CN110030944B - Large-gradient free-form surface measuring method - Google Patents
Large-gradient free-form surface measuring method Download PDFInfo
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- CN110030944B CN110030944B CN201910268302.XA CN201910268302A CN110030944B CN 110030944 B CN110030944 B CN 110030944B CN 201910268302 A CN201910268302 A CN 201910268302A CN 110030944 B CN110030944 B CN 110030944B
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- G01B11/00—Measuring arrangements characterised by the use of optical techniques
- G01B11/24—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures
- G01B11/2441—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures using interferometry
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Abstract
The invention discloses a large-gradient free-form surface measuring method, which applies a certain angle to a free-form surface to be measured to complete the spatial frequency modulation of a diffraction object light wave of the free-form surface to be measured, and the modulation is collected by an image sensor. The method comprises the steps of adjusting a plurality of angles, recording a plurality of frames of holograms of free-form surfaces at different angles, completing selection of a stripe sparse sub-region of each frame of hologram through an image processing algorithm, and recovering a three-dimensional structure of the modulated sub-region of the free-form surface to be measured through a digital reconstruction algorithm. And finally, recovering the three-dimensional structure of the original sub-region of the free-form surface to be detected according to a demodulation algorithm, and realizing the wave-front data fitting of the multi-frame sub-region by using a proper splicing algorithm, so that the three-dimensional surface shape information of the free-form surface can be recovered. The invention realizes the acquisition process of free-form surface high-frequency information by introducing the inclination angle, and provides a new solution for free-form surface measurement.
Description
Technical Field
The invention relates to the field of free-form surface measurement, in particular to a large-gradient free-form surface measurement method.
Background
With the development of modern processing technology, the free-form surface element is widely applied to important fields of aerospace, biomedicine, national defense and military industry, modern optics and the like in recent years. The free-form surface mainly comprises a rotationally symmetric aspheric surface and a non-rotationally symmetric aspheric surface, and compared with a common spherical element, the free-form surface has higher degree of freedom in structure and can be more flexibly adapted to the use requirement. Especially in the optics field, the optical system that the free-form surface lens constitutes compares traditional optical system can simplify the overall arrangement, promotes energy transmission efficiency, better correction aberration etc.. Nowadays, the complexity and the precision of the free-form surface need to be measured and evaluated sensitively and efficiently, and meanwhile, the precise measurement promotes the better design and processing of the free-form surface. With the improvement of the requirements of various fields on the surface shape precision of the free-form surface element, how to effectively solve the problem of high-precision measurement of the free-form surface is one of the current research hotspots.
The existing measuring method applied to the free-form surface aims at the free-form surface with small gradient. Whether the interference method or the digital holography which is most widely applied needs to analyze a fringe pattern to recover three-dimensional information, and in the face of a large-gradient free-form surface, the existing method still has the problem that the generated fringe pattern of a hologram area is too dense and cannot be analyzed. How to realize high-precision detection of the large-gradient free-form surface becomes one of the urgent problems in the measurement field.
Disclosure of Invention
The invention aims to: the method is used for adjusting the free-form surface through a plurality of inclination angles on the basis of not changing the structure of the conventional digital holographic system, so that the digital holographic method can be used for measuring the free-form surface with large gradient with high precision.
The technical scheme adopted by the invention is as follows: a large-gradient free-form surface measuring method comprises the following steps:
and 3, recovering the three-dimensional structure of the original sub-region of the free-form surface to be detected according to a demodulation algorithm, and realizing the wave-front data fitting of the multi-frame sub-region by using a proper splicing algorithm, so that the three-dimensional surface shape information of the free-form surface to be detected can be recovered.
The method comprises the steps of modulating dense holographic fringes generated in an original large gradient region into sparse holographic fringes which can be collected by a photoelectric detector through introducing an inclination angle, and then realizing measurement of the whole free-form surface through a subsequent algorithm.
The image sensor comprises an area array color camera, a linear array color camera, an area array black-and-white camera and a linear array black-and-white camera, and the types of the image sensor comprise a CMOS (complementary metal oxide semiconductor) and a CCD (charge coupled device).
The free-form surface to be measured comprises a transparent free-form surface and a surface-reflecting free-form surface.
The reference wavefront can be spherical wave or plane wave, and is consistent with the wavelength of the diffractometer light wave.
The diffraction object light wave of the free-form surface to be measured is formed by transmitting or reflecting collimated light beams through an object.
The sub-region selection algorithm is used for dividing regions by calculating the gradient of the acquired holographic image.
Wherein the demodulation algorithm is realized by adding a reverse tilt factor to the modulated sub-region.
The image splicing algorithm needs to ensure that all effective subregions to be spliced are overlapped to a certain extent, extracts the relative translation and rotation between the reference surfaces of the adjacent effective subregions from the overlapped region, and finally unifies the reference surfaces of the effective subregions to the appointed reference surface in sequence, thereby realizing the splicing of the whole surface shape.
The invention has the beneficial effects that:
in a common digital holographic system, an inclination angle is added to a free curved surface to be measured, so that an original large gradient area of the free curved surface to be measured relative to object light is converted into a small gradient area, and then original gradient information is demodulated through a subsequent algorithm, so that a new solution is provided for free curved surface measurement.
Drawings
FIG. 1 is a schematic diagram of a large gradient free-form surface measurement system;
FIG. 2 shows a sub-region selection step, wherein FIG. 2(a) is a image plane hologram; FIG. 2(b) is a gradient map; FIG. 2(c) is a region selected for a close operation; FIG. 2(d) shows selected sub-regions;
FIG. 3 is a schematic diagram of spectral filtering;
FIG. 4 is a schematic diagram of a basic principle of sub-region splicing;
the reference numerals in fig. 1 mean: the device comprises an electronic control rotary table 1, a free-form surface to be measured 2, a microscope objective 3, an image sensor 4 and reference light 5.
Detailed Description
The invention is described in detail below with reference to the drawings and the detailed description.
As shown in figure 1, in the large-gradient free-form surface measurement system, diffracted object light of a free-form surface 2 to be measured, which is fixed on an electric control rotating platform 1, passes through a microscope objective 3 and then forms a hologram with reference light 5, an image sensor 4 is used for continuously providing a plurality of rotating angles for the free-form surface 2 to be measured through the electric control rotating platform 1, and a plurality of frames of free-form surface holograms modulated by a tilt factor are recorded. And then, selecting each frame of holographic stripe sparse sub-region through an image processing algorithm, recovering the three-dimensional structure of the sub-region of the modulated free-form surface to be detected through a digital reconstruction algorithm, recovering the three-dimensional structure of the sub-region of the original free-form surface to be detected according to a demodulation algorithm, and realizing the wave-front data fitting of the multi-frame sub-region by using a proper splicing algorithm, namely recovering the three-dimensional surface shape information of the free-form surface to be detected.
The laser in the above optical path is a He-Ne laser with a wavelength of 632.8nm, a light beam generates a beam expanding effect of 3 times on a light spot through a beam expanding lens, and then is divided into two beams of light with the same energy by a spectroscope, one beam of light irradiates the surface of a free curved surface to be measured and is reflected to form an object light, the other beam of light is used as a reference light, after the object light is reflected by the free curved surface fixed on an electric control rotating platform, diffraction light of the object light enters a microscope objective with a magnification of 5 times, and the diffraction light and the reference light have a certain included angle and are incident on a photosensitive surface of a CCD to be coherently superposed, and an image surface of the microscope objective and the photosensitive surface of the CCD are the same surface at the moment. And finally, accurately controlling the rotation angles of the x axis and the y axis of the electric control rotating platform for multiple times according to the approximate surface shape of the free-form surface to be measured, finishing the addition of the diffraction object light wave inclination factor, and obtaining a multi-frame modulated image surface hologram.
After obtaining a multi-frame image surface hologram, processing the image through a sub-region selection algorithm, firstly, generating a gradient operator with a specification of 3 multiplied by 3, translating the gradient operator along the directions of x and y, and calculating the directional derivative of a central pixel point value f (m, n) of the operator and adjacent 8 pixel point values f (i, j):
the gradient value at this point is then the maximum of the 8 directional derivatives:
in this case, G (i, j) represents a gradient map, fig. 2(a) shows a modulated image plane hologram, and fig. 2(b) shows a gradient map of a hologram, and it can be seen that the gradient value at the sparse fringe of the hologram is small, and vice versa. Then, a selected sub-region is obtained by setting a gray threshold, but a certain non-connected part exists in the region, binarization processing needs to be performed again, then closing operation processing is performed to obtain a gradient map after the closing operation processing, as shown in fig. 2(c), and finally the region is corresponding to an image plane hologram, that is, a resolvable hologram sub-region can be selected, as shown in fig. 2 (d).
After obtaining the sub-region I (x, y) of the multi-frame hologram, because the image plane holographic optical path is used, diffraction calculation is not needed when the wave front of the object light wave is reconstructed, and only the sub-region is processed as follows:
U(x,y)＝ΓF-1{F[I(x,y)]W(fx,fy)} (3)
in the above formula, W (f)x,fy) For selecting the window function of the object wave frequency for use in correlating UR in holograms*The term is the frequency spectrum F [ I (x, y) obtained by Fourier transform from an image plane hologram]And f is a correction factor for correcting multiple phase distortions, as shown in fig. 3, and then:
the extraction of the phase of the object optical wave is realized, and a mapping relation exists between the phase information and the height of the object, so that the height information of the object to be detected can be obtained through the mapping relation, and the reconstruction of the object optical wave is completed.
Reconstructing to obtain sub-region surface shape information O (x) with tilt factor2,y2) Knowing that the rotation angle of the x axis accurately controlled by the electrically controlled rotating platform is alpha and the rotation angle of the y axis is beta, the demodulation is completed only by adding a reverse tilt factor to the sub-area:
O'(x2',y2') is the original sub-area profile information, after obtaining the sub-area profile information of the multi-frame hologram, each effective sub-area is guaranteed to have a certain overlap, the relative translation and rotation between the reference surfaces of the adjacent effective sub-areas need to be extracted from the overlapped area, and finally the reference surfaces of the effective sub-areas are unified to the appointed reference surface in sequence, thereby realizing the splicing of the whole profile.
The principle is shown in fig. 4, taking the overlapping area of two areas as an example, the phases of the two sub-areas at the overlapping position have the following relationship:
S1(x,y)＝S2(x,y)+k1x+k2y+P (6)
in the above formula k1,k2P represents S respectively1Relative to S2The amount of tilt and the amount of translation in the x, y directions. S1(x, y) and S2The height information in the (x, y) overlap region is known, and k can be obtained by taking a plurality of selected points of the overlap region to perform least square fitting1,k2And P, completing the splicing of the two areas. For the splicing of the sub-regions of multiple frames, the splicing of the whole surface shape can be realized only by fixing one reference sub-region, and the three-dimensional measurement of the whole free-form surface is realized.
The above description is only an embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can understand that the modifications or substitutions within the technical scope of the present invention are included in the scope of the present invention.
Claims (1)
1. A large-gradient free-form surface measuring method is characterized by comprising the following steps: the free-form surface measuring method utilizes a large-gradient free-form surface measuring system, diffraction object light of a free-form surface (2) to be measured fixed on an electric control rotating platform (1) passes through a microscope objective (3), then forms a hologram image sensor (4) with reference light (5), then continuously provides a plurality of rotating angles for the free-form surface (2) to be measured through the electric control rotating platform (1), and records a plurality of frames of free-form surface holograms modulated by a tilt factor; then, selecting each frame of holographic stripe sparse sub-region through an image processing algorithm, recovering the sub-region three-dimensional structure of the modulated free-form surface to be detected through a digital reconstruction algorithm, recovering the sub-region three-dimensional structure of the original free-form surface to be detected according to a demodulation algorithm, and realizing wave front data fitting of the multi-frame sub-region through a proper splicing algorithm, namely recovering the three-dimensional surface shape information of the free-form surface to be detected; the laser in the above optical path is a He-Ne laser with a wavelength of 632.8nm, a light beam generates a 3-fold beam expansion effect on a light spot through a beam expander, and then is divided into two beams of light with the same energy by a spectroscope, one beam of light irradiates the surface of a free curved surface to be measured and is reflected to form an object light, the other beam of light is used as a reference light, after the object light is reflected by the free curved surface fixed on an electric control rotating platform, diffracted light of the object light enters a microscope objective with 5-fold magnification and is incident on a photosensitive surface of a CCD (charge coupled device) with a certain included angle with the reference light for coherent superposition, and an image surface of the microscope objective and the photosensitive surface of the CCD are the same surface; finally, accurately controlling the rotation angles of the x axis and the y axis of the electric control rotating platform for multiple times according to the approximate surface shape of the free-form surface to be detected, finishing the addition of the diffraction object light wave inclination factor, and obtaining a multi-frame modulated image surface hologram;
after obtaining a multi-frame image surface hologram, processing the image through a sub-region selection algorithm, firstly, generating a gradient operator with a specification of 3 multiplied by 3, translating the gradient operator along the directions of x and y, and calculating the directional derivative of a central pixel point value f (m, n) of the operator and adjacent 8 pixel point values f (i, j):
the gradient value at this point is then the maximum of the 8 directional derivatives:
at the moment, G (i, j) represents a gradient image, the gradient value at the sparse position of the holographic image stripe is small, and vice versa, then a selected sub-area is obtained by setting a gray threshold value, but a certain non-connected part exists in the area, binarization processing needs to be carried out again, then closing operation processing is carried out to obtain the gradient image after the closing operation processing, and finally the area is corresponding to the image plane holographic image, so that the distinguishable holographic image sub-area can be selected;
after obtaining the sub-region I (x, y) of the multi-frame hologram, because the image plane holographic optical path is used, diffraction calculation is not needed when the wave front of the object light wave is reconstructed, and only the sub-region is processed as follows:
U(x,y)＝ΓF-1{F[I(x,y)]W(fx,fy)} (3)
in the above formula, W (f)x,fy) For selecting the window function of the object wave frequency for use in correlating UR in holograms*The term is the frequency spectrum F [ I (x, y) obtained by Fourier transform from an image plane hologram]And F, filtering out, wherein F is a correction factor for correcting multiple phase distortions, and then:
the extraction of the phase of the object optical wave is realized, and a mapping relation exists between the phase information and the height of the object, so that the height information of the object to be detected can be obtained through the mapping relation, and the reconstruction of the object optical wave is completed;
reconstructing to obtain sub-region surface shape information O (x) with tilt factor2,y2) Knowing that the rotation angle of the x axis accurately controlled by the electrically controlled rotating platform is alpha and the rotation angle of the y axis is beta, the demodulation is completed only by adding a reverse tilt factor to the sub-area:
O'(x2',y2') is original subregion shape information, after obtaining the subregion shape information of the multiframe hologram, each effective subregion guarantees to have certain overlap each other, need to extract the relative translation and rotation between the reference surfaces of the adjacent effective subregions from the overlapped region, unify these effective subregion reference surfaces to the appointed reference surface finally sequentially, thus realize the splice of the whole shape;
for the overlapping region of the two regions, the phases of the two sub-regions at the overlapping position have the following relationship:
S1(x,y)＝S2(x,y)+k1x+k2y+P (6)
in the above formula k1,k2P represents S respectively1Relative to S2Amount of tilt and translation in x, y directions, S1(x, y) and S2The height information in the (x, y) overlap region is known, and k can be obtained by taking a plurality of selected points of the overlap region to perform least square fitting1,k2And the splicing of the two areas is completed by the three parameters P, and for the splicing of the sub-areas of the multi-frame, the splicing of the whole surface shape can be realized by only fixing one reference sub-area, so that the three-dimensional measurement of the whole free-form surface is realized.
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