Correction method of nonlinear phase error based on digital projection 3D measurement system

Abstract

A method for correcting nonlinear phase errors based on a digital projection three-dimensional measurement system comprises the following steps: setting a fringe space period as M, setting an actual fringe phase shift step number as N, setting a phase shift step number of a phase error fringe diagram as N′, setting t as a coefficient, using a computer to generate an N×N′-step phase shift fringe diagram according to a fringe pixel period of M=t×N×N′, using a three-dimensional measurement system to project the fringe diagram onto a whiteboard, and collecting an actual phase shift fringe diagram; extracting the collected phase shift fringe diagram to obtain N′ groups of N-step phase shift fringe diagrams, respectively calculating an actual phase and a corresponding N×N′-step ideal phase and obtaining a phase error, and obtaining N′ phase error diagrams; using a least squares algorithm to calculate the amplitude of the phase shift fringe diagram, obtaining a value of a gamma correction factor of each pixel according to a relationship between the amplitude and the gamma correction factor, correcting the original fringe diagram generated by the computer according to the gamma correction factor, and using the three-dimensional measurement system to project the corrected phase shift fringe diagram for three-dimensional reconstruction.

Description

[Technical field]

[0001] The present invention relates to the field of projection measurement technology, and in particular to a method for correcting a nonlinear phase error based on a digital projection three-dimensional measurement system. [Background technology]

[0002] At present, there are many methods for correcting the gamma correction factor of the projection measurement system, which can be roughly divided into two categories: passive phase correction method and active phase correction method. The passive phase correction method mainly includes statistical model, lookup table model and iterative model. It is a method that uses the actual collected distorted fringe image to calculate the compressed phase and performs phase compensation on the compressed phase. However, the passive phase correction method is easily affected by the environment, resulting in inaccurate test results. In order to overcome the above defects, the three-step phase shift method is usually used to construct a phase error model using the corrected gamma correction factor. The value of the optimal gamma correction factor is solved by estimating the maximum amplitude of the phase error, and then used for the correction of the projection fringe, thereby weakening the nonlinear response of the system and correcting the projection fringe image. Although the active phase correction method can more conveniently calculate the gamma correction factor of the projection measurement system, the corrected phase error is still high, the data is not accurate enough, and it still cannot meet the actual measurement needs.

[0003] In view of this, it is necessary to provide a new method for correcting the nonlinear phase error of a digital projection three-dimensional measurement system to overcome the above-mentioned defects. [Summary of the invention]

[0004] The purpose of the present invention is to provide a method for correcting the nonlinear phase error of a digital projection three-dimensional measurement system, in which the phase errors before and after the correction are small and the test data are accurate.

[0005] In order to achieve the above object, the present invention provides a nonlinear phase error correction method based on a digital projection three-dimensional measurement system, comprising the following steps:

[0006] S1: Set the fringe space period to M, set the actual fringe phase shift steps to N, set the phase shift steps of the phase error fringe diagram to N', set t as the coefficient, and the computer generates a N×N'-step phase shift fringe diagram with a fringe space period of M according to the fringe pixel period of M=t×N×N'. m}, a three-dimensional measurement system is used to measure the fringe pattern {I m} Project onto a whiteboard and collect the actual phase-shift fringe pattern

[0007] S2: Phase shift fringe pattern collected Extract and get N′ groups of N-step phase shift fringe patterns The least square method is used to calculate the actual phase of N′ groups of N-step phase-shifted fringe patterns. and the ideal phase corresponding to the fringe spatial period M With actual phase Subtract the ideal phase at the corresponding phase shift step The corresponding phase error is obtained Get N′ phase error images The phase error Sinusoidal stripes distribution;

[0008] S3: Calculate the phase shift fringe pattern using the least squares algorithm Amplitude A Δφ , according to the amplitude A Δφ The relationship between the gamma correction factor γ and the gamma correction factor γ is used to obtain the value of the gamma correction factor γ of each pixel, the original fringe pattern generated by the computer is corrected according to 1 / γ of the gamma correction factor γ, and the three-dimensional measurement system is used to project the corrected phase-shift fringe pattern for three-dimensional reconstruction.

[0009] In a preferred embodiment, the computer generates a N×N′-step phase-shifted fringe pattern {I m}, where N≥3, coefficient t is a positive integer, N′≥3, n ranges from 1 to N, and k ranges from 1 to N′.

[0010] In a preferred embodiment, the phase shift fringe pattern collected in S2 The extraction is based on the phase shift fringe pattern collected Starting from the kth phase-shift fringe pattern in the image, a fringe pattern is extracted every t·N′ phase-shift fringe pattern, and a total of N fringe patterns are extracted to form the kth group of N-step phase-shift fringe pattern sets. N′ groups of N-step phase-shifted fringe patterns are obtained.

[0011] In a preferred embodiment, the actual phase described in S2 According to the N-step phase shift fringe pattern Through the following formula Calculated,δ n is the phase offset, and δ n =2π(n-1) / N.

[0012] In a preferred embodiment, the ideal phase described in S2 Through the following formula Obtained by calculation.

[0013] In a preferred embodiment, the phase error described in S2 The above formula (1) obtains And the above formula (2) obtained According to the following formula Calculated, and the phase error Sinusoidal fringe distribution; each phase error image has a phase shift of δ k =2π(k-1) / N′.

[0014] In a preferred embodiment, the amplitude A described in S3 Δφ Through the following formula Obtained by calculation.

[0015] In a preferred embodiment, the value of the gamma correction factor γ of the amplitude-phase shift fringe pattern in S3 is obtained according to the amplitude A obtained by the above formula (4): Δφ Through the following formula The average value of the gamma correction factor γ of all pixels is calculated and taken as the value of the gamma correction factor γ of the three-dimensional measurement system.

[0016] Compared with the prior art, the beneficial effect is that the present invention provides a method for correcting nonlinear phase errors based on a digital projection three-dimensional measurement system, the phase errors before and after correction are small, the test data is accurate, and the method is easy to use.

Brief Description of the Drawings

[0017] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments are briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without creative work.

[0018] Figure 1 A flow chart of a method for correcting nonlinear phase errors of a digital projection three-dimensional measurement system provided by the present invention;

[0019] Figure 2 is a comparison diagram of the fringe image before correction and the fringe image after correction;

[0020] Figure 3 Schematic diagram of distribution curves of theoretical phase, actual phase and phase error of 100 pixel samples in the embodiment;

[0021] Figure 4 is a graph of phase errors of 100 pixel samples in an embodiment;

[0022] Figure 5 is a schematic diagram of distribution curves of theoretical phase, actual phase and phase error in 100 pixel samples in the second embodiment;

[0023] Figure 6 is a schematic diagram of a Gamma curve of 100 pixel samples in the second embodiment;

[0024] Figure 7 is a graph of the phase error Δφ of 100 pixel samples in the second embodiment;

[0025] Figure 8 FIG. 4 is a curve diagram of the calculated RSME value in the second embodiment. [Specific implementation method]

[0026] In order to make the purpose, technical solution and beneficial technical effect of the present invention clearer, the present invention is further described in detail below in conjunction with the accompanying drawings and specific implementation methods. It should be understood that the specific implementation methods described in this specification are only for explaining the present invention, not for limiting the present invention.

[0027] See also Figure 1 The present invention provides a nonlinear phase error correction method based on a digital projection three-dimensional measurement system, comprising the following steps:

[0028] S1: Set the actual fringe phase shift step number to M, set the actual fringe phase shift step number to N, set the phase shift step number of the phase error fringe diagram to N', set t as a coefficient, and the computer generates an N×N'-step phase shift fringe diagram with a fringe space period of M according to the pixel period of M=t×N×N'. m}, a three-dimensional measurement system is used to measure the fringe pattern {I m} Project onto a whiteboard and collect the actual phase-shift fringe pattern

[0029] S2: Phase shift fringe pattern collected Extract and get N′ groups of N-step phase shift fringe patterns The least square method is used to calculate the actual phase of N′ groups of N-step phase-shifted fringe patterns. and the ideal phase of the corresponding fringe spatial period M With actual phase Subtract the ideal phase at the corresponding phase shift step The corresponding phase error is obtained Get N′

[0030] Phase error diagram The phase error Sinusoidal stripes distribution;

[0031] S3: Calculate the phase shift fringe pattern using the least squares algorithm Amplitude A Δφ , according to the amplitude A ΔφThe relationship between the gamma correction factor γ and the gamma correction factor γ is used to obtain the value of the gamma correction factor γ of each pixel, the original fringe pattern generated by the computer is corrected according to 1 / γ of the gamma correction factor γ, and the three-dimensional measurement system is used to project the corrected phase-shift fringe pattern for three-dimensional reconstruction.

[0032] Specifically, the computer generates an N×N′-step phase-shifted fringe pattern {I m}, where N≥3, coefficient t is a positive integer, N′≥3, n ranges from 1 to N, and k ranges from 1 to N′.

[0033] Specifically, the phase shift fringe pattern collected in S2 The extraction is based on the phase shift fringe pattern collected Starting from the kth phase-shift fringe pattern in the image, a fringe pattern is extracted every t·N′ phase-shift fringe pattern, and a total of N fringe patterns are extracted to form the kth group of N-step phase-shift fringe pattern sets. N′ groups of N-step phase-shifted fringe patterns are obtained.

[0034] Specifically, the actual phase described in S2 According to the N-step phase shift fringe pattern Through the following formula Calculated,δ n is the phase offset, and δ n =2π(n-1) / N.

[0035] Specifically, the ideal phase described in S2 Through the following formula Obtained by calculation.

[0036] Specifically, the phase error described in S2 The above formula (1) obtains And the above formula (2) obtained Depend on Calculated, and the phase error Sinusoidal fringe distribution, N′ phase error images are obtained Each phase error graph The phase shift δ k =2π(k-1) / N′.

[0037] Specifically, the amplitude |c| described in S3 is obtained according to the phase error A Δφ Through the following formula Obtained by calculation.

[0038] Specifically, the phase shift fringe pattern in S3 The value of the gamma correction factor γ is obtained according to the amplitude A obtained by the above formula (4)Δφ Through the following formula The average value of the gamma correction factor γ of all pixels is calculated and taken as the value of the gamma correction factor γ of the three-dimensional measurement system.

[0039] First embodiment:

[0040] The actual fringe phase shift step number is set to N = 3; the phase shift step number of the selected phase error fringe pattern is N' = 4. The computer generates a N × N' step phase shift fringe pattern with a fringe space period of M according to the pixel period of M = t × N × N'. The coefficient t is a positive integer. The fringe pattern {I m} Projected onto a flat white board and collected the actual phase shift fringe pattern formed

[0041] Phase shift fringe pattern collected Starting from the kth phase-shift fringe pattern in the image, a fringe pattern is extracted every t·N′ phase-shift fringe pattern, and a total of N fringe patterns are extracted to form the kth group of N-step phase-shift fringe pattern sets. The actual phase of N′ groups of N-step phase-shifted fringe patterns is calculated by the least squares method. and the ideal phase of the corresponding fringe spatial period M Then through The corresponding phase error is obtained Then we get N′ phase error graphs

[0042] Phase Error Plot Phase error The periodicity is sinusoidal and the phase error The period is 1 / N of the projected fringe period, and the least squares algorithm is used to calculate the N′ amplitude phase error Phase shift fringe pattern Amplitude A Δφ ,like: According to the phase shift fringe pattern Amplitude A Δφ The relationship with the gamma correction factor γ is as follows: The value of the gamma correction factor γ of the phase corresponding to each pixel is obtained, and the average value of the gamma correction factor γ of each pixel is taken as the value of the gamma correction factor γ of the three-dimensional measurement system, and the phase shift fringe pattern generated by the computer is corrected according to 1 / γ of the gamma correction factor γ, and the three-dimensional measurement system is used to project the corrected phase shift fringe pattern for three-dimensional reconstruction; the gamma correction factor γ is preset 1 =1.7, get the fringe image Estimation of distorted fringe image I using a three-step phase shift method 1 The gamma correction factor γ'1 =1.6214, and the corrected fringe image is obtained according to The maximum amplitude A of the phase error change before and after precoding is calculated using the correction coefficient 1 / γ in Table 1. Δφ The values ​​of the minimum mean square error RSME are shown in Table 1.

[0043] Table 1:

[0044] Correction factor 1 / γ Maximum A Δφ RMSE

[0045] Before correction 1 0.1732 0.1225

[0046] After correction 0.6168 0.0141 0.0098

[0047] Second embodiment:

[0048] The actual fringe phase shift step number is set to N = 3, and the projected fringe periods are 36, 36, 30, and 36 pixels respectively; the phase shift step number of the phase error fringe pattern is selected to be N' = 3, 4, 5, and 6; the computer generates a phase shift fringe pattern with a fringe space period of M according to the pixel period of M = t × N × N'. m}, the coefficient t is a positive integer, where N×N′ is 9, 12, 15 and 18 respectively. The three-dimensional measurement system is used to measure the phase shift fringe pattern {I m} Project it onto a flat object and collect the actual phase-shifted fringe pattern after formation

[0049]

[0050] Phase shift fringe pattern collected Starting from the kth phase-shift fringe pattern in the image, a fringe pattern is extracted every t·N′ phase-shift fringe pattern, and a total of N fringe patterns are extracted to form the kth group of N-step phase-shift fringe pattern sets. The actual phase of N′ groups of N-step phase-shifted fringe patterns is calculated by the least squares method. And the ideal phase under the corresponding phase shift step Then use the actual phase Subtract the ideal phase at the corresponding phase shift step The corresponding phase error is obtained Then we get N′ phase error graphs The phase error diagram Phase error Sinusoidal fringe distribution, and phase error The period is 1 / N of the projected fringe period, and the least squares algorithm is used to calculate the N′ amplitude phase error Phase shift fringe pattern The amplitude |c|, such as:

[0051] According to the phase error Phase shift fringe pattern The relationship between the amplitude |c| and the gamma correction factor γ is as follows: The value of the gamma correction factor γ of the phase corresponding to each pixel is obtained, and the average value of the gamma correction factor γ of each pixel is taken as the value of the gamma correction factor γ of the three-dimensional measurement system, and the phase shift fringe pattern generated by the computer is corrected according to 1 / γ of the gamma correction factor γ, and the three-dimensional reconstruction is performed using the phase shift fringe pattern after projection correction by the three-dimensional measurement system; the phase calculated by the 24-step phase shift projection fringe image with a period of 24 pixels is taken as the ideal phase, and the phase calculated by the 3-step phase shift fringe image is taken as the actual phase.

[0052] The following takes the projection fringe phase shift step number N=3 as an example, as shown in Table 2, for example, when N'=4, the 1st, 2nd, 3rd, and 4th projection fringe image sequences are [1,5,9], [2,6,10], [3,7,11], and [4,8,12], then the corresponding projection fringe image starting phase sequences can be obtained as [0,5*2π / 12, 9*2π / 12], [2π / 12, 6*2π / 12, 10*2π / 12], respectively.

[0053] [2*2π / 12, 7*2π / 12, 11*2π / 12], [3*2π / 12, 8*2π / 12, 12*2π / 12]; the phase errors of the four groups of three-step projection fringes are calculated according to the above formula (3), the amplitude of the phase error fringes of the four-step phase shift is estimated according to the above formula (4), and then the correction factor γ value of each pixel is calculated according to the above formula (5), and the average of the γ values ​​of all pixels is taken as the correction factor γ of the system. In order to reduce the phase error and perform phase error compensation, the sinusoidal fringe pattern generated by the computer is corrected according to the calculated correction factor γ value before the three-dimensional system scans:

[0054] Table 2:

[0055]

[0056] The maximum amplitude and minimum mean square error RSME of the phase error before and after correction are obtained, as shown in Table 3.

[0057] Table 3:

[0058]

[0059]

[0060] Table 1 is a statistical table of the maximum amplitude and minimum mean square error RSME of the phase error in the image samples before and after correction in the first embodiment of the present invention; Table 2 is a statistical table of the fringe image extracted for the collected phase-shift fringe pattern in the second embodiment; Table 3 is a data table of the fringe period and correction coefficient in the image samples in the second embodiment; Figure 1 A flow chart of a method for correcting nonlinear phase errors based on a digital projection measurement system provided by the present invention; Figure 2 1 is a comparison diagram of the fringe image before correction (left) and the fringe image after correction (right) of the first embodiment; Figure 3 is a schematic diagram of distribution curves of the ideal phase, actual phase and phase error of 100 pixel samples of the first embodiment; Figure 4 is a graph of phase errors of 100 pixel samples in the first embodiment.

[0061] Table 4:

[0062]

[0063] Table 4 is a statistical table of the correction coefficient 1 / γ, the maximum phase error and the minimum mean square error RSME in the second embodiment; Figure 5 is a schematic diagram of distribution curves of theoretical phase, actual phase and phase error in 100 pixel samples in the second embodiment; Figure 6 is a schematic diagram of a Gamma curve of 100 pixel samples in the second embodiment; Figure 7 is a graph of phase error using 100 pixel samples in the second embodiment; Figure 8 FIG. 1 is a curve diagram of the RSME value calculated in the second embodiment. Figure 6 and Figure 7 It can be seen that the maximum phase error after precoding is reduced.

[0064] The beneficial effect is that the method for phase error based on a projection three-dimensional measurement system provided by the present invention makes the phase error and the minimum mean square error smaller after correction, which is beneficial to improving the measurement accuracy and facilitating the measurement.

[0065] The present invention is not limited to what is described in the specification and implementation modes, and therefore additional advantages and modifications can be easily realized by those skilled in the art. Therefore, without departing from the spirit and scope of the general concept defined by the claims and their equivalents, the present invention is not limited to the specific details, representative devices, and illustrative examples shown and described herein.

Claims

1. A nonlinear phase error correction method based on a digital projection three-dimensional measurement system, characterized in that: The steps include: S1: Set the fringe space period to M, set the actual fringe phase shift steps to N, set the phase shift steps of the phase error fringe diagram to N', set t as the coefficient, and the computer generates a N×N'-step phase shift fringe diagram with a fringe space period of M according to the fringe pixel period of M=t×N×N'. m }, a three-dimensional measurement system is used to measure the fringe pattern {I m } Project onto a whiteboard and collect the actual phase-shift fringe pattern S2: Phase shift fringe pattern collected Extract and get N′ groups of N-step phase shift fringe patterns The least square method is used to calculate the actual phase of N′ groups of N-step phase-shifted fringe patterns. The ideal phase corresponding to the fringe space period M is obtained by subtracting the corresponding ideal phase from the actual phase. The corresponding phase error is obtained Get N′ phase error images The phase error Sinusoidal stripes distribution; S3: Calculate the phase shift fringe pattern using the least squares algorithm Amplitude A Δφ , according to the amplitude A Δφ The relationship between the gamma correction factor γ and the gamma correction factor γ is used to obtain the value of the gamma correction factor γ of each pixel, the original fringe pattern generated by the computer is corrected according to 1 / γ of the gamma correction factor γ, and the phase-shift fringe pattern after correction is projected by a three-dimensional measurement system for three-dimensional reconstruction; Phase-shifted fringe patterns collected as described in S2 The extraction is based on the collected phase shift fringe pattern Starting from the kth phase-shift fringe pattern in the image, a fringe pattern is extracted every t·N′ phase-shift fringe pattern, and a total of N fringe patterns are extracted to form the kth group of N-step phase-shift fringe pattern sets. The actual phase described in S2 According to the N-step phase shift fringe pattern Through the following formula Calculated,δ n is the phase offset, and δ n =2π(n-1) / N; The ideal phase described in S2 Through the following formula Calculate and obtain; The phase error described in S2 pass Calculated, and the phase error Sinusoidal fringe distribution, N′ phase error images are obtained Each phase error graph The phase shift δ k =2π(k-1) / N′; The amplitude A described in S3 Δφ Through the following formula Calculate and obtain; Phase shift fringe pattern in S3 The value of the gamma correction factor γ is obtained according to the amplitude A obtained by the above formula (4) Δφ Through the following formula The average value of the gamma correction factor γ of all pixels is calculated and taken as the value of the gamma correction factor γ of the three-dimensional measurement system.

2. The nonlinear phase error correction method based on the digital projection three-dimensional measurement system according to claim 1 is characterized in that: The computer generates a N×N′-step phase-shifted fringe pattern {I m }, where N≥3, coefficient t is a positive integer, N′≥3, n ranges from 1 to N, and k ranges from 1 to N′.

Images