A method for suppressing spurious reflections based on a multi-frequency phase shift method

Abstract

The application discloses a kind of based on parasitic reflection inhibition method of multi-frequency phase shift method, comprising: obtaining the deformed fringe image after object reflection;According to intensity information, using phase shift method, calculate truncated phase and generate modulation curve;Truncated phase is expanded into continuous phase per frequency;Judge whether there is minimum value in modulation curve, if yes, use auxiliary function peak position search continuous phase in which the fringe frequency that phase error is zero;Extract the truncated phase corresponding to the fringe frequency that phase error is zero, carry out phase expansion, and with the minimum number of 0 in modulation curve as the demarcation line, the phase order of the best frequency in the fringe frequency that phase error is zero is corrected in regional, to obtain correction result;According to correction result, calculate upper surface screen coordinate;Otherwise, according to maximum fringe frequency, calculate upper surface screen coordinate.

Description

A Parasitic Reflection Suppression Method Based on Multi-Frequency Phase Shift Technical Field

[0001] This invention relates to the field of reflection suppression technology, and more specifically to a parasitic reflection suppression method based on multi-frequency phase shifting. Background Technology

[0002] Optical 3D measurement technology, as a non-contact, high-speed, and high-precision measurement method, is widely used in many fields. With the development of modern high-end manufacturing, the demand for measuring mirror objects in fields such as automobiles, aerospace, and precision optics is becoming increasingly strong. Phase Measuring Deflectometry (PMD) is suitable for measuring mirrors or mirror-like surfaces, especially aspherical and freeform optical surfaces. Its high precision and high speed also make it of great research value.

[0003] However, when the object being measured is a transparent element, the deformed fringe pattern captured by the camera includes reflections not only from the upper surface but also from the lower surface; these lower surface reflections are often referred to as parasitic reflections. This phenomenon causes fringe pattern overlap, resulting in compromised phase accuracy calculated using the phase-shifting method, and consequently reducing the accuracy of PMD measurements. The simplest solution is to roughen the lower surface, but this method is destructive.

[0004] Most existing methods are designed for planar elements, but lenses play a crucial role in optical components. Therefore, reconstructing the surface shape of a transparent lens from overlapping fringes is equally important. Some researchers have also proposed a hybrid reflection-refraction deflection model using the multi-frequency method, which reconstructs the surface shapes of the front and back surfaces of a transparent lens. However, this requires obtaining the initial values ​​of the surface shape of the test piece through reverse ray tracing.

[0005] In summary, there are still many gaps in our understanding of how to restore the surface shape of a lens with a certain curvature. Summary of the Invention

[0006] The purpose of this invention is to provide a parasitic reflection suppression method based on multi-frequency phase shifting, which can effectively suppress the reflection of the lower surface of a transparent object, thereby accurately restoring the three-dimensional surface shape of a curved surface with parasitic reflection.

[0007] The technical solution of the present invention to solve the above-mentioned technical problems is as follows:

[0008] This invention provides a parasitic reflection suppression method based on a multi-frequency phase shift method, characterized in that the parasitic reflection suppression method based on the multi-frequency phase shift method includes:

[0009] S1: Acquire a deformed stripe image after reflection from an object, wherein the deformed stripe image includes surface shape information of the upper and lower surfaces of the object to be tested, that is, a certain pixel in the deformed stripe image corresponds to points p1 and p2 on the LCD screen respectively, and the intensity information of the pixel in the deformed stripe image includes the intensity information of points p1 and p2.

[0010] S2: Based on the intensity information of a certain pixel in the deformed stripe image, the phase shift method is used to calculate the truncated phase and generate a modulation curve;

[0011] S3: Expand the truncated phase frequency by frequency into a continuous phase;

[0012] S4: Determine whether there is a minimum value in the modulation curve. If yes, proceed to S5; otherwise, proceed to S8.

[0013] S5: Use the peak position of the auxiliary function to search for the fringe frequency in the continuous phase that makes the phase error zero;

[0014] S6: Extract the truncated phase corresponding to the stripe frequency that makes the phase error zero, perform phase expansion, and use the pixel point where the number of minimum values ​​in the modulation curve is 0 as the boundary line to correct the phase order of the best frequency in the stripe frequency that makes the phase error zero in different regions, and obtain the correction result.

[0015] S7: Calculate the screen coordinates of the upper surface based on the correction results;

[0016] S8: Calculate the screen coordinates of the upper surface based on the maximum stripe frequency;

[0017] S9: Obtain the upper surface reconstruction result based on the upper surface screen coordinates.

[0018] Alternatively, in S1, the intensity information I of a certain pixel in the deformed stripe image can be represented as:

[0019] I = A + M1cosΦ t +M2cosΦ b

[0020] Where M1 and M2 are the modulation degrees of the upper and lower surfaces, respectively, A is the background light intensity, and Φ is the background light intensity. t and Φ b These represent the phase information of the upper surface and the phase information of the lower surface, respectively.

[0021] Alternatively, in step S2, based on the intensity information of a pixel in the deformed stripe image, the truncated phase is calculated using the phase-shifting method. include:

[0022]

[0023] Among them, I j To add phase shift factor δ j Subsequent intensity information and I j =A+M1cos[Φ t +δ j ]+M2cos[Φ b +δ j A represents the background light intensity, M1 and M2 represent the modulation degree of the upper surface and the lower surface, respectively, and Φ t and Φ b δ represents the phase information of the upper surface and the phase information of the lower surface, respectively. j Denotes the phase shift factor and δ j = 2πj / N, where N represents the number of phase shift steps and N≥3, j represents the j-th phase shift step and j=0,1,......,N-1, and π is pi. This indicates the cutoff phase when there is no parasitic effect. Indicates phase error and η = M2 / M1 represents the ratio of the modulation density of the lower surface to that of the upper surface.

[0024] Alternatively, S3 includes:

[0025]

[0026] in, Φ represents the cutoff phase at the i-th frequency. i Indicates to The expanded phase, where n is the phase order and floor indicates rounding down, f i f represents the i-th frequency. i-1 This represents the (i-1)th frequency. This represents the expanded phase of the truncated phase at the (i-1)th frequency. This represents the cutoff phase at the i-th frequency, and π represents pi.

[0027] Alternatively, in step S5, the auxiliary function g(f) is:

[0028] g(f) = Φ(f) - fΦ'(f)

[0029] Where Φ(f) represents the continuous phase, f represents the fringe frequency, and Φ'(f) represents the first derivative of the continuous phase.

[0030] Alternatively, S5 includes:

[0031] The number of peaks of the auxiliary function is determined based on the number of minimum values ​​in the modulation curve.

[0032] The corresponding stripe frequency is determined based on the peak position and the position between adjacent peaks. When the number of peaks is greater than 2, the stripe frequency includes even-numbered multiples of the stripe frequency and odd-numbered multiples of the stripe frequency.

[0033] The difference between the screen coordinates of the upper and lower surfaces is determined based on the stripe frequency.

[0034] The optimal frequency is determined based on the difference between the screen coordinates of the upper and lower surfaces; wherein the optimal frequency is the largest even multiple of a series of fringe frequencies that satisfy a phase error of 0.

[0035] Alternatively, determining the difference in screen coordinates between the upper and lower surfaces based on the fringe frequency includes:

[0036] When the number of peaks is unique, the fringe frequency f1 = 1 / (2Δx), where Δx represents the difference between the screen coordinates of the upper and lower surfaces;

[0037] When the number of peaks is not unique, search for a series of odd multiples of stripe frequencies;

[0038] The difference between the upper and lower surface screens is obtained based on a series of odd-numbered multiples of stripe frequency and peak count;

[0039] At this time, the difference Δx between the upper and lower surface screens is:

[0040] △x=[(f3-f1)+(f5-f3)+…+(f kmodd -f kmodd-1 )] / (count-1)

[0041] Among them, f1, f3, f5…f kmodd For a series of odd-numbered multiples of fringe frequency, count is the number of peaks.

[0042] Alternatively, determining the optimal frequency based on the difference in screen coordinates between the upper and lower surfaces includes:

[0043] When the number of peaks is unique, if floor[f max If Δx]=0, then the optimal frequency f0=f1; if floor[f max If Δx]=1, then the optimal frequency f0=2f1; where, floor[f max Δx] represents the number of even multiples of frequencies that satisfy the condition of zero phase error within the fringe frequency range, f1 represents the fringe frequency corresponding to the unique peak, and Δx represents the difference between the screen coordinates of the upper and lower surfaces.

[0044] When the number of peaks is not unique, if floor[f maxIf Δx] = count - 1, then the optimal frequency f0 = f kmeven , if floor[f max If Δx]>count-1, then the optimal frequency f0=f kmodd +(f kmodd -f kmodd-1 ) / 2; where f kmeven f represents the largest even frequency among the fringe frequencies where the phase error is zero. kmodd This represents the largest odd frequency among the fringe frequencies where the phase error is zero, and count is the number of peaks.

[0045] Alternatively, in S7, the pixel with zero minimum modulation values ​​is used as the dividing line. Ideally, for a vertical stripe direction, the left side of the dividing line is g(f) kodd If ) < 0, then g(f) is on the right side of the dividing line. kodd )>0; For stripes with a horizontal direction, g(f) above the boundary line kodd )>0, below the dividing line g(f) kodd If the screen coordinates of the upper surface are less than 0, then taking the vertical stripe direction as an example, they are calculated as follows:

[0046] To the left of the dividing line

[0047]

[0048] To the right of the dividing line

[0049]

[0050] Where, sum(g(f) kodd )<0) represents the number of peak values ​​less than 0, sum(g(f kodd `)>0)` represents the number of peaks greater than 0, `sum()` represents the quantity, `g()` represents the auxiliary function, and `g(f` represents the peak value greater than 0. kodd ) indicates the peak position, f kodd Let f0 represent the odd-numbered fringe frequencies that satisfy the condition of zero phase error, scount represent the number of even-numbered fringe frequencies that satisfy the condition of zero phase error, and scount = 1 when f0 = f1, and x1 represent the screen coordinates of the upper surface. n represents the continuous phase corresponding to the optimal frequency expanded using the frequency-by-frequency method. keven This indicates the fringe order corresponding to the frequency-sequential method. n' represents the continuous phase corresponding to the optimal frequency expanded using the frequency-sampling method. kevenThe frequency sampling method indicates the corresponding fringe order, f0 represents the optimal frequency, f1 represents the fringe frequency corresponding to the unique peak, other represents other cases, and π represents pi.

[0051] Alternatively, in S8, the upper surface screen coordinate x1 is calculated in the following manner:

[0052] x1=φ(f max ) / f max / 2 / π

[0053] Wherein, φ(f max f represents the continuous phase corresponding to the maximum fringe frequency. max This represents the maximum fringe frequency, and π represents pi.

[0054] The present invention has the following beneficial effects:

[0055] Due to the fringe aliasing phenomenon when measuring transparent objects, traditional phase measurement deflection techniques introduce significant errors in object reconstruction due to inaccurate phase extraction. To successfully extract the phase of the upper surface from overlapping fringes, this invention proposes a parasitic reflection suppression method based on a multi-frequency phase shift method. This method concludes that the phase error is zero at a certain frequency, effectively suppressing reflections from the lower surface and thus accurately recovering the three-dimensional surface shape of curved surfaces with parasitic reflections. Attached Figure Description

[0056] Figure 1 is a flowchart of the parasitic reflection suppression method based on the multi-frequency phase shift method of the present invention;

[0057] Figure 2 is a schematic diagram of the system for acquiring deformed stripe images according to the present invention.

[0058] Figure 3(a) shows the positive and negative distribution of the peak value of the auxiliary function g(f) in the vertical direction under ideal conditions according to the present invention; Figure 3(b) shows the positive and negative distribution of the peak value of the auxiliary function g(f) in the horizontal direction under ideal conditions according to the present invention.

[0059] Explanation of reference numerals in the attached figures

[0060] 1-Transparent object; 2-LCD; 3-Camera. Detailed Implementation

[0061] The principles and features of the present invention are described below with reference to the accompanying drawings. The examples given are only for explaining the present invention and are not intended to limit the scope of the present invention.

[0062] This invention provides a parasitic reflection suppression method based on a multi-frequency phase shift method. Referring to Figure 1, the parasitic reflection suppression method based on a multi-frequency phase shift method includes:

[0063] S1: Acquire a deformed stripe image after reflection from an object, wherein the deformed stripe image includes surface shape information of the upper and lower surfaces of the object to be tested, that is, a certain pixel in the deformed stripe image corresponds to points p1 and p2 on the LCD screen respectively, and the intensity information of the pixel in the deformed stripe image includes the intensity information of points p1 and p2.

[0064] Referring to Figure 2, computer-encoded sinusoidal stripes are displayed on LCD2, and the deformed stripe pattern reflected by transparent object 1 is captured by camera 3. At this time, the same pixel on camera 3 corresponds to two points p1 and p2 on the screen; therefore, the intensity of the image captured by camera 3 will include the intensity information of p1 and p2. Of course, this invention does not limit the method of acquiring deformed stripe images; other methods can be used to acquire deformed stripe images, such as infrared sensors, cameras, etc.

[0065] The intensity information I of a certain pixel in the deformed stripe can be represented as:

[0066] I = A + M1cosΦ t +M2cosΦ b

[0067] Where M1 and M2 are the modulation degrees of the upper and lower surfaces, respectively, A is the background light intensity, and Φ is the background light intensity. t and Φ b These represent the phase information of the upper surface and the phase information of the lower surface, respectively.

[0068] S2: Based on the intensity information of a certain pixel in the deformed stripe image, the truncated phase is calculated using the phase-shifting method. And generate a modulation curve;

[0069] Specifically, based on the intensity information of a pixel in the deformed stripe image, the truncated phase is calculated using the phase-shifting method. include:

[0070]

[0071] Among them, I j To add phase shift factor δ j Subsequent intensity information and I j =A+M1cos[Φ t +δ j ]+M2cos[Φ b +δ j A represents the background light intensity, M1 and M2 represent the modulation degree of the upper surface and the lower surface, respectively, and Φ t and Φ b δ represents the phase information of the upper surface and the phase information of the lower surface, respectively. j Denotes the phase shift factor and δj = 2πj / N, where N represents the number of phase shift steps and N≥3, j represents the j-th phase shift step and j=0,1,......,N-1, and π is pi. This indicates the cutoff phase when there is no parasitic effect. Indicates phase error and η = M2 / M1 represents the ratio of the modulation degree of the lower surface to that of the upper surface. As shown in Figure 2, if the line connecting points p1 and p2 aligns with the direction of the sinusoidal fringes displayed on the screen, and this line is considered the x-direction of the screen, since the phase value is linearly related to the screen pixel coordinates, the absolute phase values ​​of p1 and p2 can be expressed as: Φ b =2πfx1,Φ t =2πfx², where f is the fringe frequency, and x1 and x2 are the screen coordinates corresponding to points p1 and p2, respectively. Therefore, the offset between points p1 and p2 is Δx = x2 - x1. Hence, the formula... It can be rewritten as:

[0072]

[0073] At this point, the adjustment mechanism should be expressed as:

[0074]

[0075] S3: Expand the truncated phase frequency by frequency into a continuous phase;

[0076] Let the cutoff phase at the i-th frequency be . Its corresponding expansion phase is Φ i If the order is n, then the expansion is as follows:

[0077]

[0078] in, Φ represents the cutoff phase at the i-th frequency. i Indicates to The expanded phase, where n is the phase order and floor indicates rounding down, f i f represents the i-th frequency. i-1 Φ represents the (i-1)th frequency. i-1 This represents the expanded phase at the (i-1)th frequency. This represents the cutoff phase at the i-th frequency, and π represents pi.

[0079] The starting point for expansion is Due to parasitic reflection, the continuous phase Φ is superimposed with a periodic phase error, which can be expressed as:

[0080]

[0081] S4: Determine whether there is a minimum value in the modulation curve. If yes, proceed to S5; otherwise, proceed to S8.

[0082] S5: Use the peak position of the auxiliary function to search for the fringe frequency in the continuous phase that makes the phase error zero;

[0083] To search for the fringe frequency f from the continuous phase Φ with phase error, where the phase error is zero. k And f k =k / (2Δx) (k∈N), firstly, an auxiliary function g(f) = Φ(f) - fΦ'(f) is constructed using the continuous phase and its first derivative, where Φ(f) represents the continuous phase, f represents the fringe frequency, and Φ'(f) represents the first derivative of the continuous phase. The peak positions of the g(f) function and the positions between the two peaks are... Furthermore, the fringe frequency corresponding to the peak is an odd multiple of 1 / (2Δx) (kodd), while the fringe frequency corresponding to the midpoint between the two peaks is an even multiple of 1 / (2Δx) (keven). As shown in Figure 3, Δx and g(f) have the same sign, and this information will be used to assist in subsequent absolute phase order correction. To avoid the influence of the sign of Δx, the absolute value of g(f) |g(f)| is used to find f. keven .

[0084] Alternatively, S5 includes:

[0085] The number of peaks of the auxiliary function is determined based on the number of minimum values ​​in the modulation curve.

[0086] If the number of local minima in the modulation curve is m = 1, then |g(f)| has one and only one peak.

[0087] If the number of minimum values ​​m in the modulation curve is greater than or equal to 2, then |g(f)| will have multiple peaks.

[0088] The fringe frequency that satisfies zero phase error is determined based on the peak position, wherein when the number of peaks is greater than 2, the fringe frequency includes even multiples of the fringe frequency and odd multiples of the fringe frequency;

[0089] The difference between the screen coordinates of the upper and lower surfaces is determined based on the stripe frequency.

[0090] When the number of peaks is unique, the fringe frequency f1 = 1 / (2Δx), where Δx represents the difference between the screen coordinates of the upper and lower surfaces;

[0091] When the number of peaks is not unique, search for a series of odd multiples of stripe frequencies;

[0092] The difference between the upper and lower surface screens is obtained based on a series of odd-numbered multiples of stripe frequency and peak count;

[0093] At this time, the difference Δx between the upper and lower surface screens is:

[0094] Δx=[(f3-f1)+(f5-f3)+…+(f kmodd -f kmodd-1 )] / (count-1)

[0095] Among them, f1, f3, f5…f kmodd For a series of odd-numbered multiples of fringe frequency, count is the number of peaks.

[0096] The optimal frequency is determined based on the difference between the screen coordinates of the upper and lower surfaces; wherein the optimal frequency is the largest even multiple of a series of fringe frequencies that satisfy the phase error of 0, because the modulation index corresponding to this frequency is the largest and a larger fringe frequency should be selected considering the phase measurement accuracy.

[0097] When the number of peaks is unique, if floor[f max If Δx]=0, then the optimal frequency f0=f1; if floor[f max If Δx]=1, then the optimal frequency f0=2f1; where, floor[f max Δx] represents the number of even multiples of frequencies that satisfy the condition of zero phase error within the fringe frequency range, f1 represents the fringe frequency corresponding to the unique peak, and Δx represents the difference between the screen coordinates of the upper and lower surfaces.

[0098] When the number of peaks is not unique, if floor[f max If Δx] = count - 1, then the optimal frequency f0 = f kmeven , if floor[f max If Δx]>count-1, then the optimal frequency f0=f kmodd +(f kmodd -f kmodd-1 ) / 2; where f kmeven f represents the largest even frequency among the fringe frequencies where the phase error is zero. kmodd This represents the largest odd frequency among the fringe frequencies where the phase error is zero, and count is the number of peaks.

[0099] S6: Extract the truncated phase corresponding to the stripe frequency that makes the phase error zero, perform phase expansion, and use the pixel point where the number of minimum values ​​in the modulation curve is 0 as the boundary line to correct the phase order of the best frequency in the stripe frequency that makes the phase error zero in different regions, and obtain the correction result.

[0100] S7: Calculate the screen coordinates of the upper surface based on the correction results;

[0101] Using the pixels where the number of modulation minimum values ​​is 0 as the dividing line, ideally, for a vertical stripe direction, g(f) to the left of the dividing line... kodd If ) < 0, then g(f) is on the right side of the dividing line. kodd )>0; For stripes with a horizontal direction, g(f) above the boundary line kodd )>0, below the dividing line g(f) kodd If the screen coordinates of the upper surface are less than 0, then taking the vertical stripe direction as an example, they are calculated as follows:

[0102] To the left of the dividing line

[0103]

[0104] To the right of the dividing line

[0105]

[0106] Where, sum(g(f) kodd )<0) represents the number of peak values ​​less than 0, sum(g(f kodd ()>0) represents the number of peaks greater than 0, sum() represents the quantity, g() represents the auxiliary function, g(f kodd ) indicates the peak position, f kodd The odd-numbered frequencies among the fringe frequencies where the phase error is zero are represented; scount represents the number of even-numbered fringe frequencies that satisfy the condition of zero phase error, and scount = 1 when f0 = f1; x1 represents the screen coordinates of the upper surface; Φ f0 n represents the continuous phase corresponding to the optimal frequency expanded using the frequency-by-frequency method. keven Φ' represents the corresponding fringe order in the frequency-sequential mode. f0 n' represents the continuous phase corresponding to the optimal frequency expanded using the frequency-sampling method. keven The frequency sampling method indicates the corresponding fringe order, f0 represents the optimal frequency, f1 represents the fringe frequency corresponding to the unique peak, other represents other cases, and π represents pi.

[0107] S8: Calculate the screen coordinates of the upper surface based on the maximum stripe frequency;

[0108] At this point, the screen coordinate x1 of the upper surface is calculated in the following way:

[0109] x1=φ(f max ) / f max / 2 / π

[0110] Wherein, φ(fmax f represents the continuous phase corresponding to the maximum fringe frequency. max This represents the maximum fringe frequency, and π represents pi.

[0111] S9: Obtain the upper surface reconstruction result based on the upper surface screen coordinates.

[0112] The result of the upper surface reconstruction is the result of parasitic reflection suppression.

[0113] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for suppressing parasitic reflections based on multi-frequency phase shifting, characterized in that, The parasitic reflection suppression method based on the multi-frequency phase shift method includes: S1: acquiring a deformed fringe image after reflection from an object, wherein the deformed fringe image includes surface shape information of the upper and lower surfaces of the object under test, that is, a certain pixel in the deformed fringe image corresponds to points p1 and p2 on the LCD screen respectively, and the intensity information of the pixel in the deformed fringe image includes the intensity information of points p1 and p2; S2: calculating the truncated phase and generating a modulation curve based on the intensity information of a certain pixel in the deformed fringe image using the phase shift method; S3: expanding the truncated phase frequency by frequency into a continuous phase; S4: determining whether there is a minimum value in the modulation curve, if yes, proceeding to S5; otherwise, proceeding to S8; S5: S6: Search for the fringe frequency in the continuous phase that makes the phase error zero using the peak position of the auxiliary function; S7: Extract the truncated phase corresponding to the fringe frequency that makes the phase error zero, perform phase expansion, and use the pixel with zero minimum values ​​in the modulation curve as the boundary line to correct the phase order of the best frequency in the fringe frequency that makes the phase error zero in different regions to obtain the correction result; S8: Calculate the screen coordinates of the upper surface based on the correction result; S9: Calculate the screen coordinates of the upper surface based on the maximum fringe frequency; S10: Obtain the upper surface reconstruction result based on the screen coordinates of the upper surface; In S2, the truncated phase is calculated using the phase shift method based on the intensity information of a certain pixel in the deformed fringe image. include: in, To add phase shift factor Subsequent intensity information and ， Indicates background light intensity. and These represent the modulation of the upper surface and the modulation of the lower surface, respectively. and These represent the phase information of the upper surface and the phase information of the lower surface, respectively. Represents the phase shift factor and ， Indicates the number of phase shift steps and Let j represent the j-th phase shift, where j = 0, 1, ..., N-1. Pi This indicates the cutoff phase when there is no parasitic effect. Indicates phase error and ， Indicates the ratio of the lower surface tone density to the upper surface tone density; S3 includes: = in, This represents the cutoff phase at the i-th frequency. Indicates to The expanded phase, where n is the phase order and ， Indicates rounding down. Represents the i-th frequency. This represents the (i-1)th frequency. This represents the expanded phase at the (i-1)th frequency. This represents the cutoff phase at the i-th frequency. Represents pi; in S7, the pixel with zero minimum modulation values ​​is used as the dividing line. Ideally, for a vertical stripe direction, g(f) is to the left of the dividing line. kodd If ) < 0, then g(f) is on the right side of the dividing line. kodd ) > 0; For horizontal fringe direction, g(f) above the boundary line kodd ) > 0, below the dividing line g(f) kodd If ) < 0; then the screen coordinates of the upper surface, taking the vertical stripe direction as an example, are calculated as follows: to the left of the dividing line, To the right of the dividing line in, This indicates the number of peak values ​​less than 0. This indicates the number of peak values ​​greater than 0. Indicate quantity, Describes an auxiliary function. Indicates the peak position. This represents the odd-numbered frequencies in the fringe frequencies where the phase error is zero. This represents the number of even-numbered fringe frequencies that satisfy the condition that the phase error is 0, and when... hour ， Indicates the screen coordinates of the upper surface. This represents the continuous phase corresponding to the optimal frequency when expanded using a frequency-by-frequency method. This indicates the fringe order corresponding to the frequency-sequential method. This represents the continuous phase corresponding to the optimal frequency obtained by the frequency-sampling method. This indicates the fringe order corresponding to the frequency sweep method. Indicates the optimal frequency. This represents the fringe frequency corresponding to the unique peak. Indicates other situations, It represents pi (π).

2. The parasitic reflection suppression method based on the multi-frequency phase shift method according to claim 1, characterized in that, In S1, the intensity information of a certain pixel in the deformed stripe image It can be represented as: in, and These are the modulation values ​​of the upper surface and the lower surface, respectively. It is the background light intensity. and These represent the phase information of the upper surface and the phase information of the lower surface, respectively.

3. The parasitic reflection suppression method based on the multi-frequency phase shift method according to claim 1, characterized in that, In S5, the auxiliary function for: in, Indicates continuous phase. Indicates the fringe frequency. The first derivative represents the continuous phase.

4. The parasitic reflection suppression method based on the multi-frequency phase shift method according to claim 1, characterized in that, S5 includes: determining the number of peaks of the auxiliary function based on the number of minimum values ​​in the modulation curve; determining the corresponding fringe frequency based on the peak position and the position between adjacent peaks, wherein when the number of peaks is greater than 2, the fringe frequency includes even-numbered fringe frequencies and odd-numbered fringe frequencies; determining the difference between the screen coordinates of the upper and lower surfaces based on the fringe frequencies; determining the optimal frequency based on the difference between the screen coordinates of the upper and lower surfaces; wherein the optimal frequency is the largest even-numbered multiple of a series of fringe frequencies that satisfy a phase error of 0.

5. The parasitic reflection suppression method based on the multi-frequency phase shift method according to claim 4, characterized in that, Determining the difference between the upper and lower surface screen coordinates based on the stripe frequency includes: when the number of peaks is unique, the stripe frequency... ,in This represents the difference in screen coordinates between the upper and lower surfaces; when the number of peaks is not unique, a series of odd-multiple fringe frequencies are searched; based on the series of odd-multiple fringe frequencies and the number of peaks, the difference between the upper and lower surface screens is obtained; at this point, the difference between the upper and lower surface screens... for: in, For a series of odd multiples of fringe frequency, This represents the peak number.

6. The parasitic reflection suppression method based on the multi-frequency phase shift method according to claim 5, characterized in that, Determining the optimal frequency based on the difference in screen coordinates between the upper and lower surfaces includes: when the number of peak values ​​is unique, if The optimal frequency = ;like The optimal frequency =2 ;in, This indicates the number of even-numbered frequencies within the fringe frequency range that satisfy the condition of zero phase error. This represents the fringe frequency corresponding to the unique peak. This represents the difference in screen coordinates between the upper and lower surfaces; when the number of peaks is not unique, if The optimal frequency = ,like The optimal frequency = ;in, This represents the largest even frequency among the fringe frequencies where the phase error is zero. This represents the largest odd frequency among the fringe frequencies where the phase error is zero. This represents the peak number.

7. The parasitic reflection suppression method based on the multi-frequency phase shift method according to any one of claims 1-6, characterized in that, In S8, the upper surface screen coordinates Calculated in the following way: in, This represents the continuous phase corresponding to the maximum fringe frequency. Indicates the maximum fringe frequency. It represents pi (π).

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