Multi-wavelength phase unwrapping method and object height measurement method and height measurement system

Abstract

The present invention discloses a multi-wavelength phase unwrapping method and an object height measurement method and height measurement system. The multi-wavelength phase unwrapping method is used to obtain the optimal phase sequence of the coordinates at the surface of the object to be measured at the optical wavelength based on a multi-wavelength off-axis digital hologram of the object to be measured at the optical wavelength, using a height distribution model based on synthetic wavelength chain guidance and phase sequence search: the height distribution of any coordinate at the surface of the object to be measured at the optical wavelength in the hologram is used as an initial value, and a phase sequence is searched for at a certain interval within a preset range of the initial value. The phase sequences found by the search are used to form a criterion function. When the minimum value of the envelope of the criterion function is taken, the corresponding phase sequence is considered to be the optimal phase sequence. The present invention determines the optimal phase sequence by searching for the minimum value of the envelope of the criterion function, rather than by finding the minimum value of the criterion function. This greatly solves the problem of errors in the optimal phase sequence caused by noise damage to the criterion function.

Description

Technical Field

[0001] The present invention relates to the field of three-dimensional morphology measurement based on digital holography, and in particular to a highly robust multi-wavelength phase unwrapping method based on synthetic wavelength chain guidance and phase sequence search (used for phase unwrapping of multi-wavelength wrapped phases and large-depth, high-precision three-dimensional surface reconstruction), an object height measurement method that uses the multi-wavelength phase unwrapping method to measure the height of an object at any coordinate on its surface, and an object height measurement system that uses the object height measurement method. Background Art

[0002] Currently, the surfaces of intelligent integrated instrument chips are characterized by tiny size, stepped shapes, and high aspect ratios. Non-contact surface topography measurement technologies with large millimeter-level measurement depths and ultra-high spatial resolution are urgently needed. Digital holography, with its advantages of non-contact, full field of view, and high precision, holds broad application prospects in fields such as biomedical imaging and chip testing. However, when using single-wavelength digital holography, the maximum axial measurement range is limited to a full wavelength for transparent objects (cells) or half a wavelength for reflective objects (chips) due to phase wrapping.

[0003] Therefore, existing single-wavelength phase unwrapping techniques can only perform phase unwrapping on objects with continuous surfaces and cannot accurately reconstruct stepped, high-aspect-ratio surfaces like chips. Dual-(or multi-) wavelength digital holography can extend the measurement range to half the synthesized wavelength (for reflective objects), but this also amplifies phase noise, significantly reducing measurement accuracy. Furthermore, when the noise at the synthesized wavelength exceeds one-quarter of the wavelength, the height distribution will be incorrectly determined, resulting in jump points. Summary of the Invention

[0004] In order to solve the technical problem of low height measurement accuracy of objects such as chips with stepped surfaces and high-depth points, the present invention provides a highly robust multi-wavelength phase unwrapping method based on synthetic wavelength chain guidance and phase sequence search (for phase unwrapping of multi-wavelength wrapped phases and large-depth, high-precision three-dimensional surface reconstruction), an object height measurement method that uses the multi-wavelength phase unwrapping method to measure the height of any coordinate on the body surface of the object to be measured, and an object height measurement system that uses the object height measurement method. The multi-wavelength phase unwrapping method of the present invention aims to expand the measurement range while reducing the noise to the level of single-wavelength phase noise, and is used to achieve high-precision three-dimensional morphology measurement of the surface of intelligent integrated instrument chips. The object height measurement method proposed in the present invention has the characteristics of large measurement range, high precision, good noise resistance, etc., and has strong applicability. It is not only for chips with stepped surfaces and high-depth points, but also for stepped objects. The height measurement can be performed very accurately.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] A multi-wavelength phase unwrapping method based on synthetic wavelength chain guidance and phase sequence search is used to i The multi-wavelength off-axis digital hologram under the condition of light wavelength λ is obtained by using the height distribution model. i The optimal phase sequence of the coordinates (x0, y0) at the surface of the object to be measured is as follows: The multi-wavelength phase unwrapping method obtains the optimal phase sequence based on synthetic wavelength chain guidance and phase sequence search.

[0007] First, the wavelength of light in the hologram is i Height distribution of coordinates (x0, y0) on the surface of the object to be measured As an initial value, the phase sequence is searched at intervals of Δh within the preset range of the initial value. The phase sequence during the search process is expressed as:

[0008]

[0009] Where, is the phase sequence of the coordinates (x0, y0) on the surface of the object to be measured when the number of search steps is s, is the wavelength of light λ i The coordinates of the object surface under test (x o ,y o ), is the wavelength of light in the hologram λ i The coordinates of the surface of the object to be measured (x o ,y o )’s wrapping phase, is the wavelength of light λ i The reconstructed height of the coordinate (x0, y0) at the surface of the object to be measured, s is the number of search steps, s = 1, 2, ..., M, Δh is the search step length, which represents the minimum interval distance during the search process;

[0010] Secondly, the phase sequences found by the search are used to form a criterion function. When the minimum value of the envelope of the criterion function is taken, the corresponding phase sequence is considered to be the optimal phase sequence. The criterion function is expressed as:

[0011]

[0012] Where, X(x o ,y o ,s) is the criterion function, which represents the coordinates (x o ,y o ) criterion value;

[0013] At this time, the optimal phase sequence for:

[0014] [v,X(v)]=min{envelope[X(x o ,y o ,s)]}

[0015]

[0016] Where [v, X(v)] is the coordinate position corresponding to the minimum value X(v) of the envelope when the number of steps is v, min is the minimum value operation, and envelope is the envelope function. is the phase sequence of the coordinates (x0, y0) on the surface of the object to be measured when the number of search steps is v.

[0017] As a further improvement of the above solution, the height distribution model is:

[0018]

[0019] Where h(x0,y0) is the height distribution of the coordinate (x0,y0) on the surface of the object to be measured in the hologram, is the wavelength of light in the hologram λ i The coordinates of the surface of the object to be measured (x o ,y o ), is the coordinate of the surface of the object to be measured under the synthetic wavelength Λ1 (x o ,y o )’s wrapping phase, is the coordinate of the surface of the object to be measured under the synthetic wavelength Λ1 (x o ,y o ), is the coordinate (x o ,y o )’s wrapping phase, is the coordinate (x o ,y o ), is the synthetic wavelength Λ N-1 The coordinates of the surface of the object to be measured (x o ,y o )'s wrapping phase.

[0020] As a further improvement to the above scheme, the diffraction process of light waves propagating from the hologram plane to the surface of the object to be measured is used to numerically reproduce the complex amplitude distribution of the object light wave. The inverse tangent function is used to calculate the wrapped phase distribution at different wavelengths for the reproduced complex amplitude of the object light wave.

[0021]

[0022] Where U(x0,y0,λ i ) represents the wavelength of light λ i The coordinates on the surface of the object to be measured (x o ,y o ), Im represents the complex amplitude of the object light wave at U(x0,y0,λ i );Re represents the complex imaginary part of U(x0,y0,λ i ) is the complex real part of .

[0023] Furthermore, the complex amplitude of the object light wave U(x0,y0,λ i ):

[0024] U(x o ,y o ,λ i )=FFT -1 {FFT[A(x,y,λ i )]·H(f x ,f y ,λ i )}

[0025] Where, (f x ,f y ) is the coordinate of the complex amplitude of the object light wave in the frequency domain, f x =x / L x , f y =y / L y , L x and L y are the length and width of the CCD format of the camera that obtains the hologram, H(f x ,f y ,λ i ) is the wavelength of light λ i The coordinates of the complex amplitude of the object light wave in the frequency domain (f x ,f y ) is the angular spectrum diffraction transfer function, A(x,y,λ i ) represents the wavelength of light λ i The complex amplitude of the object light wave at the coordinate (x,y) in the spatial domain under .

[0026] Furthermore, A(x,y,λ i ) is expressed as:

[0027] A(x,y,λ i )=∫∫U(x o ,y o ,λ i)exp{jk[(xx o ) 2 +(yy o ) 2 ] / 2d}dx o dy o

[0028] Where j is the imaginary unit, k is the wave number of light, k = 2π / λ i , d is the propagation distance, that is, the distance between the object to be measured and the recording surface of the camera.

[0029] Preferably, A(x, y, λ i ) is designed as follows:

[0030] Perform two-dimensional Fourier transform (FFT) on the multi-wavelength off-axis digital hologram to obtain its spectrum distribution. The intensity of the hologram is expressed as:

[0031] I(x,y,λ i )=|O(x,y,λ i )| 2 +|R(x,y,λ i )| 2 +O(x,y,λ i )R * (x,y,λ i )+O * (x,y,λ i )R(x,y,λ i )

[0032] Where, I(x,y,λ i ) represents the wavelength of light λ i The intensity of the interference light at the coordinate (x, y) in the hologram under i ) consists of four terms, the first two of which constitute the zero-order image, and the third term OR * is a positive first-order image, the fourth term O*R is a negative first-order image, O(x,y,λ i ) represents the wavelength of light λ i The light intensity of the object light at the coordinate (x, y) in the hologram under i ) represents the wavelength of light λ i The light intensity of the reference light at the coordinate (x, y) in the hologram below, * represents the conjugate sign;

[0033] For the spectrum distribution of the third item, perform inverse two-dimensional FFT processing and convert it into the spatial domain, OR * Expressed as:

[0034] O(x,y,λ i )R *=A(x,y,λ i )exp[jk(x 2 +y 2 ) / 2d-jk(cosα·x+cosβ·y)]

[0035] Where α and β represent the angles between the reference light and the X-axis and Y-axis on the recording surface of the camera, respectively.

[0036] Furthermore, H(f x ,f y ,λ i ) is designed as:

[0037]

[0038] Where j is the imaginary unit, k is the wave number of light, k = 2π / λ i , z is the distance between the recording surface of the camera and the object to be measured, that is, z = -d.

[0039] As a further improvement of the above solution, the object to be tested is a chip with a stepped surface and high depth points.

[0040] The present invention also provides an object height measurement method, which is used to measure the height of an object at any coordinate (x0, y0) on the surface of the object to be measured. The object height measurement method comprises the following steps:

[0041] Define different light wavelengths λ i A beam of light emitted by a light source is defined as reference light, and another beam of light emitted by a light source having the same source as the reference light and reflected from the surface of a step-shaped object to be measured is defined as object light. The object light and the reference light form interference light, and a multi-wavelength off-axis digital hologram is imaged on a recording surface of a camera using the interference light.

[0042] The hologram is obtained by using any of the above multi-wavelength phase unwrapping methods based on synthetic wavelength chain guidance and phase sequence search at the optical wavelength λ i The optimal phase sequence of the coordinates (x0, y0) at the surface of the object to be measured is as follows:

[0043] According to the optimal phase sequence Reconstruct the correct height of the object to be measured at coordinate (x0, y0).

[0044] The present invention also provides an object height measurement system, which includes:

[0045] Several light sources for emitting light of different wavelengths λ i light, defining different light wavelengths λ iA beam of light emitted by a light source is defined as reference light, and another beam of light emitted by a light source having the same source as the reference light and irradiated on the surface of the step-shaped object to be measured is defined as object light, and the object light and the reference light form interference light;

[0046] a camera for imaging a multi-wavelength off-axis digital hologram on a recording surface of the camera using the interference light;

[0047] A processor is used to obtain the hologram at the optical wavelength λ by using any of the above multi-wavelength phase unwrapping methods based on synthetic wavelength chain guidance and phase sequence search. i The optimal phase sequence of the coordinates (x0, y0) at the surface of the object to be measured is as follows: Also used to determine the optimal phase sequence Reconstruct the correct height of the object to be measured at coordinate (x0, y0).

[0048] Compared with the prior art, the present invention has the following advantages:

[0049] 1. Using multi-wavelength cascade phase unwrapping, a high-axial-resolution height distribution is obtained to guide subsequent phase sequence searches, solving the problem of search failure in traditional height searches while reducing the search range and improving the algorithm speed.

[0050] 2. Use the minimum value of the envelope of the search criterion function to determine the optimal phase sequence Instead of determining the optimal phase sequence by finding the minimum value of the criterion function To a great extent, it solves the problem of optimal phase sequence caused by noise destruction of the criterion function. An error occurred.

[0051] 3. The method of the present invention perfectly solves the problems of noise amplification and jump points in the previous dual (multi) wavelength phase unwrapping. While expanding the axial measurement range to the submillimeter level, it can also maintain the nanometer-level axial resolution and reduce the impact of noise on the final result to the level of a single wavelength.

[0052] 4. The present invention is very suitable for objects with stepped and high-depth points such as chip surfaces, and can achieve a larger measurement range and higher measurement accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 This is a flow chart of a robust multi-wavelength phase unwrapping method based on synthetic wavelength chain guidance and phase sequence search in the present invention;

[0054] Figure 2 This is a flow chart of the cascaded multi-wavelength phase unwrapping guidance and phase sequence search algorithm based on the present invention;

[0055] Figure 3is the three-dimensional surface height map of the initial object;

[0056] Figure 4 It is a noisy multi-wavelength off-axis digital hologram generated by computer simulation;

[0057] Figure 5 is the multi-wavelength wrapped phase diagram obtained by the inverse tangent function;

[0058] Figure 6 is the initial height map and its error map obtained by the cascaded synthetic wavelength chain method;

[0059] Figure 7 The object surface height map and its error map reconstructed using phase sequence search. DETAILED DESCRIPTION

[0060] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0061] Example 1

[0062] The multi-wavelength phase unwrapping method of the present invention is used to determine the phase of the object to be measured at the wavelength λ i The multi-wavelength off-axis digital hologram under the condition of light wavelength λ is obtained by using the height distribution model. i The optimal phase sequence of the coordinates (x0, y0) at the surface of the object to be measured is as follows: The multi-wavelength phase unwrapping method obtains the optimal phase sequence based on the synthetic wavelength chain guidance and phase sequence search. According to the optimal phase sequence The correct height of the object to be measured at the coordinate (x0, y0) can be reconstructed. Therefore, based on the optimal phase sequence A method for measuring the height of an object is designed to measure the height of any coordinate (x0, y0) on the surface of the object to be measured.

[0063] The object height measurement method includes the following steps: defining different light wavelengths λ i A beam of light emitted by a light source is defined as reference light, and another beam of light emitted by a light source having the same source as the reference light and reflected from the surface of a step-shaped object to be measured is defined as object light. The object light and the reference light form interference light, and the interference light is used to form a multi-wavelength off-axis digital hologram on the recording surface of the camera; the hologram is subjected to the multi-wavelength phase unwrapping method based on synthetic wavelength chain guidance and phase sequence search of the present invention to obtain the phase sequence of the hologram at the optical wavelength λ i The optimal phase sequence of the coordinates (x0, y0) at the surface of the object to be measured is as follows: According to the optimal phase sequence Reconstruct the correct height of the object to be measured at coordinate (x0, y0).

[0064] When the object height measurement method is applied, the following object height measurement system can be designed. The object height measurement system includes: several light sources, cameras, and a processor.

[0065] Several light sources are used to emit light of different wavelengths λ i light, defining different light wavelengths λ i A beam of light emitted by a light source is defined as reference light, and another beam of light emitted by a light source having the same source as the reference light and reflected from the surface of a step-shaped object to be measured is defined as object light. The object light and the reference light form interference light. The camera is used to use the interference light to form a multi-wavelength off-axis digital hologram on the recording surface of the camera. The processor is used to use the multi-wavelength phase unwrapping method based on synthetic wavelength chain guidance and phase sequence search of the present invention to obtain the phase sequence of the hologram at the optical wavelength λ. i The optimal phase sequence of the coordinates (x0, y0) at the surface of the object to be measured is as follows: Also used to determine the optimal phase sequence Reconstruct the correct height of the object to be measured at coordinates (x0, y0). The processor can be a circuit integrated into the camera circuit, a CPU running independently of the camera, or a computer program embedded in the camera, as long as it can realize the above functions of the processor.

[0066] Optimal phase sequence The design method mainly includes the following two steps.

[0067] First, the wavelength of light in the hologram is i Height distribution of coordinates (x0, y0) on the surface of the object to be measured As an initial value, the phase sequence is searched at intervals of Δh within the preset range of the initial value. The phase sequence during the search process is expressed as:

[0068]

[0069] Where, is the phase sequence of the coordinates (x0, y0) on the surface of the object to be measured when the number of search steps is s, is the wavelength of light λ i The coordinates of the object surface under test (x o ,y o ), is the wavelength of light in the hologram λ i The coordinates of the surface of the object to be measured (x o ,y o )’s wrapping phase, is the wavelength of light λi The reconstructed height of the coordinate (x0, y0) on the surface of the object to be measured is s, the number of search steps is s = 1, 2, ..., M, and Δh is the search step length, which represents the minimum interval distance during the search process.

[0070] Secondly, the phase sequences found by the search are used to form a criterion function. When the minimum value of the envelope of the criterion function is taken, the corresponding phase sequence is considered to be the optimal phase sequence. The criterion function is expressed as:

[0071]

[0072] Where, X(x o ,y o ,s) is the criterion function, which represents the coordinates (x o ,y o ) criterion value.

[0073] At this time, the optimal phase sequence for:

[0074] [v,X(v)]=min{envelope[X(x o ,y o ,s)]}

[0075]

[0076] Where [v, X(v)] is the coordinate position corresponding to the minimum value X(v) of the envelope when the number of steps is v, min is the minimum value operation, and envelope is the envelope function. is the phase sequence of the coordinates (x0, y0) on the surface of the object to be measured when the number of search steps is v.

[0077] In order to prove the feasibility of the multi-wavelength phase unwrapping method of the present invention, the following reasoning is performed.

[0078] The highly robust multi-wavelength phase unwrapping method based on synthetic wavelength chain guidance and phase sequence search of the present invention comprises the following steps: S1 to S6.

[0079] S1: Perform two-dimensional FFT on the collected or simulated multi-wavelength off-axis digital hologram to obtain its spectrum distribution. The intensity of the multi-wavelength digital hologram is expressed as:

[0080] I(x,y,λ i )=|O(x,y,λ i )| 2 +|R(x,y,λ i )| 2 +O(x,y,λ i )R *(x,y,λ i )+O * (x,y,λ i )R(x,y,λ i )

[0081] Among them, the hologram consists of four items, the first two items constitute the zero-order image, the third item OR * is a positive first-order image, the fourth term O*R is a negative first-order image, λ i Represents the wavelength of light with different serial numbers i, i = 1, 2, ..., N; (x, y) represents the coordinates of any point in the hologram. i ) represents the wavelength of light λ i The intensity of the interference light at the coordinate (x,y) in the hologram under i ) represents the wavelength of light λ i The light intensity of the object light at the coordinate (x, y) in the hologram under i ) represents the wavelength of light λ i The light intensity of the reference light at the coordinate (x, y) in the hologram under i The object light is a beam of light emitted by a light source, and the object light is another beam of light emitted by the same light source as the reference light. The object light and the reference light form the interference light and form a corresponding hologram on the recording surface of the camera. * indicates a conjugate symbol.

[0082] In order to obtain only the complex amplitude information of the object's wavefront, spatial filtering technology is used to remove the first two terms and the fourth term in the formula, leaving only the spectral distribution of the third term.

[0083] S2: For the spectrum distribution of the third item, perform inverse two-dimensional FFT processing and convert it into the spatial domain, OR * Expressed as:

[0084] O(x,y,λ i )R * =A(x,y,λ i )exp[jk(x 2 +y 2 ) / 2d-jk(cosα·x+cosβ·y)]

[0085] Where k is the wave number of light, k = 2π / λ i ; d is the propagation distance, that is, the distance between the object to be measured and the recording surface of the camera; j is the imaginary unit, α and β represent the angles between the reference light and the X-axis and Y-axis on the camera's recording surface, respectively. i ) represents the wavelength of light λ iThe complex amplitude of the object light wave at coordinate (x, y) in the spatial domain under is expressed as:

[0086] A(x,y,λ i )=∫∫U(x o ,y o ,λ i )exp{jk[(xx o ) 2 +(yy o ) 2 ] / 2d}dx o dy o

[0087] Among them, (x o ,y o ) is the two-dimensional coordinate of the surface of the object to be measured. o ,y o ,λ i ) represents the wavelength of light λ i The coordinates on the surface of the object to be measured (x o ,y o ) Complex amplitude of the object light wave

[0088] By simulating the reference light illuminating the hologram by computer, the conjugate term R is eliminated. * . Then, according to the Rayleigh-Sommerfeld diffraction theory, the diffraction process of the object light wave propagating from the hologram plane to the surface of the object to be measured is simulated, and the complex amplitude distribution of the object light wave is numerically reproduced. Common hologram reconstruction algorithms mainly include the angular spectrum method and the Fresnel method. Since the angular spectrum method strictly satisfies the Helmholtz equation and is an accurate solution to the diffraction problem, the angular spectrum method is used as the reconstruction method this time. According to the scalar diffraction theory, the angular spectrum diffraction formula is expressed as

[0089] U(x o ,y o ,λ i )=FFT -1 {FFT[A(x,y,λ i )]·H(f x ,f y ,λ i )}

[0090] Among them, (f x ,f y ) is the coordinate of the complex amplitude of the object light wave in the frequency domain, f x =x / L x , f y =y / L y , L x and L yThe length and width of the CCD format are different for different cameras. For the same camera, the length and width of the CCD format are constants rather than variables. x ,f y ,λ i ) is the wavelength of light λ i The coordinates of the complex amplitude of the object light wave in the frequency domain (f x ,f y ) is expressed as:

[0091]

[0092] It is worth noting that when using the angular spectrum method for numerical reconstruction, only one forward and one inverse FFT are required, eliminating the scale factor between the holographic and image planes. Therefore, the reconstructed pixel size is equal to the CCD pixel size. z is the distance between the camera recording surface and the object, that is, z = -d.

[0093] S3: Use the inverse tangent function to calculate the parcel phase distribution at different wavelengths for the complex amplitude of the reconstructed light wave, expressed as:

[0094]

[0095] in, is the wavelength of light λ i The coordinates of the surface of the object to be measured (x o ,y o ). arctan represents the inverse tangent function; Im represents the imaginary part of the complex number; and Re represents the real part of the complex number. Due to the limitations of the inverse tangent function, the obtained phase is wrapped in the range [0, 2π]. If the height of the object to be measured exceeds the wavelength of light (for transmissive objects) or half the wavelength of light (for reflective objects), its phase must be unwrapped to determine the correct height.

[0096] S4: In the shape measurement of the base phase distribution in a reflective multi-wavelength digital holographic configuration, the height distribution of the object to be measured is expressed as follows:

[0097]

[0098] Among them, h(x o ,y o ) is the coordinate of the surface of the object to be measured (x o ,y o )’s height distribution. is the wavelength of light λ i The coordinates of the surface of the object to be measured (x o ,y o ) is the integer part of the phase sequence. is the coordinate of the surface of the object to be measured under the synthetic wavelength Λ1 (x o ,y o )'s wrapping phase; is the coordinate (x o ,y o )’s wrapping phase; and so on, is the synthetic wavelength Λ N-1 The coordinates of the surface of the object to be measured (x o ,y o ) phase. pass and The difference is obtained, the corresponding synthetic wavelength Λ1=λ1λ N / (λ N -λ1); and so on, pass and The difference is obtained, the corresponding synthetic wavelength Λ n =λ1λ2 / (λ2-λ1). And we assume No phase wrapping occurs, where Λ N-1 >Λ N-2 >…>2>Λ1, that is, λ N >λ N-1 >…>λ2>λ1. is the coordinate (x o ,y o )'s wrapping phase; is the coordinate (x o ,y o )’s wrapping phase; and so on, is the wavelength of light λ N The coordinates of the surface of the object to be measured (x o ,y o )'s wrapping phase.

[0099] If it is possible to synthesize the longest wavelength Λ n To the shortest synthetic wavelength Λ1 determine each It can be finally determined The value of this is obtained from the maximum synthetic wavelength Λ n to the shortest synthetic wavelength Λ1 and then to the optical wavelength λ i The multi-stage chain wavelength chain can achieve Λ n / 2 maximum axial range and high axial resolution, and finally the optical wavelength λ i Height distribution is the synthetic wavelength Λ i The coordinates of the surface of the object to be measured (x o ,yo ) can be expressed as:

[0100]

[0101] in is the synthetic wavelength Λ i+1 The coordinates of the surface of the object to be measured (x o ,y o ) is reconstructed by and Λ i+1 OK; round is a rounding operation. is the synthetic wavelength Λ i The coordinates of the surface of the object to be measured (x o ,y o ) phase.

[0102] S5: According to the obtained Take it as an initial value and search for the correct phase sequence at intervals of Δh within a certain range of the initial value. The phase sequence during the search process is expressed as:

[0103]

[0104] Δh is the minimum interval distance during the search process, that is, the search step length. s is the number of search steps, s = 1, 2, ..., M. The coordinates (x o ,y o ) phase sequence. is the wavelength of light λ i The coordinates of the surface of the object to be measured (x o ,y o )'s reconstruction height. is the wavelength of light λ i The coordinates of the object surface under test (x o ,y o ) height. The m number, i.e., the phase sequence, corresponding to each optical wavelength is calculated, and then these m numbers are used to form a criterion function. When the minimum value of the envelope of the criterion function is taken, the m number corresponding to the optical wavelength is considered to be the most appropriate value. The criterion function is expressed as:

[0105]

[0106] Among them, X(x o ,y o ,s) is the coordinate (x o ,y o ) criterion value.

[0107] Optimal phase sequence The determination can be expressed as:

[0108] [v,X(v)]=min{envelope[X(x o ,y o ,s)]}

[0109]

[0110] Where min is the minimum operation, v is the coordinate position corresponding to the minimum value X(v), and envelope is the envelope function.

[0111] [v,X(v)] is a position v and the minimum value of the corresponding envelope in the search process of finding its minimum value based on the envelope. is the wavelength of light λ i The coordinates of the surface of the object to be measured (x o ,y o ), which is the correct phase sequence we searched for.

[0112] S6: Optimal phase sequence according to the searched phase sequence Reconstruct the correct height of the object:

[0113]

[0114] In summary, the multi-wavelength phase unwrapping method based on synthetic wavelength chain guidance and phase sequence search provided by the present invention can use spatial filtering technology and angular spectrum inverse diffraction to obtain the complex amplitude of the object's wavefront for a multi-wavelength off-axis digital hologram recorded on a certain object, and calculate the arc tangent function of the complex amplitude of each optical wavelength to obtain its wrapped phase; the wrapped phase diagrams are subtracted from each other in the order of corresponding wavelengths from small to large to obtain phase diagrams at different synthetic wavelengths, and then the phases of the synthetic wavelengths are gradually unwrapped in the order of wavelengths from large to small; then, based on the phase unwrap of the synthetic wavelength chain as a reference, the correct phase sequence corresponding to a certain optical wavelength is found to avoid phase ambiguity and obtain the true phase. Compared with traditional dual-wavelength phase unwrapping, cascaded multi-wavelength phase unwrapping and height search methods, the present invention has better noise resistance within a larger measurement range; at the same time, it also avoids the noise amplification of dual-wavelength phase unwrapping, the failure of traditional height search, and the occurrence of jump points in cascaded multi-wavelength phase unwrapping; even if the noise at the synthetic wavelength is greater than one-quarter of the optical wavelength, the correct height distribution of the object can still be solved.

[0115] Example 2

[0116] This embodiment 2 is a specific application of embodiment 1. This embodiment is based on a robust multi-wavelength phase unwrapping method based on synthetic wavelength chain guidance and phase sequence search, such as Figure 1 As shown, the detailed steps are: S1 to S6.

[0117] Note: The initial object simulated in this example is a stepped object with a reflection amplitude of 1 and a height of 100 to 400 microns. The simulation size is 120×120 pixels, which is used to simulate the stepped and high aspect ratio surface of the chip. Its three-dimensional surface distribution is as follows: Figure 3 At the same time, in order to show the strong anti-noise ability of this method, Gaussian phase white noise with a mean of 0 and a standard deviation of 0.025 is added to the multi-wavelength off-axis digital hologram generated according to the initial object.

[0118] S1: Noisy multi-wavelength off-axis digital hologram Figure 3 As shown in the figure, it is a 240×240×17 three-dimensional cube. The first and second dimensions represent its spatial dimensions, namely 240×240 pixels. This is due to the Nyquist sampling limitation. The pixels required for the off-axis digital hologram must be at least four times the object size. Only in this way can the object size of 120×120 pixels be restored. The third dimension represents its spectral dimension, namely 17 off-axis digital holograms at different wavelengths. A two-dimensional FFT is performed on the off-axis digital hologram at each wavelength to remove the DC and twin images, retaining only the spectral distribution of the object light wave.

[0119] S2: Perform a two-dimensional inverse FFT on the retained object lightwave spectrum to obtain the complex amplitude distribution on the recording surface. This is then transmitted back to the object surface via inverse angular spectrum diffraction to obtain the complex amplitude distribution of the object's wavefront. Since the reflection amplitude at the object surface is 1, the amplitude distribution is all 1 and is not displayed here. The phase distribution is obtained by taking the inverse tangent of the complex amplitude.

[0120] S3: Use the inverse tangent function to obtain the wrapped phase distribution at each wavelength and limit it to [0,2π], such as Figure 5 shown

[0121] S4: For the obtained multi-wavelength wrapped phases, subtract the two of them in the order of corresponding wavelengths from small to large to obtain the phase difference, which is expressed as:

[0122]

[0123] where Λ i =λ i λ i+1 / (λ i+1 -λ1).

[0124] Synthetic wavelength Λ i Build a wavelength chain in descending order, expand the synthetic phase corresponding to each synthetic wavelength step by step in descending order, and calculate the phase sequence integer part of each synthetic phase Finally, the phase sequence integer part corresponding to the optical wavelength phase is obtained Reconstruct the initial height of the object as Figure 6 The reconstructed height map (the left area is the reconstructed height map, and the right area is the error map) can be expressed as:

[0125]

[0126] in, Must be an unwrapped phase; Λ N-1 >800μm;λ i The range is 1533.22nm~1576.18nm, with a total of 17 wavelengths; the constructed synthetic wavelength chain is 900μm~56.25μm, with a total of 16 synthetic wavelengths; It can be expressed as:

[0127]

[0128] It can be seen It is always determined by the synthetic wavelength and its corresponding synthetic phase and the height of the object reconstructed based on the synthetic wavelength of the previous level. After determining the height of the object reconstructed by the shortest synthetic wavelength, the optical wavelength phase corresponding to It can be expressed as:

[0129]

[0130] Since the shortest synthetic wavelength is 36 times that of the light wavelength and the noise amplification effect, the i The final cascade link between the two has a discrete and uneven error, resulting in h(x o ,y o ,λ i ) appears on the surface, which is caused by the noise at the shortest synthetic wavelength being larger than a quarter of the wavelength of light. Figure 6 As shown in the error diagram (the left area is the reconstructed height map, and the right area is the error map), it can be seen that there is a jump point at half the wavelength height. This is because the phase of the light wavelength corresponds to Incorrect expansion.

[0131] S5: h(x o ,y o ,λ i ) is used as the initial height to guide the subsequent phase sequence search. In order to balance the speed of the algorithm and the reconstruction accuracy, the search step Δh is set to 20nm and the search range is h(x o ,y o ,λ i)±10μm. During the search process, the phase sequence corresponding to each package phase is solved according to the height corresponding to each wavelength, which can be expressed as:

[0132]

[0133] Where i = 1, 2, …, 17; s is the number of search steps, s = 1, 2, …, M; M = 1000.

[0134] The criterion function X(x o ,y o ,s), can be expressed as:

[0135]

[0136] The criterion function X is a one-dimensional curve with multiple minimum values. Due to the noise damage, the optimal phase sequence that should appear at the horizontal coordinate u corresponding to the minimum value of the curve is The phase sequence at the horizontal coordinate w corresponding to a minimum value near the minimum value may appear To avoid the optimal phase sequence The search error is here, a more robust judgment method is adopted: first obtain the envelope curve of X, and then determine the most correct optimal phase sequence according to the horizontal coordinate v corresponding to the minimum value of the envelope curve. Expressed as:

[0137] [v,X(v)]=min{envelope[X(x o ,y o ,s)]}

[0138]

[0139] The algorithm flow of S5 is as follows Figure 2 As shown in part 2.

[0140] S6: Round the phase sequence corresponding to the wrapped phase of the 17 light wavelengths searched by S5, then reconstruct the object height at each wavelength and average them to obtain the final reconstructed object height h m (x o ,y o ),like Figure 7 The reconstructed height map (the left area is the reconstructed height map, and the right area is the error map) is shown as follows:

[0141]

[0142] By comparing the surface height distribution of the initial object, this example correctly reconstructed a stepped object with a height of 100 to 400 microns. When Gaussian phase white noise with a mean of 0 and a standard deviation of 0.025 was added, the root mean square error of the reconstructed object was only 2.4nm, and the maximum error was 9nm. Figure 7 (The left area is the reconstructed height map, and the right area is the error map).

[0143] Compared with related technologies, the present invention has the following advantages: using multi-wavelength cascade phase unwrapping to obtain a height distribution with higher axial resolution, guiding the subsequent phase sequence search, solving the problem of search failure in traditional height search, while reducing the search range and improving the algorithm speed; using the minimum value of the envelope of the search criterion function to determine the optimal phase sequence Instead of determining the optimal phase sequence by finding the minimum value of the criterion function To a great extent, it solves the problem of optimal phase sequence caused by noise destruction of the criterion function. An error occurs. The method of the present invention perfectly solves the problems of noise amplification and jump points in the previous dual (multi) wavelength phase unwrapping. Even if the noise of the synthetic wavelength is greater than a quarter of the wavelength, the correct object height distribution can be solved. While expanding the axial measurement range to the submillimeter level, the nanometer-level axial resolution can be maintained, and the influence of noise on the final result can be reduced to the level of a single wavelength. The present invention is very suitable for objects with stepped, high-depth points such as chip surfaces, and achieves a larger measurement range and higher measurement accuracy.

[0144] 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 and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A multi-wavelength phase unwrapping method based on synthetic wavelength chain guidance and phase sequence search, which is used to determine the phase of the object to be measured at the optical wavelength λ i The multi-wavelength off-axis digital hologram under the condition of light wavelength λ is obtained by using the height distribution model. i The optimal phase sequence of the coordinates (x0, y0) at the surface of the object to be measured is as follows: It is characterized in that The multi-wavelength phase unwrapping method obtains the optimal phase sequence based on synthetic wavelength chain guidance and phase sequence search. First, the wavelength of light in the hologram is i Height distribution of coordinates (x0, y0) on the surface of the object to be measured As an initial value, the phase sequence is searched at intervals of Δh within the preset range of the initial value. The phase sequence during the search process is expressed as: Where, is the phase sequence of the coordinates (x0, y0) on the surface of the object to be measured when the number of search steps is s, is the wavelength of light λ i The coordinates of the object surface under test (x o ,y o ), is the wavelength of light in the hologram λ i The coordinates of the surface of the object to be measured (x o ,y o )’s wrapping phase, is the wavelength of light λ i The reconstructed height of the coordinate (x0, y0) at the surface of the object to be measured, s is the number of search steps, s = 1, 2, ..., M, Δh is the search step length, which represents the minimum interval distance during the search process; Secondly, the phase sequences found by the search are used to form a criterion function. When the minimum value of the envelope of the criterion function is taken, the corresponding phase sequence is considered to be the optimal phase sequence. The criterion function is expressed as: Where, X(x o ,y o ,s) is the criterion function, which represents the coordinates (x o ,y o ) criterion value; At this time, the optimal phase sequence for: [v,X(v)]=min{envelope[X(x o ,y o ,s)]} Where [v, X(v)] is the coordinate position corresponding to the minimum value X(v) of the envelope when the number of steps is v, min is the minimum value operation, and envelope is the envelope function. is the phase sequence of the coordinates (x0, y0) on the surface of the object to be measured when the number of search steps is v.

2. The multi-wavelength phase unwrapping method based on synthetic wavelength chain guidance and phase sequence search according to claim 1, characterized in that: The height distribution model is: Where h(x0,y0) is the height distribution of the coordinate (x0,y0) on the surface of the object to be measured in the hologram, n λi (x o ,y o ) is the wavelength λ of the light in the hologram i The coordinates of the surface of the object to be measured (x o ,y o ), is the coordinate of the surface of the object to be measured under the synthetic wavelength Λ1 (x o ,y o )’s wrapping phase, is the coordinate of the surface of the object to be measured under the synthetic wavelength Λ1 (x o ,y o ), is the coordinate (x o ,y o )’s wrapping phase, is the coordinate (x o ,y o ), is the synthetic wavelength Λ N-1 The coordinates of the surface of the object to be measured (x o ,y o )'s wrapping phase.

3. The multi-wavelength phase unwrapping method based on synthetic wavelength chain guidance and phase sequence search according to claim 1, characterized in that: The diffraction process of light waves propagating from the hologram plane to the surface of the object to be measured numerically reproduces the complex amplitude distribution of the object light wave, and the inverse tangent function is used to calculate the wrapped phase distribution at different wavelengths for the reproduced complex amplitude of the object light wave. Where U(x0,y0,λ i ) represents the wavelength of light λ i The coordinates on the surface of the object to be measured (x o ,y o ), Im represents the complex amplitude of the object light wave at U(x0,y0,λ i );Re represents the complex imaginary part of U(x0,y0,λ i ) is the complex real part of .

4. The multi-wavelength phase unwrapping method based on synthetic wavelength chain guidance and phase sequence search according to claim 3, characterized in that: According to the scalar diffraction theory, the complex amplitude of the object light wave U(x0,y0,λ i ): U(x o ,y o ,λ i )=FFT -1 {FFT[A(x,y,λ i )]·H(f x ,f y ,λ i )} Where, (f x ,f y ) is the coordinate of the complex amplitude of the object light wave in the frequency domain, f x =x / L x , f y =y / L y , L x and L y are the length and width of the CCD format of the camera that obtains the hologram, H(f x ,f y ,λ i ) is the wavelength of light λ i The coordinates of the complex amplitude of the object light wave in the frequency domain (f x ,f y ) is the angular spectrum diffraction transfer function, A(x,y,λ i ) represents the wavelength of light λ i The complex amplitude of the object light wave at the coordinate (x,y) in the spatial domain under .

5. The multi-wavelength phase unwrapping method based on synthetic wavelength chain guidance and phase sequence search according to claim 4, characterized in that: A(x,y,λ i ) is expressed as: Where j is the imaginary unit, k is the wave number of light, k = 2π / λ i , d is the propagation distance, that is, the distance between the object to be measured and the recording surface of the camera.

6. The multi-wavelength phase unwrapping method based on synthetic wavelength chain guidance and phase sequence search according to claim 5, characterized in that: A(x,y,λ i ) is designed as follows: Perform two-dimensional Fourier transform (FFT) on the multi-wavelength off-axis digital hologram to obtain its spectrum distribution. The intensity of the hologram is expressed as: I(x,y,λ i )=|O(x,y,λ i )| 2 +|R(x,y,λ i )| 2 +O(x,y,λ i )R * (x,y,λ i )+O * (x,y,λ i )R(x,y,λ i ) Where, I(x,y,λ i ) represents the wavelength of light λ i The intensity of the interference light at the coordinate (x, y) in the hologram under i ) consists of four terms, the first two of which constitute the zero-order image, and the third term OR * It is a positive first-order image, the fourth term O * R is the negative first-order image, O(x,y,λ i ) represents the wavelength of light λ i The light intensity of the object light at the coordinate (x, y) in the hologram under i ) represents the wavelength of light λ i The light intensity of the reference light at the coordinate (x, y) in the hologram below, * represents the conjugate sign; For the spectrum distribution of the third item, perform inverse two-dimensional FFT processing and convert it into the spatial domain, OR * Expressed as: O(x,y,λ i )R * =A(x,y,λ i )exp[jk(x 2 +y 2 ) / 2d-jk(cosα·x+cosβ·y)] Where α and β represent the angles between the reference light and the X-axis and Y-axis on the recording surface of the camera, respectively.

7. The multi-wavelength phase unwrapping method based on synthetic wavelength chain guidance and phase sequence search according to claim 4, characterized in that: H(f x ,f y ,λ i ) is designed as: Where j is the imaginary unit, k is the wave number of light, k = 2π / λ i , z is the distance between the recording surface of the camera and the object to be measured, that is, z = -d.

8. The multi-wavelength phase unwrapping method based on synthetic wavelength chain guidance and phase sequence search according to claim 1, characterized in that: The object to be tested is a chip with a stepped surface and high depth points.

9. A method for measuring the height of an object, which is used to measure the height of an arbitrary coordinate (x0, y0) on the surface of an object to be measured, characterized in that: The object height measurement method comprises the following steps: Define different light wavelengths λ i A beam of light emitted by a light source is defined as reference light, and another beam of light emitted by a light source having the same source as the reference light and reflected from the surface of a step-shaped object to be measured is defined as object light. The object light and the reference light form interference light, and a multi-wavelength off-axis digital hologram is imaged on a recording surface of a camera using the interference light. The hologram is obtained by using the multi-wavelength phase unwrapping method based on synthetic wavelength chain guidance and phase sequence search as described in any one of claims 1 to 8 at the optical wavelength λ i The optimal phase sequence of the coordinates (x0, y0) at the surface of the object to be measured is as follows: According to the optimal phase sequence Reconstruct the correct height of the object to be measured at coordinate (x0, y0).

10. An object height measurement system, comprising: Several light sources for emitting light of different wavelengths λ i light, defining different light wavelengths λ i A beam of light emitted by a light source is defined as reference light, and another beam of light emitted by a light source having the same source as the reference light and irradiated on the surface of the step-shaped object to be measured is defined as object light, and the object light and the reference light form interference light; a camera for imaging a multi-wavelength off-axis digital hologram on a recording surface of the camera using the interference light; A processor for obtaining a hologram at an optical wavelength λ by using a multi-wavelength phase unwrapping method based on synthetic wavelength chain guidance and phase sequence search as described in any one of claims 1 to 8. i The optimal phase sequence of the coordinates (x0, y0) at the surface of the object to be measured is as follows: Also used to determine the optimal phase sequence Reconstruct the correct height of the object to be measured at coordinate (x0, y0).

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