CN108489422A - A kind of method of frequency conversion phase shift least-squares iteration superposition face shape separation - Google Patents
A kind of method of frequency conversion phase shift least-squares iteration superposition face shape separation Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- 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
- G01B11/25—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures by projecting a pattern, e.g. one or more lines, moiré fringes on the object
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Abstract
The present invention propose it is a kind of based on variation fringe frequency phase shift phase measurement deviation art in be superimposed face shape separation method, basic device includes pinhole camera, detected element and display.First, the bar graph of projection a set of frequencies variation is captured after the reflection superposition of detected element front and rear surfaces by pinhole camera with realizing phase shift；Next using least-squares iteration algorithm to resolve the corresponding phase distribution of front and rear surfaces, and display coordinate is obtained according to phase distribution；Slope calculation formula is finally substituted into calculate detected element front surface slope and integrate recovery face shape.This method, which has, does not change traditional PMD devices, it is easy to accomplish and it is of low cost, the advantages that quickly measurement.
Description
Technical Field
The invention relates to the technical field of optical element surface shape detection by Phase Measurement Deflection (PMD), in particular to a Phase measurement deflection for separating and detecting an optical element with superposed front and rear surface shapes.
Background
The phase measurement deflection technology is a non-contact type high-precision surface shape detection means for optical elements, and has the advantages of relatively low cost, easiness in implementation, insensitivity to environmental factors such as temperature, vibration and the like, high dynamic range and the like. In PMD detection, sinusoidal fringes are projected by an LCD display, reflected off the optical surface being detected and collected by a pinhole camera. And resolving the phase information of the acquired fringe pattern by using a phase shift algorithm, thereby calculating the surface slope and reconstructing the surface shape. However, for an optical element with back surface reflection, the fringes will be aliased after being reflected by the front and back surfaces, respectively, and the phase shift algorithm cannot accurately solve the phase distribution. Sprenger proposed an ultraviolet deflection technique to eliminate back surface reflection, which has special requirements for both the light source and the camera, resulting in high cost. Miyazaki D et al use a polarizing filter to accomplish the inspection of the surface of the transparent element based on the partial polarization characteristics of the reflected light, but this technique is rather complicated and difficult to implement. The scan line shift deflection technique of tianqun Su can intuitively separate the reflected light from the front and back surfaces, but is often time consuming and presents areas that are not detectable.
Aiming at the problem, the invention provides a method for separating the frequency conversion phase shift least square iteration superposition surface shape. Phase shift is realized by changing the fringe frequency, phase distribution is solved by utilizing a least square iterative algorithm, and finally the surface slope and the reconstructed surface shape are calculated.
Disclosure of Invention
The invention provides a frequency conversion phase shift least square iteration superposition surface shape separation method aiming at overcoming the defects in the background technology and aiming at the problem that the PMD detection precision is influenced by the back surface reflection. The method has the advantages of no change of the traditional PMD device, easy realization of low cost, quick measurement and the like.
The invention provides a method for detecting the surface shape of a reflecting element based on frequency change sine stripe projection. The LCD sequentially projects sine fringe patterns with variable frequencies, the sine fringe patterns are respectively reflected by the front surface and the rear surface of the element to be measured and then are superposed, the sine fringe patterns are collected by a pinhole camera, and the phase distribution corresponding to the front surface and the rear surface can be respectively calculated through a least square iterative algorithm. The coordinates of the display point corresponding to each pixel point on the image collected by the CCD can be obtained according to the phase distribution corresponding to the front surface, and the method comprises the following steps:
step 1: the LCD display projects the N frame frequency sinusoidal fringe patterns in the horizontal (x) and vertical (y) directions respectively, and since the processing modes in the two directions are completely the same, taking the x direction as an example, the light intensity signal collected by the pinhole camera CCD can be expressed as:
Iij＝A+B1cos(2π(f+iΔf)x1j)+B2cos(2π(f+iΔf)x2j) (1)
where Δ f is the step size of the frequency change between each frame; f is the frequency of the first frame; a is a direct current component; b is1、B2The contrast of the front and back surfaces, respectively; x is the number of1j、x2jAre the display coordinates corresponding to the front and back surfaces. Subscript 1 represents the front surface, and table 2 below represents the back surface; j denotes the jth pixel; i represents the ith frame stripe (i is 1,2, …, N, N represents the total number of frames, N ≧ 5). Through approximation, equation (1) can be expressed as:
wherein,is the phase value of the jth pixel of the front surface of the first frame;is the phase value of the jth pixel of the first frame back surface; delta1iIs the phase shift amount of the ith frame front surface caused by frequency change; delta2iIs the ith frame back tableThe amount of phase shift due to frequency variation.
Step 2: phase shift quantity delta of N frame stripe image by using least square algorithm1i、δ2iIterating pixel by pixel as a known quantity to obtain the phase distribution of the front and back surfaces of the first frame
And step 3: using least square algorithm to distribute the phase calculated in step 2 As a known quantity, iterate frame by frame to obtain a phase shift quantity delta1i、δ2i。
And 4, step 4: the phase shift obtained in step 3 can be substituted into step 2 as a known value, and iterative operation can be carried out. And (3) each time the two steps of iterative operations of the step 2 and the step 3 are sequentially completed, obtaining a group of new phase shift values, and checking whether the iterative result meets the convergence condition or not. If so, stopping iteration and taking the latest phase distribution and phase shift amount as a final calculation result. According to the phase value corresponding to the front surface, the coordinates of the display can be obtained through conversion, the coordinates are substituted into a slope calculation formula to calculate the slope distribution of the measured surface, and the surface shape is reconstructed through a slope integration algorithm.
The technical scheme provided by the invention has the beneficial effects that: by introducing the fringe projection with changed frequency and combining the least square iterative algorithm, the problem that the measurement precision is low and even the measurement fails due to aliasing of front and back surface shapes in the traditional phase measurement deflection operation is solved. The method does not need to modify the device of the traditional phase measurement deflection operation, thereby being easy to realize and relatively low in cost. The measurement result has high precision, and is suitable for detecting the three-dimensional surface shape of the high-precision optical element.
Drawings
FIG. 1 is a schematic diagram of a frequency-conversion phase-shift least-square iterative superposition surface-shape separation method according to the invention.
Fig. 2 is a two-frame horizontally superimposed fringe pattern.
Detailed Description
The invention is described in detail below by way of example with reference to the accompanying drawings. It should be noted that the following examples are only for illustrative purposes and should not be construed as limiting the scope of the present invention, and that the skilled person in the art may make modifications and adaptations of the present invention without departing from the scope of the present invention. In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention will be further described with reference to the accompanying drawings.
Referring to fig. 1, the present invention provides a method of frequency-variable phase-shift least-square iterative superposition surface shape separation. The basic components include a front surface 1 of the tested element, a back surface 2 of the tested element, a pinhole camera 3 and a display 4. The display 4 sequentially projects sine fringe patterns with frequency change, the sine fringe patterns are respectively reflected by the front surface 1 of the element to be measured and the rear surface 2 of the element to be measured and then are mutually superposed, the sine fringe patterns are collected by the pinhole camera 3, and the phase distribution corresponding to the front surface 1 of the element to be measured and the phase distribution corresponding to the rear surface 2 of the element to be measured can be respectively calculated through a least square iterative algorithm. The coordinates of the display point corresponding to each pixel point on the image collected by the pinhole camera 3 can be obtained according to the phase distribution corresponding to the front surface 1 of the element to be measured, and the specific steps are as follows:
step 1: the display 4 respectively projects the sinusoidal fringe patterns with N frame frequencies changing at equal intervals in the horizontal (x) and vertical (y) directions, and since the processing modes in the two directions are completely the same, taking the x direction as an example, the light intensity signal collected by the pinhole camera 3 can be represented as:
where Δ f is the step size of the frequency change between each frame; f is the frequency of the first frame; a is background light intensity; b is1、B2Modulation degrees of the front and rear surfaces, respectively; x is the number of1j、x2jAre the display coordinates corresponding to the front and back surfaces. Subscript 1 represents the front surface, and table 2 below represents the back surface; j denotes the jth pixel; i represents the ith frame stripe pattern (i is 1,2, …, N, N represents the total frame number, N ≧ 5);the average values of the display coordinates corresponding to the front and rear surfaces, respectively; Δ x1j、Δx2jDisplay coordinates and corresponding front and back surfaces, respectivelyThe deviation of (2).
If the conditions can be satisfied: Δ f < f andΔ x can be ignoredjAnd Δ f, the light intensity signal collected by the pinhole camera 3 can be represented again as:
wherein,is the phase value of the jth pixel of the front surface of the first frame; is the jth image of the back surface of the first frameA phase value of the pixel;is the phase shift amount of the ith frame front surface caused by frequency change;is the amount of phase shift of the surface due to frequency change after the ith frame.
ConditionThe method can be completed by moving the origin of coordinates to the negative direction of the coordinate axis when generating the N frames of frequency conversion fringe graphs, and the moving size can be m times of the width of the display 4; at this time, the step length delta f of frequency change between frames can be set as the reciprocal of N +1 times of movement amount to ensure that the phase shift amount between frames is less than 2 pi/N; and selecting the frequency f of the first frame of fringe pattern to satisfy delta f & lt f, wherein m is an empirical parameter and can be adjusted in the measuring process.
Step 2: phase shift quantity delta of N frame stripe image by using least square algorithm1i、δ2iIterating pixel by pixel as a known quantity to obtain the phase distribution of the front and back surfaces of the first frame
The expression of the light intensity signal collected by the pinhole camera 3 in the step 1 is based on the assumption that the background light intensity and the modulation degree among the sinusoidal stripes of each frame are only the function of the pixel position, and a group of new variables a are definedj＝A、 The theoretical light intensity value of the light intensity signal collected by the pinhole camera 3 is assumed to bePractice ofThe light intensity value is Iij, the sum Ej of the squares of the differences between the theoretical light intensity value and the actual light intensity value of the jth pixel point of each frame is
According to the least squares principle, when Ej is minimum
Then is formed by
Can calculate to obtain aj、bj、cj、dj、ejThe phase distributions in two orthogonal directions are finally obtained simultaneously, i.e.
And step 3: using least square algorithm to distribute the phase calculated in step 2As a known quantity, iterate frame by frame to obtain a phase shift quantity delta1i、δ2iI.e. by
And 4, step 4: the phase shift obtained in step 3 can be substituted into step 2 as a known value, and iterative operation can be carried out. Each time the iteration operations of the steps 2 and 3 are completed in sequence, a new set of phase shift values is obtained, and whether the iteration result meets the convergence condition or not is checked:
where k is the number of iterations; ε is a predetermined convergence threshold and can be set according to the accuracy required in practice. If yes, the phase distribution and the phase shift quantity obtained after the k iteration are the finally obtained phase distribution and the finally obtained phase shift quantity respectively. And (3) converting to obtain the coordinates of the display according to the phase value corresponding to the front surface, substituting the coordinates into a slope calculation formula to calculate the slope distribution of the measured surface, and finally obtaining the three-dimensional surface shape of the front surface 1 of the measured element by a southwell algorithm or zernike polynomial fitting.
Claims (2)
1. A method for separating a frequency conversion phase shift least square iteration superposition surface shape is characterized by comprising the following steps: changing the frequency of the projected fringe pattern to realize fringe pattern phase shift, simultaneously recording deformed fringe patterns reflected by the front and rear surfaces of the tested element by using a pinhole camera, calculating the phase distribution of the front and rear surfaces under the first frequency by using a least square iterative algorithm, and calculating the display coordinate according to the phase distribution of the front surface, wherein the specific form is as follows:
the display respectively projects N frames of sinusoidal fringe patterns with sequentially and equally-spaced frequency changes in the horizontal (x) direction and the vertical (y) direction, and light intensity signals collected by the pinhole camera in the x direction are as follows:
where Δ f is the step size of the frequency change between each frame; f is the frequency of the first frame; a is background light intensity; b is1、B2Modulation degrees of the front and rear surfaces, respectively; x is the number of1j、x2jAre the display coordinates corresponding to the front and back surfaces, with subscript 1 representing the front surface and table 2 below representing the back surface; j denotes the jth pixel; i represents the ith frame stripe pattern (i is 1,2, …, N, N represents the total frame number, N ≧ 5);the average values of the display coordinates corresponding to the front and rear surfaces, respectively; Δ x1j、Δx2jDisplay coordinates and corresponding front and back surfaces, respectivelyA deviation of (a);
when the condition is satisfied: Δ f<<f andthen, Δ x can be ignoredjAnd the light intensity signal collected by the pinhole camera is the product term of Δ f:
wherein,is the phase value of the jth pixel of the front surface of the first frame; is the phase value of the jth pixel of the first frame back surface;is the phase shift amount of the ith frame front surface caused by frequency change;is the phase shift amount of the back surface of the ith frame caused by frequency change, and similarly, the principle that the display projects a sinusoidal fringe pattern with N frame frequencies which are sequentially changed at equal intervals in the vertical (y) direction is the same as that described above.
2. The method for separating the frequency conversion phase shift least square iteration superposition surface shape according to claim 1, is characterized in that: conditionWhen generating N frames of frequency conversion stripe graphs, moving the origin of coordinates to the negative direction of the coordinate axis to meet the requirement, wherein the moving size is set to be m times of the width of the display; setting the step length delta f of frequency change between frames to be the reciprocal of N +1 times of movement amount to ensure that the phase shift amount between frames is less than 2 pi/N, and selecting the frequency f of the first frame of the fringe pattern to meet the requirement of delta f<<f is, m is an empirical parameter and can be adjusted in the measuring process.
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Cited By (2)
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| CN110411376A (en) * | 2019-07-03 | 2019-11-05 | 复旦大学 | A kind of transparent element front and rear surfaces PHASE SEPARATION method for the measurement of phase deviation |
| CN117168357A (en) * | 2023-09-12 | 2023-12-05 | 成都飞机工业（集团）有限责任公司 | Method, device, equipment and medium for correcting aircraft shape scanning error |
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| CN117168357A (en) * | 2023-09-12 | 2023-12-05 | 成都飞机工业（集团）有限责任公司 | Method, device, equipment and medium for correcting aircraft shape scanning error |
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