Data processing method of multi-phase image velocity interferometer for arbitrary reflecting surface

Abstract

The present invention provides a multi-phase image arbitrary reflection surface velocity interferometer data processing method, the key points of which are as follows: S1, processing a single original image to obtain a plurality of multi-phase images; S2, using the multi-phase images to perform phase solution; S3, phase unwrapping, and calculating the shock wave velocity; wherein, step S2 is performed according to the following steps: S21, calculating the phase distribution of the original image; S22, solving the phase error, thereby solving the phase; S23, using a probability density function to determine whether the phase distribution is correct; using this method, by comparing the curves before and after the probability density function processing, it is found that the use of this method significantly improves the uniformity of the phase distribution; and compared with the traditional data processing method, a "point-to-point" phase calculation method is adopted, which effectively improves the spatial resolution of data processing, and compensates for the influence of the phase error during the processing, thereby effectively reducing the data processing error.

Description

Technical Field

[0001] The present invention relates to the field of laser measurement technology, and in particular to a data processing method for a multi-phase image arbitrary reflection surface velocity interferometer. Background Art

[0002] The image arbitrary reflecting surface velocity interferometer mainly utilizes the optical Doppler effect and optical mixing technology to track the frequency conversion process and thus obtain the change process of shock wave velocity. In inertial confinement fusion, the image arbitrary reflecting surface velocity interferometer is an important diagnostic device and is widely used in shock wave velocity regulation, state equation and other experiments. It can be used to diagnose shock wave velocity and shock wave front. Therefore, data processing of the image arbitrary reflecting surface velocity interferometer is crucial.

[0003] In the fringe image recorded by the velocity interferometer of any reflecting surface, the fringe variation is expressed as F(t) and the fringe constant is expressed as VPF; the fringe variation F(t) is the change in the number of fringes relative to the static fringe, that is, Where φ(x0, t0) represents the reference zero phase, Δφ represents the phase change, and the fringe constant VPF is a fixed value representing the velocity change corresponding to one fringe movement cycle. Therefore, the shock wave velocity calculation formula is: u(t) = VPF·F(t), and the integral form of this formula is:

[0004] Therefore, the key to image arbitrary reflecting surface velocity interferometer data processing lies in accurately solving the variation of the fringes, or usually converted into solving the phase variation of the fringes of the image arbitrary reflecting surface velocity interferometer. Currently, the most commonly used method for image arbitrary reflecting surface velocity interferometer data processing is to use Fourier transform to transform, filter and calculate the phase of the image. However, this method does not process point by point, but rather homogenizes the image in the spatial direction, and some information will be lost in the filtering process, thereby reducing the spatial resolution and ultimately affecting the accuracy of data processing. Summary of the Invention

[0005] In order to solve the above technical problems, the present invention provides a multi-phase image arbitrary reflection surface velocity interferometer data processing method. The main purpose is to obtain a multi-phase image by shifting the phase of the original display image, and then use the probability density function as a criterion to compensate the phase error of the multi-phase image to obtain a phase distribution uniform image and calculate the phase, thereby realizing point-by-point processing of the display image and effectively improving the data processing accuracy.

[0006] Based on the above technical problems, the following technical solutions are proposed:

[0007] The present invention provides a method for processing multi-phase image arbitrary reflection surface velocity interferometer data, the gist of which is to follow the following steps:

[0008] S1, processing a single original image to obtain several multi-phase images;

[0009] S2. performing phase solution using the multi-phase image;

[0010] S3, phase unwrapping, calculate the shock wave velocity;

[0011] Wherein, the step S2 includes the following steps:

[0012] S21, calculating and obtaining the phase distribution of the original image;

[0013] S22, solving the phase error, thereby solving the phase;

[0014] S23. Use the probability density function to determine whether the phase distribution is correct.

[0015] By using the above method, the uniformity of the phase distribution is significantly improved by comparing the curves before and after the probability density function processing.

[0016] Furthermore, in step S1, the fringe image recorded by any reflecting surface velocity interferometer is expressed by the following formula:

[0017] I n (x,y)=A(x,y)+B(x,y)cos[φ(x,y)+δ n ] (1)

[0018] In formula (1), (x, y) represents any position on the image; A(x, y) represents the background intensity, which is related to the ambient noise and the uneven reflection of the surface to be measured; B(x, y) represents the intensity modulation distribution of the probe light; B(x, y) / A(x, y) gives the contrast of the fringe, φ(x, y) represents the phase to be measured; δ n It is expressed as the phase shift amount, n is a positive integer, where for the four-step phase shift, I1(x,y) is the original image in several multi-phase images; the original image shift term δ1 = 0, I n (x,y) is the shift term δ from the original image n get.

[0019] Furthermore, the step S21 includes the following steps:

[0020] In an ideal situation, the second phase image shift term δ2 = π / 2, the third phase image shift term δ3 = π, and the fourth phase image shift term δ4 = 3π / 2, so Equation (1) can be rewritten as follows:

[0021]

[0022] According to the above formula (2), we can get:

[0023]

[0024] Due to the influence of laser speckle noise and the uneven surface shape of optical elements, phase error will be introduced into the original signal, so formula (1) is transformed into the following formula:

[0025] I n (x,y)=A(x,y)+B(x,y)cos[φ(x,y)+δ n +Δδ n ] (4)

[0026] In formula (4), Δδ n Expressed as phase error;

[0027] When the phase shift error is incorporated into the phase shift amount, equation (4) can be written as:

[0028] I n (x,y)=A(x,y)+B(x,y)cos[φ(x,y)+δ n ] (5)

[0029] The least square method is used for phase calculation. For multi-phase images, its phase distribution can be expressed as:

[0030]

[0031] Solving equation (6) yields the truncated phase φ:

[0032]

[0033] Substitute the phase error of the multi-phase image into equation (6), and then use equation (7) to obtain the truncated phase distribution of the original image of the velocity interferometer of any reflecting surface.

[0034] Using the above steps, the phase of each point is calculated separately, while the original Fourier transform law processes the data points as a whole and cannot achieve "point-to-point" processing. Therefore, using this method can effectively improve the spatial resolution of data processing.

[0035] Furthermore, in step S22, a phase interval is set: [-π / 10, π / 10], and a set of phase values is obtained with a step size of π / 50. The phase error combinations are respectively taken as (-π / 10, -π / 10, -π / 10) through permutation and combination. A total of 11 3Combination method, each group of phase errors is substituted into formula (6) to obtain the corresponding phase distribution;

[0036] By adopting the above steps, the phase error caused by non-ideal factors can be reduced to a certain extent, thereby improving the final data processing accuracy.

[0037] Furthermore, in step S23, it can be known from the properties of the inverse trigonometric function that the phase obtained by the above formula (7) is a truncated phase distributed in the interval [-π,π); and the probability density function can analyze the statistical characteristics of the image, wherein the distribution of the random variable is mainly revealed by calculating the probability of occurrence. The probability density function is applied to the truncated phase of the fringe image of any reflecting surface velocity interferometer to describe the influence of the phase error on the truncated phase;

[0038] Therefore, the probability density function F(φ m ) is calculated as follows: divide [-π,π) into M sampling areas, where M is a positive integer, and count the number of phase points where the truncated phase φ calculated by formula (7) falls in each sampling area. Divide this number by the total number of phase points to obtain the probability of the sampling area, and then count the probabilities of all sampling areas to obtain the corresponding probability density function F(φ) m );

[0039] When P is used to represent the probability, the probability density function F(φ m ) is expressed as:

[0040]

[0041] In formula (8), the median value φ of the phase in the mth sampling area is m As the mth sampling point, the probability F is the value of the mth sampling point, then F and φ m The curve is the probability density curve of the truncated phase φ; for any reflecting surface velocity interferometer fringe image, its phase distribution is complete, the corresponding probability density function is a straight curve, and the probability of each sampling point is 1 / M;

[0042] For each phase error combination, the truncated phase φ obtained can be obtained with a corresponding probability density function curve. That is, the probability density function curve is closest to a uniform straight line, and the phase distribution corresponding to the probability density function curve with the smallest standard deviation is the final phase calculation result. Further, step S3 includes the following steps:

[0043] S31. The process of phase unwrapping or phase unwrapping is to restore the truncated phase obtained by the above formula (7) to the real continuous phase. The basic principle of phase unwrapping is to compare the truncated phase values of two adjacent points according to the continuity principle, and add an integer multiple of 2π to the truncated phase value of the latter point so that the absolute value of the phase difference between the two points is less than 2π, thereby restoring the phase to continuity. Phase unwrapping is performed according to the following formula:

[0044]

[0045] In formula (9), φ d (k) represents the truncated phase of the kth point, φ c (k) represents the unwrapped phase at the kth point, φ d (k-1) represents the truncated phase of the k-1th point, INT represents the rounding operator, and n k Expressed as the phase order corresponding to the kth point, n k-1 It is expressed as the phase order corresponding to the k-1th point, and n0 is the phase order of the starting point of phase unwrapping, so n0 = 0; that is, a point is selected as the starting point of phase unwrapping, and the second point is obtained according to the second formula in formula (9) to obtain the phase order corresponding to the point, and then the first formula in formula (9) is used to obtain the unwrapped phase of the point, and all points are traversed in turn to obtain all the unwrapped phases; the phase order n k For every increase of one, the overall phase is raised by 2π, thus restoring the phase to continuity;

[0046] After obtaining the expanded phase, the shock wave velocity is calculated using the formula: u(t) = VPF·F(t). By selecting the position where the velocity is zero as the reference phase, the fringe change F(t) at any moment can be obtained, thereby calculating the velocity value of the shock wave u(t).

[0047] Compared with the prior art, the present invention has the following beneficial effects:

[0048] The multi-phase image arbitrary reflection surface velocity interferometer data processing method using the above technical solution has a result error of no more than 0.1 km / s and is relatively stable. Compared with the traditional Fourier transform method, the error between the processing result and the original data is more than 0.5 km / s at most and has a large fluctuation, which proves that the method involved in the present invention is significantly superior to the traditional method and effectively improves the data processing accuracy of the shock wave velocity. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 Schematic diagram of a four-phase image obtained by processing a single original image in the present invention;

[0050] Figure 2 A schematic diagram of phase image de-superposition in the present invention;

[0051] Figure 3 is a flow chart of data processing in the present invention;

[0052] Figure 4 This is a curve comparison chart using the probability density function after processing the data. DETAILED DESCRIPTION

[0053] The present invention will be further described below with reference to the embodiments and accompanying drawings.

[0054] The present invention provides a method for processing multi-phase image arbitrary reflection surface velocity interferometer data, which is specifically divided into the following steps:

[0055] S1, processing a single original image to obtain several multi-phase images;

[0056] Reference Figure 1 As shown, the fringe image recorded by the velocity interferometer of any reflecting surface can be expressed as follows:

[0057] I n (x,y)=A(x,y)+B(x,y)cos[φ(x,y)+δ n ] (1)

[0058] In formula (1), (x, y) represents any position on the image; A(x, y) represents the background intensity, which is related to the ambient noise and the uneven reflection of the surface to be measured; B(x, y) represents the intensity modulation distribution of the probe light; B(x, y) / A(x, y) gives the contrast of the fringe, φ(x, y) represents the phase to be measured; δ n It is expressed as the phase shift amount, n is a positive integer, where for the four-step phase shift, I1(x,y) is the original image in several multi-phase images; the original image shift term δ1 = 0, I n (x,y) is the shift term δ from the original image n get.

[0059] S2. performing phase solution using the multi-phase image;

[0060] The specific steps are as follows:

[0061] S21, calculating and obtaining the phase distribution of the original image;

[0062] Ideally, the second phase image I2(x, y) is shifted by δ2 = π / 2, the third phase image I3(x, y) is shifted by δ3 = π, and the fourth phase image I4(x, y) is shifted by δ4 = 3π / 2. Therefore, Equation (1) can be rewritten as follows:

[0063]

[0064] According to the above formula (2), we can get:

[0065]

[0066] Due to the influence of laser speckle noise and the uneven surface shape of optical elements, phase error will be introduced into the original signal, so formula (1) is transformed into the following formula:

[0067] I n (x,y)=A(x,y)+B(x,y)cos[φ(x,y)+δ n +Δδ n ] (4)

[0068] In formula (4), Δδ n Expressed as phase error;

[0069] When the phase shift error is incorporated into the phase shift amount, equation (4) can be written as:

[0070] I n (x,y)=A(x,y)+B(x,y)cos[φ(x,y)+δ n ] (5)

[0071] It should be noted that: δ in Equation 5 n The artificial phase shift and phase error are included. The benefit of this is to reduce the amount of calculation required for further calculations.

[0072] The least square method is used for phase calculation. For multi-phase images, its phase distribution can be expressed as:

[0073]

[0074] Solving equation (6) yields the truncated phase φ:

[0075]

[0076] Substitute the phase error of the multi-phase image into equation (6), and then use equation (7) to obtain the truncated phase distribution of the original image of the velocity interferometer of any reflecting surface.

[0077] S22. Solve the phase error to solve the phase:

[0078] δ for each image n The artificial phase shift and phase error Δδ n The artificial phase shift is known, and the phase error Δδ introduced by external non-ideal factors is calculated. n That's it;

[0079] The phase error caused by factors such as noise is small and remains constant during the VIASR system diagnostic time (<20ns), where "ns" represents nanoseconds. The phase error is found by traversal. The specific method is as follows:

[0080] Set a phase interval: [-π / 10,π / 10], get a set of phase values with a step size of π / 50, and use permutations and combinations to get phase error combinations of (-π / 10, -π / 10, -π / 10)... a total of 11 3 By substituting each phase error into formula (6), the corresponding phase distribution can be obtained.

[0081] It should be noted that the selection of the phase interval and the step size can be set freely. By designing a better algorithm to reduce the amount of calculation and improve the accuracy, the ultimate goal is to obtain the phase error combination that is closest to the actual situation.

[0082] S23. Use the probability density function to determine whether the phase distribution is correct:

[0083] The properties of inverse trigonometric functions show that the phase obtained by equation (7) is a truncated phase distributed in the interval [-π,π). The probability density function can analyze the statistical characteristics of an image, mainly by calculating the probability of occurrence of a random variable to reveal its distribution. The probability density function is applied to the truncated phase of the fringe image of an arbitrary reflecting surface velocity interferometer to describe the impact of the phase error on the truncated phase.

[0084] Therefore, the probability density function F(φ m ) is calculated as follows: divide [-π,π) into M sampling areas, where M is a positive integer, and count the number of phase points where the truncated phase φ calculated by formula (7) falls in each sampling area. Divide this number by the total number of phase points to obtain the probability of the sampling area, and then count the probabilities of all sampling areas to obtain the corresponding probability density function F(φ) m );

[0085] When P is used to represent the probability, the probability density function F(φ m ) is expressed as:

[0086]

[0087] In formula (8), the median value φ of the phase in the mth sampling area is m As the mth sampling point, the probability F is the value of the mth sampling point, then F and φ mThe curve is the probability density curve of the truncated phase φ; for any reflecting surface velocity interferometer fringe image, its phase distribution is complete, the corresponding probability density function is a straight curve, and the probability of each sampling point is 1 / M;

[0088] For each phase error combination, the corresponding probability density function curve can be obtained for the truncated phase φ. That is, the probability density function curve is closest to a uniform straight line. The phase distribution corresponding to the minimum standard deviation of the probability density function curve is the final phase calculation result.

[0089] S3, phase unwrapping, calculate the shock wave velocity;

[0090] The specific steps are:

[0091] Reference Figure 2 As shown in Figure 1, the process of phase unwrapping or phase unwrapping is to restore the truncated phase obtained by the above formula (7) to the real continuous phase. The basic principle of phase unwrapping is to compare the truncated phase values of two adjacent points according to the continuity principle, and add an integer multiple of 2π to the truncated phase value of the latter point so that the absolute value of the phase difference between the two points is less than 2π, thereby restoring the phase to continuity. Phase unwrapping is performed according to the following formula:

[0092]

[0093] In formula (9), φ d (k) represents the truncated phase of the kth point, φ c (k) represents the unwrapped phase at the kth point, φ d (k-1) represents the truncated phase of the k-1th point, INT represents the rounding operator, and n k Expressed as the phase order corresponding to the kth point, n k-1 It is expressed as the phase order corresponding to the k-1th point, and n0 is the phase order of the starting point of phase unwrapping, so n0 = 0; that is, a point is selected as the starting point of phase unwrapping, and the second point is obtained according to the second formula in formula (9) to obtain the phase order corresponding to the point, and then the first formula in formula (9) is used to obtain the unwrapped phase of the point, and all points are traversed in turn to obtain all the unwrapped phases; the phase order n k For every increase of one, the overall phase is raised by 2π, thus restoring the phase to continuity;

[0094] Reference Figure 2 As shown in (C), after the expanded phase is obtained, the shock wave velocity is calculated using the formula: u(t) = VPF·F(t). The position where the velocity is zero is selected as the reference phase. The fringe change F(t) at any time can be obtained, thereby calculating the velocity value of the shock wave u(t).

[0095] Through this algorithm Figure 1 The image shown is processed, refer to Figure 4 The figure shows the probability density function curve results before and after processing; the number of sampling intervals M = 63, so its ideal probability density is 1 / 63 = 0.0159. According to the comparison of the black dotted line in the figure, it can be seen that after processing using this method, the uniformity of the phase distribution is significantly improved.

[0096] The embodiments of the present invention are described in detail above, and examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described above with reference to the accompanying drawings are exemplary and are intended to be used to explain the present invention, and are not to be construed as limiting the present invention.

[0097] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "length", "width", "thickness", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "clockwise", "counterclockwise" and the like to indicate orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be understood as limiting the present invention.

[0098] In the present invention, unless otherwise expressly specified or limited, the terms "mounted," "connected," "connect," "fixed," etc. should be understood broadly. For example, they may refer to fixed, detachable, or integral connections; mechanical or electrical connections; direct or indirect connections through an intermediary; or internal communication between two components. Those skilled in the art will understand the specific meanings of the above terms in the present invention based on specific circumstances.

[0099] In the present invention, unless otherwise expressly specified or limited, a first feature being "above" or "below" a second feature may include the first and second features being in direct contact, or may include the first and second features being in contact not directly but through another feature between them. Furthermore, a first feature being "above," "above," and "above" a second feature may include the first feature being directly above or obliquely above the second feature, or may simply mean that the first feature is higher in level than the second feature. A first feature being "below," "below," and "below" a second feature may include the first feature being directly below or obliquely below the second feature, or may simply mean that the first feature is lower in level than the second feature.

[0100] Finally, it should be noted that the above description is only a preferred embodiment of the present invention. Under the guidance of the present invention, ordinary technicians in this field can make various similar expressions without violating the purpose and claims of the present invention. Such changes fall within the scope of protection of the present invention.

Claims

1. A method for processing multi-phase image arbitrary reflection surface velocity interferometer data, characterized in that: Follow these steps: S1, processing a single original image to obtain several multi-phase images; S2. performing phase solution using the multi-phase image; S3, phase unwrapping, calculate the shock wave velocity; Wherein, the step S2 includes the following steps: S21, calculating and obtaining the phase distribution of the original image; S22, solving the phase error, thereby solving the phase; S23, using the probability density function to determine whether the phase distribution is correct; In step S1, the fringe image recorded by the velocity interferometer of any reflecting surface is expressed by the following formula: Yo n (x,y)=A(x,y)+B(x,y)cos[φ(x,y)+δ n ] (1) In formula (1), (x, y) represents any position on the image; A(x, y) represents the background intensity, which is related to the ambient noise and the uneven reflection of the surface to be measured; B(x, y) represents the intensity modulation distribution of the probe light; B(x, y) / A(x, y) gives the contrast of the fringe, φ(x, y) represents the phase to be measured; δ n It is expressed as the phase shift amount, n is a positive integer, where for the four-step phase shift, I1(x,y) is the original image in several multi-phase images; the original image shift term δ1 = 0, I n (x,y) is the shift term δ from the original image n get; The step S21 includes the following steps: In an ideal situation, the second phase image shift term δ2 = π / 2, the third phase image shift term δ3 = π, and the fourth phase image shift term δ4 = 3π / 2, so Equation (1) can be rewritten as follows: According to the above formula (2), we can get: Due to the influence of laser speckle noise and the uneven surface shape of optical elements, phase error will be introduced into the original signal, so formula (1) is transformed into the following formula: Yo n (x,y)=A(x,y)+B(x,y)cos[φ(x,y)+δ n +△δ n ] (4) In formula (4), Δδ n Expressed as phase error; When the phase shift error is incorporated into the phase shift amount, equation (4) can be written as: Yo n (x,y)=A(x,y)+B(x,y)cos[φ(x,y)+δ n ] (5) The least square method is used for phase calculation. For multi-phase images, the phase distribution is expressed as: Solving equation (6) yields the truncated phase φ: Substitute the phase error of the multi-phase image into equation (6), and then use equation (7) to obtain the truncated phase distribution of the original image of the velocity interferometer of any reflecting surface; In step S23, the properties of the inverse trigonometric function show that the phase obtained by the above formula (7) is a truncated phase distributed in the interval [-π, π). The probability density function can analyze the statistical characteristics of the image, wherein the distribution of the random variable is mainly revealed by calculating the probability of occurrence. The probability density function is applied to the truncated phase of the fringe image of any reflecting surface velocity interferometer to describe the influence of the phase error on the truncated phase. Therefore, the probability density function F(φ m ) is calculated as follows: divide [-π,π) into M sampling areas, where M is a positive integer, and count the number of phase points where the truncated phase φ calculated by formula (7) falls in each sampling area. Divide this number by the total number of phase points to obtain the probability of the sampling area, and then count the probabilities of all sampling areas to obtain the corresponding probability density function F(φ) m ); When P is used to represent the probability, the probability density function F(φ m ) is expressed as: In formula (8), the median value φ of the phase in the mth sampling area is m As the mth sampling point, the probability F is the value of the mth sampling point, then F and φ m The curve is the probability density curve of the truncated phase φ; for any reflecting surface velocity interferometer fringe image, its phase distribution is complete, the corresponding probability density function is a straight curve, and the probability of each sampling point is 1 / M; For each phase error combination, the corresponding probability density function curve can be obtained. That is, the probability density function curve is closest to a uniform straight line. The phase distribution corresponding to the minimum standard deviation of the probability density function curve is the final phase calculation result. The step S3 comprises the following steps: S31. The process of phase unwrapping or phase unwrapping is to restore the truncated phase obtained by the above formula (7) to the real continuous phase. The basic principle of phase unwrapping is to compare the truncated phase values of two adjacent points according to the continuity principle, and add an integer multiple of 2π to the truncated phase value of the latter point so that the absolute value of the phase difference between the two points is less than 2π, thereby restoring the phase to continuity. Phase unwrapping is performed according to the following formula: In formula (9), φ d (k) represents the truncated phase of the kth point, φ c (k) represents the unwrapped phase at the kth point, φ d (k-1) represents the truncated phase of the k-1th point, INT represents the rounding operator, and n k Expressed as the phase order corresponding to the kth point, n k-1 It is expressed as the phase order corresponding to the k-1th point, and n0 is the phase order of the starting point of phase unwrapping, so n0 = 0; that is, a point is selected as the starting point of phase unwrapping, and the second point is obtained according to the second formula in formula (9) to obtain the phase order corresponding to the point, and then the first formula in formula (9) is used to obtain the unwrapped phase of the point, and all points are traversed in turn to obtain all the unwrapped phases; the phase order n k For every increase of one, the overall phase is raised by 2π, thus restoring the phase to continuity; After obtaining the expanded phase, the shock wave velocity is calculated using the formula: u(t) = VPF·F(t). By selecting the position where the velocity is zero as the reference phase, the fringe change F(t) at any moment can be obtained, thereby calculating the velocity value of the shock wave u(t).

2. The multi-phase image arbitrary reflection surface velocity interferometer data processing method according to claim 1, characterized in that: In step S22, a phase interval is set: [-π / 10, π / 10], and a set of phase values is obtained with a step size of π / 50. The phase error combinations are respectively taken as (-π / 10, -π / 10, -π / 10) through permutation and combination. A total of 11 3 Substitute each set of phase errors into formula (6) to obtain the corresponding phase distribution.

Images