures is required, the spatial resolution of the traditional Hartmann wavefront sensor will decrease with the reduction of the aperture, thereby reducing the accuracy of wavefront detection.

To sum up, the present invention provides a Hartmann wavefront sensor with adjustable spatial resolution and a method for restoring wavefront. The Hartmann wavefront sensor with adjustable spatial resolution can To meet the detection requirements, adjust the spatial resolution to further improve the detection performance of the wavefront sensor.

In the present invention, the focal length conversion device is a device with adjustable focal length and capable of compensating for defocus aberration, wherein the first focal length free conversion device and the second focal length free conversion device in the process of magnification conversion, in addition to being able to realize focal length conversion , and can also play a role in eliminating aberrations and ensuring the beam quality of the system. The magnification of the magnification conversion optical system is adjusted by the focal length conversion device, the number of effective sub-apertures of the wavefront division device is controlled, and the spatial resolution is adjusted. Under the condition of large dynamic range detection requirements, the measurement accuracy can still be improved.

In the present invention, the wavefront dividing device is located between the focal length conversion device and the photoelectric detection device, which can focus the mapping beam on the receiving surface of the photoelectric detection device, and form the array spot information on the receiving surface of the photoelectric detection device, and then according to the array spot information Change the information and reconstruct the wavefront information of the measured beam.

The invention adopts the Hartmann wavefront sensor with adjustable spatial resolution for detection, and even when the size of the measured beam is relatively small, a higher spatial resolution can be achieved through magnification conversion, which is a high-precision wavefront detection. Provides a strong guarantee.

The wavefront restoration method realized by adopting the Hartmann wavefront sensor with adjustable spatial resolution of the present invention improves the spatial resolution and improves the detection accuracy of the wavefront under the condition of a large dynamic range detection requirement.

Description of drawings

FIG. 1 is a schematic structural diagram of a Hartmann wavefront sensor with adjustable spatial resolution according to the present invention.

FIG. 2 is a schematic diagram of the optical structure of the focal length conversion device.

FIG. 3 is a schematic diagram of the matching of the wavefront division device when β=2x in the first embodiment.

FIG. 4 is a residual diagram of wavefront reconstruction (RMS=0.022 μm) when β=2x in the first embodiment.

FIG. 5 is a schematic diagram of the matching of the wavefront division device when β=4x in the second embodiment.

FIG. 6 is a residual diagram of wavefront reconstruction (RMS=0.01 μm) when β=4x in the second embodiment.

In the figure, 1, focal length conversion device, 2, first focal length free conversion device, 3, second focal length free conversion device, 4, wavefront division device, 5, photoelectric detection device, 6, industrial computer, 7, conjugate compensation device.

Detailed ways

The present invention will be further described in detail below with reference to the accompanying drawings.

As shown in FIG. 1 , a Hartmann wavefront sensor with adjustable spatial resolution of the present invention mainly includes: a focal length conversion device 1 , a wavefront dividing device 4 , a photoelectric detection device 5 and an industrial computer 6 .

The focal length conversion device 1 is connected to the industrial computer 6 through a data line. The focal length conversion device 1 is placed at the front end of the system, the optical axis direction of the focal length conversion device 1 is parallel to the normal direction of the measured beam, and the optical axis of the focal length conversion device 1 is perpendicular to the wavefront dividing device 4 and the photodetecting device 5 . The focal length conversion device 1 can match the aperture of the light source to be detected and the size of the wavefront dividing device 4 . The focal length conversion device 1 is used for collecting the detected beam, for performing size transformation on the detected beam, adjusting the coverage area of the detected beam mapped to the wavefront dividing device 4, and changing the number of effective sub-apertures of the wavefront dividing device 4, thereby Change the spatial resolution.

The focal length transformation device 1 is mainly composed of a first focal length free transformation device 2 , a second focal length free transformation device 3 and a conjugate compensation device 7 . Both the first focal length free transformation device 2 and the second focal length free transformation device 3 are installed on the conjugate compensation device 7 . The second focal length free transforming device 3 is placed behind the first focal length free transforming device 2, that is, the first focal length free transforming device 2 is placed in front of the second focal length free transforming device 3, and the first focal length free transforming device 2 and the second focal length free transforming The optical separation between the devices 3 is L.

In the focal length conversion device 1, the focal length f1 of the first focal length free conversion device 2 and the focal length f2 _of the second focal length free conversion device ₃ satisfy the following geometric relationship:

(1) The optical interval of the focal length conversion device 1 is L=f ₁ +f ₂ ;

(2) The required magnification of the focal length conversion device 1 is β=f ₂ /f ₁ ;

(3) The focal length f ₁ of the first focal length free transformation device 2 =L/(1+β), and the focal length of the second focal length free transformation device 3 f ₂ =βL/(1+β).

The first focal length free conversion device 2 and the second focal length free conversion device 3 form a magnification conversion optical system. The structure of the magnification conversion optical system can be a Kepler-type telephoto structure or a Galileo-type telephoto structure, and can be arbitrarily used according to the needs of use. transformation, and can guarantee the beam quality of the system. When the conjugate detection needs to be satisfied, the Kepler-type telephoto structure is selected, as shown in (a) in Figure 2. At this time, the first focal length free transforming device 2 and the second focal length free transforming device 3 are both positive lenses , the focal lengths f ₁ and f ₂ are both greater than zero. When there is no special requirement, the Galilean telephoto structure is selected, as shown in (b) in Figure 2. At this time, the first focal length free transforming device 2 and the second focal length free transforming device 3 are both positive lenses, and the focal length f ₁ is less than zero and the focal length f ₂ is greater than zero.

The first focal length free transformation device 2 and the second focal length free transformation device 3 can be selected from liquid crystal spatial light modulators, digital micromirrors, deformable mirrors, zoom optical lens groups and other devices with zooming and aberration elimination functions.

In this embodiment, in order to meet the requirements of adaptive optics conjugate correction, the first focal length free transforming device 2 and the second focal length free transforming device 3 form a magnification transforming optical system using a Kepler-type telephoto capable of image transmission. structure.

In this embodiment, the optical distance L=30mm between the first focal length free transforming device 2 and the second focal length free transforming device 3, and the focal length of the first focal length free transforming device 2 is f ₁ =10 mm, then the second focal length free transforming device The focal length of 3 is f ₂ =β×f ₁ . The focal length of the first focal length free transformation device 2 is greater than the focal length of the second focal length free transformation device 3, and the image of the object is enlarged in the process of image transfer to meet the requirement of spatial resolution.

In this embodiment, both the first focal length free transforming device 2 and the second focal length free transforming device 3 use liquid crystal spatial light modulators to realize focal length transformation, and can eliminate defocus aberration, and the detected beam size is: D=2mm×2mm Rectangular square spot. When both the first focal length free transforming device 2 and the second focal length free transforming device 3 use liquid crystal spatial light modulators, their phase diagrams satisfy the relationship shown in formula (1):

表示空间光调制器要生成的面型，x，y分别为坐标值。将f₁、f₂分别带入到公式(1) 中，即可获得第一焦距自由变换装置2与第二焦距自由变换装置3所需要产生的面型。Among them, λ represents the wavelength of the measured beam, f represents the focal length of the focal length conversion device 1,

Indicates the surface shape to be generated by the spatial light modulator, x and y are the coordinate values respectively. Bringing f ₁ and f ₂ into formula (1) respectively, the surface shapes required by the first focal length free transforming device 2 and the second focal length free transforming device 3 can be obtained.

The conjugate compensation device 7 is connected to the industrial computer 6 through a data line. The conjugate compensation device 7 can drive the first focal length free transforming device 2 and the second focal length free transforming device 3 to move along the optical axis direction, and the movement amount is approximately equal to the difference between the focal lengths before and after the second focal length free transforming device 3 is adjusted.

The conjugate compensation device 7 is used to adjust the distance between the second focal length free transformation device 3 and the wavefront splitting device 4, which can ensure the conjugate relationship between the detected plane and the wavefront splitting plane, and meet the special requirements of the adaptive optics correction system .

The conjugate compensation device 7 can be selected as a mechanism with a linear displacement adjustment function driven by a motor, piezoelectric ceramics, or the like.

In this embodiment, the conjugate compensation device 7 adopts a linear displacement platform driven by piezoelectric ceramics, and its stroke is 30 mm.

The wavefront dividing device 4 is placed behind the second focal length free transforming device 3, and at the same time the wavefront dividing device 4 is placed in front of the photoelectric detecting device 5. The wavefront dividing device 4 is used to receive the light beam output by the focal length transforming device 1. The wavefront The dividing device 4 spatially divides the transformed light beam to form a plurality of sub-regions, and images the light beam in the divided sub-regions on the receiving surface of the photodetecting device 5 .

The normal direction of the sub-front of the wavefront splitting device 4 is consistent with the optical axis direction of the focal length conversion device 1, the overall size of the wavefront splitting device 4 is larger than the aperture of the detected light source, and the overall size of the wavefront splitting device 4 is the same as that of the photoelectric detection device. 5 to match the size of the receiving surface.

The wavefront dividing device 4 may adopt a continuous surface microlens array, a binary Fresnel microlens array or a gradient index microlens array.

In this embodiment, the wavefront dividing device 4 specifically adopts a continuous surface microlens array, the size of a single sub-aperture is 0.5 mm×0.5 mm, the overall size is 15 mm×15 mm, and the focal length is 30 mm.

In this embodiment, the wavefront splitting device 4 is coated with an anti-reflection film on both sides to improve energy utilization.

The photoelectric detection device 5 is connected with the industrial computer 6 through a data line. The receiving surface of the photodetection device 5 is located at the focal plane of the wavefront dividing device 4 . The size of the receiving surface of the photodetection device 5 matches the overall size of the wavefront dividing device 4 . The photodetection device 5 receives the image spot information in the sub-region divided by the wavefront dividing device 4, records the change information of the image spot in the sub-region, and further uses a corresponding reconstruction algorithm to reconstruct the wavefront aberration of the measured beam.

The photoelectric detection device 5 can be selected from photoelectric conversion devices such as a four-quadrant sensor, a CCD detector, or a CMOS detector.

In this embodiment, the photodetection device 5 specifically adopts a CCD detector, the resolution of the receiving surface is 1024×1024, the size of the pixel is 14 μm, and the size of the receiving surface is 14.336 mm×14.336 mm.

Utilizing a Hartmann wavefront sensor with adjustable spatial resolution of the present invention to realize the method for restoring the measured beam wavefront, the specific process is as follows:

1. Pass the measured beam through the first focal length free conversion device 2 to form a convergent beam, converge on the focus of the first focal length free conversion device 2, and form a diverging beam when it continues to transmit forward through the focus, and the diverging beam is transmitted to the second focal length free beam. The transformation device 3 is collimated, and after being collimated by the second focal length free transformation device 3, it enters the wavefront dividing device 4. After passing through the wavefront dividing device 4, it is divided into a plurality of sub-regions, which are formed at the receiving surface of the photoelectric detection device 5. Array spot.

The focal length conversion device 1 changes the magnification β by adjusting the focal length f 1 of the first focal length free conversion device ₂ and the focal length f ₂ of the second focal length free conversion device 3, and changes the spot area mapped to the wavefront dividing device 4 by β ² times , increasing the number of sub-apertures by (β ² -1) times the original.

2. The conjugate compensation device 7 is driven by the industrial computer 6 to adjust the interval between the focal length conversion device 1 and the wavefront division device 4 to meet the requirements of conjugate detection. The moving direction of the conjugate compensation device 7 is parallel to the transmission direction of the optical axis, and its adjustment amount is the focal length f ₂ of the second focal length free conversion device 3 before the zoom and the focal length f ₂ of the second focal length free conversion device 3 after the zoom. The difference between the two is f ₂ ˊ-f ₂ ; when the difference is positive, it is adjusted in the opposite direction to the transmission direction of the optical axis, so that the conjugate compensation device 7 is far away from the wavefront dividing device 4; when the difference is negative , and adjust in the same direction as the optical axis transmission direction, so that the conjugate compensation device 7 is close to the wavefront dividing device 4 .

3. Finally, the photoelectric detection device 5 transmits the array spot data at the receiving surface, that is, the light intensity information of the array spot, to the industrial computer 6 through the data line, and records and stores the array spot data through the industrial computer 6 . According to the relationship in formula (1), the requirements of focal length f ₁ and focal length f ₂ and the stored array spot data, the industrial computer 6 calculates the corresponding surface shape by using the grayscale weighting method, and calculates the centroid of the spot according to formula (2). , calculate the wavefront slope information according to formula (3), use the restoration method based on the pattern method to restore the wavefront information, and control the first focal length free transforming device 2 and the second focal length free transforming device 3 to generate the corresponding surface shape, to achieve The focal length transformation of the first focal length free transformation device 2 and the second focal length free transformation device 3 .

Among them, I _ij represents the light intensity of the (i, j)th pixel on the receiving surface of the photodetection device 5 , x _ij and y _ij represent the coordinates of the (i, j)th pixel respectively, and x _c and y _c represent the reference The beam forms the centroid of the spot at the sub-aperture.

According to the information of the centroid offset, the wavefront slope information is calculated according to formula (3).

表示微积分。Wherein, L _k (x, y) represents the k-th Legendre polynomial, and l represents the number of Legendre polynomial terms used in the wavefront restoration. f represents the focal length of the focal length conversion device 1 . a _k denotes the coefficients of the k-th Legendre polynomial. g _x (i) represents the slope in the X direction. g _y (i) represents the slope in the Y direction. s represents the number of sub-apertures. Δx represents the centroid offset in the X direction. Δy represents the offset of the center of mass in the Y direction.

Represents calculus.

Among them, the restoration method based on the pattern method is used to restore the wavefront information, and the calculation process of the wavefront slope information of the pattern method is as follows:

G=L·A (4)

Among them, the column vector G is the wavefront slope information of the M sub-apertures in the X and Y directions; L is the reconstruction matrix when the wavefront is reconstructed by the mode method; A is the mode coefficient. Using the least squares fitting method, the minimum norm solution can be obtained:

A=L ⁺ ·G (5)

Among them, L ⁺ is the generalized inverse matrix of matrix L, and the coefficients are brought into formula (6) to obtain the wavefront slope φ(x, y):

where a _k represents the coefficient of the k-th Legendre polynomial.

Specific implementation one

Assuming that the required magnification of the focal length transforming device 1 is β=2x, the focal length f ₁ =10mm of the first free focal length transforming device 2 and the focal length f ₂ =20 mm of the second free focal length transforming device 3 . At this time, the matching relationship between the size of the mapped light spot and the wavefront dividing device 4 is shown in FIG. 3 , and the number of effective sub-apertures is: 8×8. Using the restoration method of the present invention, the wavefront aberration information detected by the photoelectric detection device 5 is subtracted from the aberration actually contained in the measured beam, and the residual image of the wavefront reconstruction is obtained as shown in Figure 4. After restoration, the RMS ( rms) = 0.022 μm. The wavefront restoration residual is smaller, indicating that it is closer to the theoretical value and the measurement accuracy is higher.

Specific embodiment two

Assuming that the required magnification of the focal length conversion device 1 is β=3x, the focal length f ₁ of the first free focal length conversion device 2 is 10 mm, and the focal length of the second free focal length conversion device 3 is f ₂ =30 mm. At this time, the matching relationship between the size of the mapped light spot and the wavefront dividing device 4 is shown in FIG. 5 , and the number of effective sub-apertures is: 12×12. Using the restoration method of the present invention, the wavefront aberration information detected by the photoelectric detection device 5 is subtracted from the aberration actually contained in the measured beam, and the obtained residual image of the reconstructed wavefront is shown in Figure 6. After restoration, the RMS (root mean square value) = 0.01 μm. The wavefront restoration residual is smaller, indicating that it is closer to the theoretical value and the measurement accuracy is higher.

The above are only the preferred embodiments of the present invention. It should be pointed out that for those skilled in the art, without departing from the principles of the present invention, several improvements and modifications can be made. It should be regarded as the protection scope of the present invention.

Claims (8)

1. A wave front restoration method realized by adopting a Hartmann wave front sensor with adjustable spatial resolution is characterized in that the Hartmann wave front sensor with adjustable spatial resolution comprises the following steps:

an industrial personal computer (6);

the device comprises a focal length conversion device (1) and a photoelectric detection device (5) which are connected with an industrial personal computer (6), wherein the optical axis direction of the focal length conversion device (1) is parallel to the normal direction of a detected light beam;

a wavefront dividing device (4) arranged between the focal length transforming device (1) and the photodetection device (5), a receiving surface of the photodetection device (5) being located at a focal plane of the wavefront dividing device (4);

the focal length conversion device (1) collects the detected light beam, focuses the detected light beam on the receiving surface of the photoelectric detection device (5) through the wavefront segmentation device (4), forms array light spot information on the receiving surface of the photoelectric detection device (5), records the array light spot information through the industrial personal computer (6) and calculates wavefront restoration information;

the focal length conversion device (1) comprises: the device comprises a conjugate compensation device (7) connected with an industrial personal computer (6), and a first focal length free conversion device (2) and a second focal length free conversion device (3) which are arranged on the conjugate compensation device (7); the second focal length free conversion device (3) is arranged behind the first focal length free conversion device (2); the conjugate compensation device (7) drives the first focal length free conversion device (2) and the second focal length free conversion device (3) to move along the direction of an optical axis;

the method comprises the following steps:

(1) a measured light beam forms a converged light beam through a first focal length free conversion device (2) and converges at a focal point of the first focal length free conversion device (2), a divergent light beam is formed when the light beam is continuously transmitted forwards through the focal point and is transmitted to a second focal length free conversion device (3), the converged light beam enters a wavefront dividing device (4) after being collimated by the second focal length free conversion device (3) and is divided into a plurality of sub-apertures, and an array light spot is formed at a receiving surface of a photoelectric detection device (5);

(2) The interval between the focal length conversion device (1) and the wavefront dividing device (4) is adjusted by driving a conjugate compensation device (7) through an industrial personal computer (6);

(3) The photoelectric detection device (5) transmits the array light spot data at the receiving surface to the industrial personal computer (6), and the industrial personal computer (6) records and stores the array light spot data; the industrial personal computer (6) is in accordance with the formula (1) and the focal length f ₁ And focal length f ₂ According to the requirements and the array light spot data, a corresponding face type is calculated by using a gray scale weighting method, meanwhile, the centroid of the light spot is calculated according to a formula (2), the wavefront slope information is calculated according to centroid deviation information and a formula (3), the wavefront information is restored by adopting a mode method-based restoration method, the first focal length free conversion device (2) and the second focal length free conversion device (3) are controlled to generate corresponding face types, and the focal length conversion of the first focal length free conversion device (2) and the second focal length free conversion device (3) is realized;

wherein, I _ij Representing the light intensity, x, of the (i, j) th pixel on the receiving surface of the photo detection means (5) _ij 、y _ij Respectively represent the coordinates, x, of the (i, j) th pixel _c 、y _c Respectively representing the centroid positions of the reference beams forming the light spots in the sub-apertures;

wherein L is _k (x, y) represents the kth Legendre polynomial, and l represents the number of terms of the Legendre polynomial used in wavefront restoration; f represents the focal length of the focal length conversion device (1); a is a _k Coefficients representing the Legendre polynomial of the kth term; g is a radical of formula _x (i) Denotes the slope in the X direction, g _y (i) Denotes the slope in the Y direction, s denotes the number of sub-apertures, ax denotes the X-direction centroid shift, ay denotes the Y-direction centroid shift,

the calculus is represented.

2. A wavefront reconstruction method implemented by means of a hartmann wavefront sensor with adjustable spatial resolution as claimed in claim 1, characterized in that the focal length f of the first focal length free transformation means (2) ₁ And the focal length f of the second focal length free conversion device (3) ₂ Satisfies the following conditions:

(1) the optical distance between the first focal length free transformation device (2) and the second focal length free transformation device (3) is L = f ₁ +f ₂ ；

(2) Multiplying power beta = f required by focal length conversion device (1) ₂ /f ₁ ；

(3)f ₁ ＝L/(1+β)，f ₂ ＝βL/(1+β)。

3. The method for wavefront restoration by using the hartmann wavefront sensor with adjustable spatial resolution as claimed in claim 1, wherein the first focal length free transformation device (2) and the second focal length free transformation device (3) form a magnification transformation optical system, and the magnification transformation optical system is in a keplerian telescope structure or a galileo telescope structure.

4. The method for wavefront restoration by using a spatial resolution tunable Hartmann wavefront sensor according to claim 3, wherein when the requirement of conjugate detection is satisfied, the magnification conversion optical system selects a Kepler telescope structure, the first focal length free conversion device (2) and the second focal length free conversion device (3) are both positive lenses, and the focal length f is a positive lens ₁ 、f ₂ Are all larger than zero; when no special requirement exists, the magnification conversion optical system selects a Galileo telescopic structure, the first focal length free conversion device (2) is a negative lens, the second focal length free conversion device (3) is a positive lens, and the focal length f is ₁ Less than zero, focal length f ₂ Greater than zero.

5. The wave front restoration method implemented by the Hartmann wave front sensor with the adjustable spatial resolution as claimed in claim 1, characterized in that the first free focal length conversion device (2) adopts a liquid crystal spatial light modulator, a digital micromirror, a deformable mirror or a zoom optical mirror group; the second free focal length conversion device (3) adopts a liquid crystal spatial light modulator, a digital micromirror, a deformable mirror or a zooming optical mirror group.

6. The method for wavefront restoration by using the hartmann wavefront sensor with adjustable spatial resolution as claimed in claim 5, wherein the first focal length free transformation device (2) and the second focal length free transformation device (3) both use the liquid crystal spatial light modulator to realize focal length transformation, and the detected light beam is a rectangular square spot with a size of D =2mm x 2mm; the phase diagrams of the first focal length free transformation device (2) and the second focal length free transformation device (3) satisfy the formula (1):

wherein, λ represents the wavelength of the measured light beam, f represents the focal length of the focal length conversion device (1), phi (x, y) represents the surface type to be generated by the spatial light modulator, and x and y are coordinate values respectively; will f is mixed ₁ 、f ₂ And respectively substituting the obtained data into the formula (1) to obtain the surface shapes required to be generated by the first focal length free conversion device (2) and the second focal length free conversion device (3).

7. The method for wavefront restoration by using a Hartmann wavefront sensor with adjustable spatial resolution as claimed in claim 1, wherein in step (2), the movement direction of the conjugate compensation device (7) is parallel to the optical axis transmission direction, and the adjustment amount is the focal length f of the second focal length free transformation device (3) before zooming ₂ And the focal length f of the second focal length free conversion device (3) after zooming ₂ The difference of f ₂ ˊ-f ₂ (ii) a When the difference is positive, the transmission direction of the optical axis is adjusted in the opposite direction to make the conjugate complementThe compensation device (7) is far away from the wavefront dividing device (4); when the difference is negative, the optical axis transmission direction is adjusted in the same direction so that the conjugate compensation means (7) approaches the wavefront dividing means (4).

8. The method for wavefront reconstruction using a hartmann wavefront sensor with adjustable spatial resolution as claimed in claim 1, wherein in step (3), the wavefront information is reconstructed using a reconstruction method based on a pattern method, and the calculation process of the wavefront slope information of the pattern method is as follows:

G＝L·A (4)

the column vector G is the wave front slope information of the M sub-apertures in the X and Y directions; l represents a reconstruction matrix when wavefront reconstruction is carried out by adopting a mode method; a represents a mode coefficient;

and obtaining a minimum norm solution by using a least square fitting mode:

A＝L ⁺ ·G (5)

wherein L is ⁺ For the generalized inverse of matrix L, the wavefront slope φ (x, y) is obtained by substituting the coefficients into equation (6):

wherein, a _k Coefficients representing the Legendre polynomial of the k-th term.

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