CN110926375B - Quick phase extraction method based on diamond vector normalization - Google Patents
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Abstract
The invention relates to the field of optical detection, in particular to a rapid phase extraction method based on diamond vector normalization. The method comprises the following steps: s1, collecting two interference patterns of the appearance of a measured object; s2, filtering out direct current components from the two interference patterns; s3, constructing a diamond vector for the two interference patterns; s4, normalizing the diamond vectors; and S5, solving phase information. The method can directly extract phase information from the interference pattern by constructing the diamond vector and normalizing the diamond vector without knowing a phase shift value. Only two interferograms need to be collected, and the defect that phase information can be accurately extracted only by collecting a plurality of interferograms in the traditional phase extraction algorithm is overcome. The method adopts a non-iterative mode, can quickly extract phase information, and is suitable for dynamic morphology measurement.
Description
Technical Field
The invention relates to the field of optical detection, in particular to a rapid phase extraction method based on diamond vector normalization.
Background
With the continuous progress and development of science and technology, the precision requirement of the industry on instruments is higher and higher, and in the industrial processing process, processing errors inevitably occur. The detection of the good and bad processing of the instrument device needs to quickly and accurately restore the three-dimensional appearance of the measured object. Therefore, the rapid detection of the microscopic three-dimensional morphology is very important. The improvement of the detection speed can be divided into two aspects. On one hand, the measurement system is improved from an experimental device, and on the other hand, a key algorithm in the three-dimensional shape recovery is improved. Current measurement systems can be broadly divided into contact measurement and non-contact measurement. The non-contact measurement has the advantages of high speed and no damage, and is widely applied to three-dimensional detection of microscopic morphology. Non-contact measurements include structured light triangulation, fringe projection, stereographic projection, phase-shifting interferometry, and the like. Among the non-contact measurements, the most widely used is phase-shifting interferometry.
Therefore, the rapid and accurate recovery of the shape of the measured object in the phase-shifting interferometry system is a research hotspot of researchers. Phase extraction is a key technology for recovering a microscopic three-dimensional shape, and the phase extraction is to extract phase information from an interference pattern so as to obtain height information of a measured object. The traditional phase extraction algorithm needs to collect at least five interferograms to accurately extract phase information from the interferograms. The more interferograms that are acquired, the higher the relative accuracy. However, it takes time to acquire the interferograms, so that five interferograms are required, which is very unfavorable for real-time dynamic topography measurement.
In recent years, researchers have proposed a large number of phase extraction algorithms in order to improve the measurement speed and measurement accuracy. We can classify the algorithms into two categories according to their mathematical methods. Iterative algorithms and non-iterative algorithms. The iterative algorithm requires multiple iterations to obtain high accuracy phase information extraction, which requires a large amount of computation time. Not conducive to real-time dynamic measurement. Therefore, researchers have proposed many non-iterative algorithms for phase extraction, including three-step schmitt quadrature (GS3), Principal Component Analysis (PCA), Differential Normalization (DN), differential normalization and diamond vector normalization (DN & DDVN). The algorithms can obtain phase extraction with higher precision by adopting non-iterative algorithms, but the algorithms need to acquire at least three interferograms, and still take more time compared with the phase extraction algorithm which only needs two interferograms.
The iterative algorithm is long in time consumption, three interferograms need to be acquired by the three-step phase extraction algorithm, and the two-step non-iterative algorithm is a good solution in order to quickly extract the phase.
Disclosure of Invention
The invention provides a rapid phase extraction method based on rhombus vector normalization, and aims to provide an operational method which adopts a non-iterative mode, only needs to acquire two interferograms and can rapidly extract a phase.
The invention provides a rapid phase extraction method based on diamond vector normalization, which comprises the following steps:
s1, collecting two interference patterns of the appearance of a measured object:
in the case where the phase shift value is randomly unknown, the two interferograms are represented as:
wherein a (x, y) represents the background light intensity and b (x, y) represents the modulation amplitude; delta1Representing the phase shift value, δ, of the first graph2The phase shift value of the second interference pattern is shown, and phi (x, y) represents the phase information of the measured object; in the following analysis, we omit (x, y).
S2, filtering out direct current components for the two interference patterns:
after filtering out the dc component, equation (1) is simplified to:
s3, constructing a diamond vector for the two interference patterns:
will I1And I2Adding and subtracting respectively to construct a diamond vector, as shown in formula
Wherein S represents the sum of the light intensities of the two interferograms, and D represents the difference between the light intensities of the two interferograms.
S4, normalizing the diamond vectors:
under normal conditions
Except that at
In order to eliminate the inconsistency between the S and D amplitudes, equation (3) is normalized to obtain:
wherein S is*Representing the sum of the intensities of the two normalized interferograms, D*Representing the difference between the intensities of the normalized two interferograms.
S5, solving phase information:
wherein phi represents the phase distribution of the object to be measured,
delta is a constant independent of the pixel point, and the value of delta does not affect the phase distribution and can be ignored.
As a further improvement of the present invention, the S4 further includes:
s41, if the condition that the number of interference fringes is greater than 1 is satisfied in formula (4), the following approximation exists:
at this time S*And D*Are approximately equal to each other, thereby obtaining
Wherein,
as a further improvement of the present invention, if the number of interference fringes in formula (4) is less than or equal to 1, S is*And D*The amplitudes of (a) cannot be approximately equal,
thus S*Is not equal to D*Amplitude of (b)k≠bk', wherein,
the calculation formula of the phase distribution at this time is:
wherein
And solving r by utilizing ellipse fitting so as to obtain the phase distribution of the measured object.
Because of the fact that
Equation (8) can be written as
The general expression of an ellipse is
a*x2+b*x*y+c*y2+d*x+f*y+g＝0 (10)
Reducing equation (9) to obtain an expression similar to equation (10), let D*＝x,S*Y, the parameters from which a general elliptic formula can be derived are
The parameter b can be calculated by ellipse fittingkAnd bk' to solve for r,
as a further improvement of the present invention, in step S1, the two interferograms are acquired as follows:
the light source adopts a collimated parallel LED light source, a beam of light is divided into two beams of light with a certain shearing amount and the same direction by using a uniaxial optical flat, random phase shifting is carried out by using an 1/4 wave plate and an analyzer, and two phase-shifting interferograms are collected by using a CCD industrial camera.
As a further improvement of the invention, the method also comprises the following steps: s6, phase extraction is carried out on the phase distribution under the condition that the number of interference fringes is larger than 1. In the phase extraction, when the number of interference fringes is larger than 1, the extracted phase distribution is discontinuous. Therefore, phase unwrapping is required to recover the continuous phase distribution. The phase unwrapping adopts the current mature unwrapping technology, and a phase unwrapping algorithm based on the non-continuity path reliability sequencing is proposed by Herraez in 2002. The algorithm firstly calculates the reliability value of the wrapping phase, a boundary is constructed, and then the unwrapping path is formulated by using the reliability of adjacent wires.
The invention has the beneficial effects that: the method can directly extract phase information from the interference pattern by constructing the diamond vector and normalizing the diamond vector without knowing a phase shift value. Only two interferograms need to be collected, and the defect that phase information can be accurately extracted only by collecting a plurality of interferograms in the traditional phase extraction algorithm is overcome. The method adopts a non-iterative mode, can quickly extract phase information, and is suitable for dynamic morphology measurement.
Drawings
FIG. 1 is a flow chart of a fast phase extraction method based on diamond vector normalization according to the present invention;
FIG. 2 is a simulation diagram according to a first embodiment of the present invention;
FIG. 3 is a simulation diagram of a second embodiment of the present invention;
FIG. 4 is a simulation diagram of a third embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments.
The invention provides a rapid phase extraction method based on diamond vector normalization. The method only needs two interferograms, as shown in fig. 1, and mainly comprises the following steps:
step 1: the direct current component is filtered out. In the case where the phase shift value is randomly unknown, the two interferograms can be represented as:
a (x, y) represents the background light intensity and b (x, y) represents the modulation amplitude. Delta1Representing the phase shift value, δ, of the first graph2The phase shift value of the second interferogram is shown and phi (x, y) represents the phase information of the measured object. In the following explanation, we omit (x, y) for convenience of explanation.
After filtering out the dc component, equation (1) can be simplified to:
step 2: and constructing a diamond vector.
Will I1And I2Respectively adding and subtracting to construct a diamond vector as shown in formula (3)
And step 3: normalized diamond vector.
By normalizing equation (3), we can get:
if the number of interference fringes is greater than 1:
it is thus possible to obtain:
wherein,
and 4, step 4: and solving the phase information.
Wherein,
delta is a constant which is irrelevant to the pixel points, does not influence the phase distribution of the measured object and can be ignored, so that the phase distribution of the measured object can be accurately obtained by using the formula (7).
And 5: and (5) unwrapping the phase.
Phase extraction phase unwrapping the phase distribution when the number of interference fringes is greater than 1. In the phase extraction, when the number of interference fringes is larger than 1, the extracted phase distribution is discontinuous. And (5) performing phase unwrapping to recover continuous phase distribution.
In order to verify the effectiveness of the method, a computer is used to perform simulation on various conditions. In the following simulations, we assume that the background light intensity has been filtered out.
The first embodiment is as follows:
as shown in fig. 2, assuming the fringe shape is circular, two random interferograms are generated in computer simulation, where the modulation amplitude: bm(x,y)＝1.2exp(-0.1(x2+y2) Where m ═ 1,2, object phase: phi (x, y) being 5 pi (x)2+y2) The amount of phase shift δ of the first diagram10rad, amount of phase shift δ of second graph2＝1rad。
The initial phase of 400 × 400 pixels is generated by numerical simulation, as shown in fig. 2(a), fig. 2(b) and 2(c) are two random interferograms, fig. 2(d) is the phase extracted by the method provided by the invention, and fig. 2(e) is the object surface phase information obtained after the phase unwrapping operation.
The phase extraction time for example 1 was: 0.05 s.
Example two:
as shown in fig. 3, the interference fringes are assumed to be simple vertical fringes. Two random interferograms were generated in computer simulation, where the modulation amplitude: bm(x,y)＝1.2exp(-0.1(x2+y2) Where m ═ 1,2, object phase: phi is 5 pi (3x +4y), the phase shift amount delta of the first graph10rad, amount of phase shift δ of second graph2＝1rad。
The initial phase of 400 × 400 pixels is generated by numerical simulation, as shown in fig. 3(a), fig. 3(b) and 3(c) are two random interferograms, fig. 3(d) is the phase extracted by the method provided by the invention, and fig. 3(e) is the object surface phase information obtained after the phase unwrapping operation.
The phase extraction time for example 2 was: 0.046 s.
Example three:
as shown in fig. 4, the interference fringes are assumed to be irregular fringes. Two random interferograms were generated in computer simulation, where the modulation amplitude: bm(x,y)＝1.2exp(-0.1(x2+y2) Where m ═ 1,2, object phase: phi ═ 5 pi (5 x)2+4y3) The amount of phase shift δ of the first diagram10rad, amount of phase shift δ of second graph2＝1rad。
The initial phase of 400 × 400 pixels is generated by numerical simulation, as shown in fig. 4(a), fig. 4(b) and 4(c) are two random interferograms, fig. 4(d) is the phase extracted by the method provided by the invention, and fig. 4(e) is the object surface phase information obtained after the phase unwrapping operation.
The phase extraction time for example 3 was: 0.052 s.
Embodiments 1,2 and 3 illustrate that the method can rapidly and accurately extract phase information under circular interference fringes, strip interference fringes and irregular interference fringes, and has strong applicability.
The invention only needs two interferograms, overcomes the defect that the traditional phase extraction algorithm needs a plurality of interferograms, and can quickly and accurately extract phase information; phase information is directly extracted from the interference pattern by a non-iterative method, the running speed of the algorithm is increased, and quick measurement can be realized; the algorithm can quickly and accurately extract phase information under circular interference fringes, vertical interference fringes and irregular interference fringes.
The foregoing is a more detailed description of the invention in connection with specific preferred embodiments and it is not intended that the invention be limited to these specific details. For those skilled in the art to which the invention pertains, several simple deductions or substitutions can be made without departing from the spirit of the invention, and all shall be considered as belonging to the protection scope of the invention.
Claims (4)
1. A quick phase extraction method based on diamond vector normalization is characterized by comprising the following steps:
s1, collecting two interference patterns of the appearance of a measured object:
in the case where the phase shift value is randomly unknown, two interferograms are represented as:
wherein a (x, y) represents the background light intensity and b (x, y) represents the modulation amplitude; delta1Representing the phase shift value, delta, of the first interferogram2The phase shift value of the second interference pattern is shown, and phi (x, y) represents the phase information distribution of the measured object;
s2, filtering out direct current components for the two interference patterns:
after filtering out the dc component, equation (1) is simplified to:
s3, constructing a diamond vector for the two interference patterns:
will I1And I2Adding and subtracting respectively to construct a diamond vector, as shown in formula (3)
Wherein S represents the sum of the light intensities of the two interferograms, and D represents the difference between the light intensities of the two interferograms;
s4, normalizing the diamond vectors:
normalizing equation (3) yields:
wherein S is*Representing the sum of the intensities of the two normalized interferograms, D*Representing the difference between the light intensities of the two normalized interferograms;
s5, solving phase information:
wherein phi represents the phase distribution of the object to be measured,
Δ is a constant independent of the pixel point;
if the number of interference fringes is less than or equal to 1 in the formula (4), S*And D*The amplitudes of (a) cannot be approximately equal,
thus S*Is not equal to D*Amplitude of (b)k≠bk', wherein,
the calculation formula of the phase distribution at this time is:
wherein
Solving r by utilizing ellipse fitting so as to obtain the phase distribution of the measured object; because of the fact that
Equation (8) can be written as
The general expression of an ellipse is
a*x2+b*x*y+c*y2+d*x+f*y+g＝0 (10)
Reducing equation (9) to obtain an expression similar to equation (10), let D*＝x,S*Y, the parameters for obtaining a general elliptic formula are
The parameter b is calculated by ellipse fittingkAnd bk' to solve for r,
2. the method for fast phase extraction based on diamond vector normalization according to claim 1, wherein the S4 further comprises:
s41, if the condition that the number of interference fringes is greater than 1 is satisfied in formula (4), the following approximation exists:
at this time S*And D*Are approximately equal to each other, thereby obtaining
Wherein,
3. the method for fast phase extraction based on diamond vector normalization according to claim 1, wherein in step S1, the two interferograms are collected as follows:
the light source adopts a collimated parallel light source, a beam of light is divided into two beams of light with a certain shearing amount and the same direction by using a uniaxial optical flat, random phase shifting is carried out by using an 1/4 wave plate and an analyzer, and two phase-shifting interferograms are collected by using a camera.
4. The method for fast phase extraction based on diamond vector normalization according to claim 1, further comprising the steps of:
s6, phase extraction is carried out on the phase distribution under the condition that the number of interference fringes is larger than 1.
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