CN117451322B - Off-axis multi-inverse wavefront measurement method based on phase deflection - Google Patents
Off-axis multi-inverse wavefront measurement method based on phase deflection Download PDFInfo
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Abstract
本发明提供了一种基于相位偏折的离轴多反波前测量方法，涉及波前测量技术领域，该方法包括：获取多个不同相位和不同周期的正弦条纹图像，并进行灰度化处理，屏幕分别在至少两个不同的位置处，依次将灰度化处理后的正弦条纹图像显示到屏幕上，通过离轴多反光学系统后经过圆孔光阑在相机的焦平面处成像，得到多个正弦条纹成像图像，并对其进行相位解包裹，得到绝对相位，基于绝对相位计算相应位置处的波前斜率，对波前斜率进行积分重建，得到离轴多反波前面型。本发明中采用圆孔光阑可以根据相机焦点位置的不同进行灵活的调整，放置到准确的位置，并且根据离轴多反光学系统的口径选取屏幕满足测量需求，从而实现测量范围大、精度高的目的。
The present invention provides an off-axis multi-reflection wavefront measurement method based on phase deflection, which relates to the field of wavefront measurement technology. The method comprises: obtaining a plurality of sinusoidal fringe images with different phases and different periods, and performing grayscale processing, and displaying the grayscale processed sinusoidal fringe images on the screen in turn at at least two different positions, and imaging them at the focal plane of the camera through an off-axis multi-reflection optical system through a circular aperture diaphragm to obtain a plurality of sinusoidal fringe imaging images, and performing phase unwrapping on them to obtain an absolute phase, and calculating the wavefront slope at the corresponding position based on the absolute phase, and performing integral reconstruction on the wavefront slope to obtain an off-axis multi-reflection wavefront shape. The circular aperture diaphragm used in the present invention can be flexibly adjusted according to different camera focus positions and placed at an accurate position, and the screen is selected according to the aperture of the off-axis multi-reflection optical system to meet the measurement requirements, thereby achieving the purpose of a large measurement range and high precision.
Description
Technical Field
The invention relates to the field of wavefront measurement, in particular to an off-axis multi-inverse wavefront measurement method based on phase deviation.
Background
Currently, wavefront measurement is a key technology that can measure and analyze the phase information of light waves to understand the wavefront distortion in an optical system. In this context, research and development of wavefront measurement methods has become critical, and different wavefront measurement methods have to be employed in different optical systems and application scenarios.
Among the existing wavefront measurement methods, the first type of wavefront measurement method is to directly measure the wavefront phase of an object, for example, using a tatmann interferometer, a fizeau interferometer, etc., but is easily limited by the curvature measurement range, and is mainly applicable to near-spherical and near-planar optical elements. The second type of wavefront measurement method is to first measure the slope of the wavefront and then reconstruct the wavefront by an integration method. This method is excellent in terms of sensitivity and real-time, but is complicated in terms of processing of data and low in accuracy.
Therefore, a wavefront measurement method with a large measurement range and high accuracy is needed.
Disclosure of Invention
The present invention aims to solve at least to some extent one of the technical problems in the prior art. Therefore, the invention aims to provide the off-axis multi-inverse wavefront measuring method based on phase deflection, which has the advantages of large measuring range and high precision.
The technical scheme is as follows: an off-axis multiple inverse wavefront measurement method based on phase deflection, comprising:
Acquiring a plurality of sinusoidal fringe images with different phases and different periods, and carrying out graying treatment on the sinusoidal fringe images to obtain sinusoidal fringe gray scale images;
Sequentially displaying a plurality of sine stripe gray images at least two different positions through a screen, wherein the sine stripe gray images are incident to an off-axis multi-reflection optical system;
after the multiple reflection of light rays is carried out on the gray level images of the sinusoidal stripes based on the plurality of sinusoidal stripes incident on the off-axis multi-reflection optical system, imaging is carried out on the focal plane of the camera through a round hole diaphragm, and a plurality of sinusoidal stripe imaging images are obtained;
According to a multi-frequency phase unwrapping method, phase unwrapping is carried out on the plurality of sinusoidal fringe imaging images, and absolute phases of the plurality of sinusoidal fringe imaging images are obtained;
Calculating a wavefront slope at a corresponding position of the absolute phase through a Southwell area method model based on the absolute phase;
And carrying out integral reconstruction on the wavefront slope to obtain an off-axis multi-reflection wavefront model.
Furthermore, before the plurality of sinusoidal fringe gray scale images are sequentially displayed at least two different positions through the screen, calibrating the perpendicularity of the screen and the optical axis of the off-axis multi-reflection optical system and calibrating the focal positions of the circular aperture diaphragm and the off-axis multi-reflection optical system are further included.
Further, the calibration of the perpendicularity of the screen and the optical axis of the off-axis multi-reflection optical system comprises the following steps:
Two identical circles with certain intervals are projected onto a screen, and are incident into an off-axis multi-reflection optical system to be imaged at a focal plane of a camera through a round aperture diaphragm after being reflected for multiple times by light rays;
Calculating a first distance between circle centers of two circles after imaging;
the screen moves on the bottom plate, a second distance between the centers of the two circles at the focal plane of the camera is calculated, and a distance difference value between the first distance and the second distance is calculated;
Rotating a screen vertically connected to the electric turntable, and calculating distance difference values corresponding to circle centers of two imaged circles under different rotation angles of the screen;
obtaining a corresponding relation between the rotating angle and the distance difference value according to the corresponding distance difference value and the rotating angle;
and determining the rotation angle of the screen when the distance difference value is minimum through a particle swarm optimization algorithm based on the corresponding relation, and determining the rotation angle of the screen at the moment as a perpendicularity calibration angle.
Further, the calibration of the focal position of the round hole diaphragm and the off-axis multi-reflection optical system comprises the following steps:
Projecting any circle onto a screen, and imaging the random circle at a focal plane of a camera through a round aperture diaphragm after the random circle is incident into an off-axis multi-reflection optical system and subjected to multiple reflections of light rays;
calculating the size of an imaged circle through an image processing algorithm;
moving the round hole diaphragm on the bottom plate along with the track, and obtaining a corresponding relation between the moving distance and the size of the imaged circle by using an interpolation fitting algorithm;
and determining the focal position of the round aperture diaphragm when the circle is maximum after imaging through an ant colony algorithm based on the corresponding relation, and determining the position of the round aperture diaphragm at the moment as a focal calibration position.
Further, the calculating, based on the absolute phase, the wavefront slope at the corresponding position of the absolute phase by using a Southwell area method model includes:
determining the corresponding relation between the same phase point on the screen and the camera pixel according to a multi-frequency phase unwrapping method;
determining the ray direction of the incident ray by utilizing a ray tracing method based on the corresponding relation;
tangent line processing is carried out on the light rays, and the position points where the light rays are deflected are determined;
the wavefront slope at the corresponding position of the absolute phase is calculated by Southwell area method model.
Further, the sinusoidal fringe image comprises a transverse sinusoidal fringe image and a longitudinal sinusoidal fringe image, and the transverse sinusoidal fringe image and the longitudinal sinusoidal fringe image are subjected to graying processing, wherein the formula of the graying processing is expressed as follows:
Z＝I×255
Wherein, T 0 is the period of the set sine stripe image, X re is the transverse resolution of the screen, Y re is the longitudinal resolution of the screen, step is the phase shift number of the sine stripe image, and Z is the conversion from the sine stripe image to the gray image between 0 and 255.
Further, the formula of the multi-frequency phase unwrapping is expressed as:
Φ(x,y)＝ψ(x,y)+2π×k(x,y)
Where Φ (x, y) is the absolute phase of the sinusoidal fringe pattern, ψ (x, y) is the wrapping phase of the sinusoidal fringe pattern, and k (x, y) is the order of the sinusoidal fringe pattern.
Further, the formula for calculating the wavefront slope at the corresponding position of the absolute phase through Southwell area method model is expressed as follows:
Where g jk represents the number of active phase points at the current point. Phi jk is the effective phase value of the current point; Represents the slope in the Y-direction and, Represents the X-direction slope and N represents the matrix dimension.
Further, after the off-axis multi-reflection wavefront form is obtained, the method further includes:
Calculating the wavefront aberration of the off-axis multi-reflection wavefront surface type;
fitting 36 coefficient values of the wavefront aberration through a Zernike fitting algorithm;
subtracting the product sum of the first three terms of Zernike and the eighth term matrix and the corresponding coefficient from the wave-front image measured by the unwrapped phase, and recalculating the wave-front aberration of the off-axis multi-reflection wave-front surface;
And obtaining the off-axis multi-inverse wave front type after error removal based on the wavefront aberration.
Further, the wavefront aberration is expressed as:
Where W (x, y) is a wavefront aberration, W' (x, y) is a recalculated wavefront aberration. a nm is a coefficient of Zernike, Z (x, y) is a polynomial of Zernike, n and m are integers, n is an order of the polynomial, m is an angular frequency of the polynomial, generally n is a non-negative even number, and m is an integer satisfying-n.ltoreq.m.ltoreq.n.
The beneficial effects are that: according to the method, firstly, a plurality of sine stripe images with different phases and different periods are obtained, the gray processing is carried out, the screen is respectively arranged at least two different positions, the sine stripe images after the gray processing are sequentially displayed on the screen, are incident into the off-axis multi-reflection optical system, are imaged at the focal plane of the camera through the round aperture diaphragm after being reflected for multiple times by light rays in the off-axis multi-reflection optical system, the round aperture diaphragm can be flexibly adjusted according to different focal positions of the camera, and can be flexibly placed to an accurate position due to small volume, a plurality of sine stripe imaging images are obtained, the screen with different sizes is selected according to the caliber of the off-axis multi-reflection optical system to meet the measurement requirement, the multiple sine stripe imaging images are subjected to phase unwrapping by the multi-frequency phase unwrapping method, the absolute phase is obtained, the wavefront slope at the corresponding position is calculated based on the absolute phase, and the wavefront slope is subjected to integral reconstruction, so that the off-axis multi-reflection wavefront type is obtained.
Drawings
FIG. 1 is a schematic flow chart of an off-axis multi-inverse wavefront measurement method based on phase deviation according to the present invention;
FIG. 2 is a schematic diagram of a system structure of an off-axis multi-inverse wavefront measurement method based on phase deviation according to the present invention;
FIG. 3 is a schematic diagram of an optical measurement system according to the off-axis multi-inverse wavefront measurement method based on phase deviation;
FIG. 4 is a schematic diagram of a system light path of an off-axis multi-reflection optical system in an off-axis multi-reflection wavefront measurement method based on phase deviation according to the present invention;
fig. 5 is a schematic diagram of a measurement flow of an off-axis multi-inverse wavefront measurement method based on phase deviation according to the present invention.
Reference numerals:
I, a control and analysis module; II, off-axis multi-reflection optics; III, a high-precision measuring module; 1. a device base plate; 2. off-axis multi-reflecting system upright posts; 3. an off-axis multi-reflection optical system; 4. a round aperture stop; 5. a camera; 6. a Z-displacement stage; 7. an X-axis displacement stage; 8. a screen; 9. a device system housing; 10. an electric turntable.
Detailed Description
The following describes the embodiments of the present invention in further detail with reference to the drawings.
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments of the present invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
It should be noted that: like reference numerals and letters denote like items in the following figures, and thus once an item is defined in one figure, no further definition or explanation thereof is necessary in the following figures. Meanwhile, in the description of the present application, the terms "first", "second", and the like are used only to distinguish the description, and are not to be construed as indicating or implying relative importance.
As described in the background, wavefront measurement is a key technology that can measure and analyze the phase information of light waves to understand the wavefront distortion in an optical system. In this context, research and development of wavefront measurement methods has become critical, and different wavefront measurement methods have to be employed in different optical systems and application scenarios.
Among the existing wavefront measurement methods, the first type of wavefront measurement method is to directly measure the wavefront phase of an object, for example, using a tatmann interferometer, a fizeau interferometer, etc., but is easily limited by the curvature measurement range, and is mainly applicable to near-spherical and near-planar optical elements. The second type of wavefront measurement method is to first measure the slope of the wavefront and then reconstruct the wavefront by an integration method. This method is excellent in terms of sensitivity and real-time, but is complicated in terms of processing of data and low in accuracy.
In order to solve the problems in the prior art, the invention provides an off-axis multi-inverse wavefront measurement method based on phase deflection, and the off-axis multi-inverse wavefront measurement method based on phase deflection provided by the embodiment of the invention is introduced below.
Fig. 1 shows a schematic flow chart of an off-axis multi-inverse wavefront measurement method based on phase deviation. As shown in fig. 1, the off-axis multi-inverse wavefront measurement method based on phase deviation specifically includes the following steps:
S1, acquiring a plurality of sine stripe images with different phases and different periods, and carrying out graying treatment on the sine stripe images to obtain sine stripe gray images;
s2, sequentially displaying a plurality of sine stripe gray images at least two different positions through a screen, wherein the sine stripe gray images are incident to an off-axis multi-reflection optical system;
s3, imaging a plurality of sine stripe gray images based on the light rays reflected for multiple times by the sine stripe gray images incident on the off-axis multi-reflection optical system at the focal plane of the camera through the round hole diaphragm to obtain a plurality of sine stripe imaging images;
s4, performing phase unwrapping on the plurality of sinusoidal fringe imaging images according to a multi-frequency phase unwrapping method to obtain absolute phases of the plurality of sinusoidal fringe imaging images;
s5, calculating the wavefront slope at the corresponding position of the absolute phase through a Southwell area method model based on the absolute phase;
S6, carrying out integral reconstruction on the wavefront slope to obtain an off-axis multi-reflection wavefront model.
The method comprises the steps of firstly acquiring a plurality of sine stripe images with different phases and different periods, carrying out graying treatment, sequentially displaying the sine stripe images subjected to the graying treatment on a screen at least two different positions on the screen, entering an off-axis multi-reflection optical system, imaging the light rays in the off-axis multi-reflection optical system at a focal plane of a camera through a round aperture diaphragm after multiple reflections of the light rays in the off-axis multi-reflection optical system, flexibly adjusting the round aperture diaphragm according to different focal positions of the camera, flexibly placing the round aperture diaphragm to an accurate position due to small volume to obtain a plurality of sine stripe imaging images, selecting screens with different sizes according to the caliber of the off-axis multi-reflection optical system to meet measurement requirements, carrying out phase unwrapping on the plurality of sine stripe imaging images by utilizing a multi-frequency phase unwrapping method to obtain absolute phases, calculating wavefront slopes at corresponding positions based on the absolute phases, and carrying out integral reconstruction on the wavefront slopes to obtain off-axis multi-reflection wavefront patterns.
A specific implementation of each of the above steps is described below.
In some embodiments, in S1, as shown in fig. 2, the present invention includes a control and analysis module i, an off-axis multi-reflection optical ii, and a high precision measurement module iii, wherein the control and analysis module i is composed of an upper computer control software, the off-axis multi-reflection optical ii is composed of an off-axis multi-reflection optical system and a shafting movement mechanism screen, and the high precision measurement module iii is composed of a camera sensor and a shafting movement mechanism screen. Firstly, generating a plurality of sinusoidal fringe images with different phases and periods by utilizing a sixteen-step phase shift method according to screen resolution by utilizing upper computer control software, wherein the sinusoidal fringe images comprise transverse sinusoidal fringe images and longitudinal sinusoidal fringe images, the sinusoidal fringe images are used for subsequent screen projection, and the sinusoidal fringe images with the minimum frequency or the maximum period are required to cover the whole measured object by one period.
The method comprises the steps of carrying out graying treatment on a plurality of transverse sinusoidal fringe images and longitudinal sinusoidal fringe images with different phases and periods, wherein the graying treatment formula of the transverse sinusoidal fringe images is as follows:
Where T 0 is the period of the set sinusoidal fringe image, X re is the lateral resolution of the screen, step is the sinusoidal fringe image phase step number.
The graying processing formula of the longitudinal sine stripe image is as follows:
where T 0 is the period of the set sinusoidal fringe image, Y re is the longitudinal resolution of the screen, step is the sinusoidal fringe image phase step number.
And carrying out gray level conversion on the horizontal sinusoidal fringe image and the longitudinal sinusoidal fringe image which are subjected to gray level treatment, wherein the following formula is adopted:
Z＝I×255
where Z is a sinusoidal fringe image converted to a gray scale image between 0 and 255.
In some embodiments, after acquiring a plurality of sinusoidal fringe images of different phases and different periods, the screen 8 is controlled to move at least two different positions by the high-precision X-ray displacement table 7, and at each position, the screen 8 sequentially displays a plurality of sinusoidal fringe gray scale images, the sinusoidal fringe gray scale images are incident on the off-axis multi-reflection optical system 3, the off-axis multi-reflection optical system 3 is supported by the off-axis multi-reflection system column 2, and the sinusoidal fringe gray scale images are imaged onto the focal plane of the camera 5 by the off-axis multi-reflection optical system 3 for capturing, as shown in fig. 3. The screen 8 is moved by using the high-precision X-ray displacement stage 7 and captured a plurality of times to obtain sinusoidal fringe gray scale images at different positions. The screen with different sizes can be selected according to the caliber of the off-axis multi-reflection optical system 3 to meet the measurement requirement, and the device system shell 9 is used as a protective cover to prevent people from entering. As shown in fig. 4, the light rays in the off-axis multi-reflecting optical system 3 can undergo three reflections, and the camera 5 collects an image of each sinusoidal fringe gray scale image imaged by the off-axis multi-reflecting optical system 3. For reflected light rays, a unique surface shape point and a normal vector corresponding to the unique surface shape point are obtained, and the problem of uncertainty of the surface shape and the normal vector is effectively solved by the method. At the same time, the method can be used for measuring transparent surfaces, discontinuous surfaces and surfaces with large curvature.
The step S2 is also specifically followed by calibrating the perpendicularity of the screen and the optical axis of the off-axis multi-reflection optical system and calibrating the focal position of the round aperture diaphragm and the off-axis multi-reflection optical system.
Calibration of screen and off-axis multiple reflection optical system optical axis straightness that hangs down includes:
s2-1, projecting two identical circles with a certain interval onto a screen, and imaging the two circles on a focal plane of a camera through a circular aperture after being incident into an off-axis multi-reflection optical system and subjected to multiple reflection of light;
S2-2, calculating a first distance between circle centers of two circles after imaging;
s2-3, performing position movement on the screen on the bottom plate, calculating a second distance between circle centers of two circles at a focal plane of the camera, and calculating a distance difference between the first distance and the second distance;
S2-4, rotating a screen vertically connected to the electric turntable, and calculating distance difference values corresponding to circle centers of two imaged circles under different rotation angles of the screen;
s2-5, according to the corresponding distance difference value and the rotating angle, obtaining the corresponding relation between the rotating angle and the distance difference value;
s2-6, determining the rotation angle of the screen when the distance difference value is minimum through a particle swarm optimization algorithm based on the corresponding relation, and determining the rotation angle of the screen at the moment as a perpendicularity calibration angle.
In some embodiments, in order to quickly adjust the perpendicularity of the screen 8 with the optical axis of the off-axis multi-reflection optical system 3, a quick calibration algorithm is adopted in the present invention to ensure the perpendicularity of the screen 8 with the optical axis of the off-axis multi-reflection optical system 3.
For example, the screen 8 is simply placed at the entrance pupil position of the off-axis multi-reflecting optical system 3, and the circular aperture stop 4 is placed at the exit pupil position of the off-axis multi-reflecting optical system 3. The Z-displacement table 6 can move in cooperation with the position of the circular aperture stop 4, two circles with the same size and a certain distance are projected on the screen 8, and the two circles with the same size are imaged on the focal plane of the camera 5 through the off-axis multi-reflection optical system 3 and the circular aperture stop 4. A first distance d 1 between the centers of the two circles is calculated by a computer and stored in the computer. The screen 8 is moved in position on the base plate, imaged again at the focal plane of the camera 5, and a second distance d 2 between the centers of the two circles is calculated by the computer. And calculates a distance difference Δd between the first distance d 1 and the second distance d 2. And rotating the electric turntable 10 below the screen 8, calculating a distance difference value delta d corresponding to the circle centers of the two imaged circles under different rotation angles of the screen 8, and solving the corresponding relation between the rotation angles and the distance difference value through a best fit algorithm. When Δd is at a minimum, it is close to 0, which means that the screen 8 is best perpendicular to the optical axis of the off-axis multi-reflection optical system 3. According to the positive and negative values and the size, the angles and the angle values of different rotations of the electric turntable 10 are adjusted, the optimal position of the position is found through a particle swarm optimization method, at the moment, Δd reaches the minimum value, the perpendicularity of the screen 8 and the optical axis of the off-axis multi-reflection optical system 3 is considered to be the best at the position, and the rotation angle of the screen at the moment is determined to be the perpendicularity calibration angle.
The calibration of the focal position of the round hole diaphragm and the off-axis multi-reflection optical system comprises the following steps:
S2-7, projecting an arbitrary circle onto a screen, and imaging the arbitrary circle on a focal plane of a camera through a round aperture diaphragm after the arbitrary circle is incident into an off-axis multi-reflection optical system and subjected to multiple reflection of light rays;
S2-8, calculating the size of an imaged circle through an image processing algorithm;
S2-9, moving the round hole diaphragm on the bottom plate along with the track, and obtaining a corresponding relation between the moving distance and the size of the imaged circle by using a value fitting algorithm;
s2-10, determining the focus position of the round hole diaphragm when the imaging post-circle is maximum through an ant colony algorithm based on the corresponding relation, and determining the position of the round hole diaphragm at the moment as a focus calibration position.
In some embodiments, an arbitrary circle is projected onto the screen 8 and is imaged at the focal plane of the camera 5 through the circular aperture stop 4 after multiple reflections of light rays within the off-axis multi-reflection optical system 3. The round aperture stop 4 is placed near the focal position of the off-axis multi-reflecting optical system 3, the round aperture stop 4 is moved on the base plate 1 and photographing is performed by the camera 5 to capture an image. The imaging in the camera 5 should be maximum when the circular aperture stop 4 is placed right on the focal screen of the off-axis multi-reflecting optical system 3. The imaging size on the camera 5 can be calculated by means of an image processing algorithm. The round hole diaphragm 4 moves along the track on the bottom plate 1, the corresponding relation between the front-back movement distance and the size of the circle imaged by the camera 5 can be obtained through an interpolation fitting algorithm, the focal position of the round hole diaphragm 4 when the imaging is maximum is obtained through optimization by utilizing an ant colony algorithm according to the corresponding relation, and the position of the round hole diaphragm is considered to be determined as a focal calibration position at the moment.
In some embodiments, in S3, the above-mentioned method generates a plurality of sinusoidal fringe images with different phases and different periods according to the resolution of the screen 8 by using a sixteen-step phase shift method by using computer software, and performs graying processing on the plurality of sinusoidal fringe images to obtain a sinusoidal fringe gray scale image. The sine stripe gray images are incident into the off-axis multi-reflection optical system 3, and are imaged at the focal plane of the camera 5 through the round hole diaphragm 4 after being reflected for a plurality of times based on the sine stripe gray images incident into the off-axis multi-reflection optical system 3, so as to obtain a plurality of sine stripe imaging images.
In some embodiments, in S4, the plurality of sinusoidal fringe imaging images are phase unwrapped according to a multi-frequency phase unwrap Bao Guofa, the phase obtained being an absolute phase. In the process of multi-frequency phase unwrapping, the phase of each point is only related to the point at the same position on the phase diagram of different frequencies and is irrelevant to the adjacent point, so that even if the phase of a certain point causes multi-frequency phase unwrapping errors due to phase aliasing and phase noise, the errors are not transmitted. In addition, by tracing the incident light by using the ray tracing method, it is possible to find out the one-to-one correspondence between the same pixels on the camera 5 and the same points of the phase. Thereby establishing a mapping relation between the screen 8 coordinate system and the camera 5 coordinate system.
In some embodiments, in S5, the incident light is traced back by using a ray tracing method, so that after determining the direction of the incident light of the off-axis multi-reflection optical system 3, tangent processing is performed on each light, and the positions of the deflection points and the wavefront slopes of the corresponding positions of the plurality of light rays in the optical system are obtained. These wavefront slopes can be calculated by a Southwell area method model, followed by an integral reconstruction to produce the final wavefront profile.
The step S5 specifically includes:
s5-1, determining the corresponding relation between the same phase point on the screen and the camera pixel according to a multi-frequency phase unwrapping method;
s5-2, determining the ray direction of the incident ray by utilizing a ray tracing method based on the corresponding relation;
s5-3, carrying out tangential processing on the light rays, and determining position points where the light rays are deflected;
s5-4, calculating the wavefront slope at the corresponding position of the absolute phase through Southwell area method model.
In some embodiments, phase unwrapping is performed based on multi-frequency phase solutions Bao Guofa based on absolute phases obtained at the same location or at different times of the same pixel. In the process of multi-frequency phase unwrapping, the phase of each point is only related to the point at the same position on the phase diagram of different frequencies and is irrelevant to the adjacent point, so that even if the phase of a certain point causes multi-frequency phase unwrapping errors due to phase aliasing and phase noise, the errors are not transmitted. The association between the camera 5 and the screen 8 is established by multi-frequency phase unwrapping.
The phase unwrapping of the sinusoidal fringe image at each frequency results in a wrapped phase in the form of ψ (x, y) as in the following equation, which cannot be directly used for phase matching, and in order to obtain the absolute phase, one fringe order k (x, y) needs to be obtained, and then the wrapped phase is unwrapped into the absolute phase by the following equation, where the multi-frequency phase unwrapping equation is expressed as:
Φ(x,y)＝ψ(x,y)+2π×k(x,y)
Where Φ (x, y) is the absolute phase of the sinusoidal fringe pattern, ψ (x, y) is the wrapping phase of the sinusoidal fringe pattern, and k (x, y) is the order of the sinusoidal fringe pattern.
By means of ray tracing, incident rays are traced to the screen end, integral reconstruction is carried out on the traced screen rays, and the wavefront surface type of the off-axis multi-reflection optical system 3 is calculated. In the invention, the wavefront slope is calculated through Southwell area method model.
In some embodiments, in S6, the wavefront slope is calculated by using the Southwell area method model in the above description, and then the wavefront of the off-axis multi-reflection optical system 3 is obtained by performing integral reconstruction according to the wavefront slope, where the Southwell area method model formula is:
Where g jk represents the number of active phase points at the current point. Phi jk is the effective phase value of the current point; Represents the slope in the Y-direction and, Represents the X-direction slope and N represents the matrix dimension.
The step S6 specifically further includes:
S6-1, calculating the wavefront aberration of the off-axis multi-reflection wavefront type;
s6-2, fitting 36 coefficient values of the wavefront aberration through a Zernike fitting algorithm;
s6-3, subtracting the product sum of the first three terms of Zernike and the eighth term matrix and the corresponding coefficient from the wave-front image measured by the unwrapped phase, and recalculating the wave-front aberration of the off-axis multi-reflection wave-front surface;
S6-4, obtaining the off-axis multi-inverse wave front type after error removal based on the wave front aberration.
In some embodiments, in general, the measured wavefront surface shape often contains a certain inclination error and a certain spherical error, which cannot be removed in the calibration process of the round hole diaphragm 4, and the magnitude of the inclination and the spherical error is different according to the fact that the round hole diaphragm 4 is placed at different positions of the focal plane of the off-axis multi-reflection optical system 3, so that the round hole diaphragm 4 is placed at different positions, and the obtained wavefront surface shape is also different, so as to prevent the occurrence of the phenomenon. The error is removed by using Zernike fitting, firstly, the three-dimensional point cloud of the wave front, namely the wave front surface shape measured by the method, is fitted by using the Zernike, and 36 coefficients of the Zernike are fitted. Wherein, the 0 th term in the fitted Zernike coefficients represents a translation term, the 1 st term and the 2 nd term represent inclination terms, and the 8 th term represents spherical aberration and defocus terms. Subtracting the sum of the multiplier of the first three terms of Zernike and the eighth term of matrix and the corresponding coefficient from the wave-front image measured by the unwrapped phase, and obtaining the real wave-front image without inclination error and spherical error. By the method, the round aperture diaphragm 4 can be placed at any position, and the accurate wavefront surface type can be obtained through measurement. Wherein the formula of the wavefront aberration is expressed as:
Where W (x, y) is a wavefront aberration, W' (x, y) is a recalculated wavefront aberration. a nm is a coefficient of Zernike, Z (x, y) is a polynomial of Zernike, n and m are integers, n is an order of the polynomial, m is an angular frequency of the polynomial, generally n is a non-negative even number, and m is an integer satisfying-n.ltoreq.m.ltoreq.n.
For complete description of the present invention, as shown in fig. 5, stripe encoding is performed first, according to resolution of a screen, sinusoidal stripe images with different periods and different phases are generated by upper computer control software, and are imaged onto a focal plane of a camera 5 through multiple reflections in an off-axis multiple reflection optical system 3, and a one-to-one correspondence between points with the same phase and the same pixel of the camera 5 can be determined by using a multi-frequency phase unwrapping method, and meanwhile, incident light can be traced to a screen 8 by using a light tracing method, so as to determine a relationship between a coordinate system of the screen 8 and a coordinate system of the pixel of the camera 5. According to the direction of the light rays at the incident end, tangential processing can be carried out on each light ray, namely, the wavefront slope at the deflection position and the corresponding position, which are generated after a series of light rays pass through the off-axis multi-reflection optical system 3, is subjected to integral reconstruction of the wavefront slope, so that a wavefront surface type is obtained, but under normal conditions, the measured wavefront surface type often contains a certain inclination error and a certain spherical error, and then the spherical error is needed to be removed to calculate the wavefront, so that a real wavefront map without the inclination error and the spherical error is obtained.
The method comprises the steps of firstly acquiring a plurality of sine stripe images with different phases and different periods, carrying out graying treatment, sequentially displaying the sine stripe images subjected to the graying treatment on a screen at least two different positions on the screen, entering an off-axis multi-reflection optical system, imaging the light rays in the off-axis multi-reflection optical system at a focal plane of a camera through a round aperture diaphragm after multiple reflections of the light rays in the off-axis multi-reflection optical system, flexibly adjusting the round aperture diaphragm according to different focal positions of the camera, flexibly placing the round aperture diaphragm to an accurate position due to small volume to obtain a plurality of sine stripe imaging images, selecting screens with different sizes according to the caliber of the off-axis multi-reflection optical system to meet measurement requirements, carrying out phase unwrapping on the plurality of sine stripe imaging images by utilizing a multi-frequency phase unwrapping method to obtain absolute phases, calculating wavefront slopes at corresponding positions based on the absolute phases, and carrying out integral reconstruction on the wavefront slopes to obtain off-axis multi-reflection wavefront patterns.
It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media having computer-usable program code embodied therein. The storage medium may be implemented by any type of volatile or non-volatile Memory device or combination thereof, such as static random access Memory (Static Random Access Memory, SRAM), electrically erasable Programmable Read-Only Memory (ELECTRICALLY ERASABLE PROGRAMMABLE READ-Only Memory, EEPROM), erasable Programmable Read-Only Memory (Erasable Programmable Read Only Memory, EPROM), programmable Read-Only Memory (PROM), read-Only Memory (ROM), magnetic Memory, flash Memory, magnetic disk, or optical disk. These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
In the embodiments provided in the present application, it should be understood that the disclosed apparatus and method may be implemented in other manners. The above-described apparatus embodiments are merely illustrative, for example, the division of the units is merely a logical function division, and there may be other manners of division in actual implementation, and for example, multiple units or components may be combined or integrated into another system, or some features may be omitted, or not performed. Alternatively, the coupling or direct coupling or communication connection shown or discussed with each other may be through some communication interface, device or unit indirect coupling or communication connection, which may be in electrical, mechanical or other form.
Claims (10)
1. An off-axis multiple inverse wavefront measurement method based on phase deflection, comprising:
S1, acquiring a plurality of sine stripe images with different phases and different periods, and carrying out graying treatment on the sine stripe images to obtain sine stripe gray images;
s2, sequentially displaying a plurality of sine stripe gray images at least two different positions through a screen, wherein the sine stripe gray images are incident to an off-axis multi-reflection optical system;
s2-1, calibrating the perpendicularity of the screen and the optical axis of the off-axis multi-reflection optical system, and calibrating the focus positions of the round hole diaphragm and the off-axis multi-reflection optical system;
s2-1-1, projecting two identical circles with a certain interval onto a screen, and imaging the two circles on a focal plane of a camera through a circular aperture after being incident into an off-axis multi-reflection optical system and subjected to multiple reflection of light;
s2-1-2, calculating a first distance between circle centers of two circles after imaging;
S2-1-3, performing position movement on a screen on a bottom plate, calculating a second distance between circle centers of two circles at a focal plane of the camera, and calculating a distance difference between the first distance and the second distance;
s2-1-4, rotating a screen vertically connected to the electric turntable, and calculating distance difference values corresponding to circle centers of two imaged circles under different rotation angles of the screen;
s2-1-5, according to the corresponding distance difference value and the rotating angle, obtaining the corresponding relation between the rotating angle and the distance difference value;
s2-1-6, determining the rotation angle of the screen when the distance difference value is minimum through a particle swarm optimization algorithm based on the corresponding relation, and determining the rotation angle of the screen at the moment as a perpendicularity calibration angle;
s3, imaging a plurality of sine stripe gray images based on the light rays reflected for multiple times by the sine stripe gray images incident on the off-axis multi-reflection optical system at the focal plane of the camera through the round hole diaphragm to obtain a plurality of sine stripe imaging images;
s4, performing phase unwrapping on the plurality of sinusoidal fringe imaging images according to a multi-frequency phase unwrapping method to obtain absolute phases of the plurality of sinusoidal fringe imaging images;
s5, calculating the wavefront slope at the corresponding position of the absolute phase through a Southwell area method model based on the absolute phase;
S6, carrying out integral reconstruction on the wavefront slope to obtain an off-axis multi-reflection wavefront model.
2. The method for measuring off-axis multiple back wave front based on phase deflection according to claim 1, wherein before the plurality of sinusoidal fringe gray scale images are sequentially displayed at least two different positions through the screen, calibrating the perpendicularity of the screen and the optical axis of the off-axis multiple reflection optical system and calibrating the focal positions of the circular aperture diaphragm and the off-axis multiple reflection optical system are further performed.
3. The method for measuring the off-axis multiple reflection wavefront based on phase deviation according to claim 2, wherein the calibration of the perpendicularity of the screen and the optical axis of the off-axis multiple reflection optical system comprises the following steps:
Two identical circles with certain intervals are projected onto a screen, and are incident into an off-axis multi-reflection optical system to be imaged at a focal plane of a camera through a round aperture diaphragm after being reflected for multiple times by light rays;
Calculating a first distance between circle centers of two circles after imaging;
the screen moves on the bottom plate, a second distance between the centers of the two circles at the focal plane of the camera is calculated, and a distance difference value between the first distance and the second distance is calculated;
Rotating a screen vertically connected to the electric turntable, and calculating distance difference values corresponding to circle centers of two imaged circles under different rotation angles of the screen;
obtaining a corresponding relation between the rotating angle and the distance difference value according to the corresponding distance difference value and the rotating angle;
and determining the rotation angle of the screen when the distance difference value is minimum through a particle swarm optimization algorithm based on the corresponding relation, and determining the rotation angle of the screen at the moment as a perpendicularity calibration angle.
4. The method for off-axis multiple back wave front measurement based on phase deviation according to claim 3, wherein the calibration of the focal position of the circular aperture diaphragm and the off-axis multiple back wave optical system comprises the following steps:
Projecting any circle onto a screen, and imaging the random circle at a focal plane of a camera through a round aperture diaphragm after the random circle is incident into an off-axis multi-reflection optical system and subjected to multiple reflections of light rays;
calculating the size of an imaged circle through an image processing algorithm;
moving the round hole diaphragm on the bottom plate along with the track, and obtaining a corresponding relation between the moving distance and the size of the imaged circle by using an interpolation fitting algorithm;
and determining the focal position of the round aperture diaphragm when the circle is maximum after imaging through an ant colony algorithm based on the corresponding relation, and determining the position of the round aperture diaphragm at the moment as a focal calibration position.
5. The method of off-axis multiple inverse wavefront measurement based on phase bias according to claim 1, wherein said calculating a wavefront slope at a corresponding position of an absolute phase based on said absolute phase by a Southwell area method model comprises:
determining the corresponding relation between the same phase point on the screen and the camera pixel according to a multi-frequency phase unwrapping method;
determining the ray direction of the incident ray by utilizing a ray tracing method based on the corresponding relation;
tangent line processing is carried out on the light rays, and the position points where the light rays are deflected are determined;
the wavefront slope at the corresponding position of the absolute phase is calculated by Southwell area method model.
6. The off-axis multiple inverse wavefront measurement method based on phase deviation according to claim 1, wherein the sinusoidal fringe images include a transverse sinusoidal fringe image and a longitudinal sinusoidal fringe image, and the transverse sinusoidal fringe image and the longitudinal sinusoidal fringe image are subjected to graying processing, wherein a formula of the graying processing is expressed as:
Z＝I×255
Wherein, T 0 is the period of the set sine stripe image, X re is the transverse resolution of the screen, Y re is the longitudinal resolution of the screen, step is the phase shift number of the sine stripe image, and Z is the conversion from the sine stripe image to the gray image between 0 and 255.
7. The method of off-axis multiple inverse wavefront measurement based on phase bias of claim 6, wherein the formula of multi-frequency phase unwrapping is expressed as:
Φ(x,y)＝ψ(x,y)+2π×k(x,y)
Where Φ (x, y) is the absolute phase of the sinusoidal fringe pattern, ψ (x, y) is the wrapping phase of the sinusoidal fringe pattern, and k (x, y) is the order of the sinusoidal fringe pattern.
8. The off-axis multiple inverse wavefront measurement method according to claim 7, wherein the calculating the wavefront slope at the absolute phase corresponding position by Southwell area method model is expressed as:
Wherein g jk represents the number of effective phase points of the current point, and phi jk is the effective phase value of the current point; Represents the slope in the Y-direction and, Represents the X-direction slope and N represents the matrix dimension.
9. The method of off-axis multiple inverse wavefront measurement based on phase deviation of claim 1, further comprising, after obtaining the off-axis multiple inverse wavefront profile:
Calculating the wavefront aberration of the off-axis multi-reflection wavefront surface type;
fitting 36 coefficient values of the wavefront aberration through a Zernike fitting algorithm;
subtracting the product sum of the first three terms of Zernike and the eighth term matrix and the corresponding coefficient from the wave-front image measured by the unwrapped phase, and recalculating the wave-front aberration of the off-axis multi-reflection wave-front surface;
And obtaining the off-axis multi-inverse wave front type after error removal based on the wavefront aberration.
10. The off-axis multiple inverse wavefront measurement method based on phase deviation of claim 9, wherein the wavefront aberration is expressed as:
Wherein W (x, y) is wavefront aberration, W' (x, y) is wavefront aberration after recalculation, a nm is a coefficient of Zernike, Z (x, y) is a polynomial of Zernike, n and m are integers, n is an order of the polynomial, m is an angular frequency of the polynomial, n is usually a non-negative even number, and m is an integer satisfying-n.ltoreq.m.ltoreq.n.
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