Phase shift digital holographic three-dimensional measurement method and device for vibration of measured body

Abstract

The application discloses a precision surface three-dimensional appearance measurement device and method based on phase shift digital holography, which comprises the following modules: a light beam splitting module for generating a reference light and an object light beam irradiated to the surface of a measured object and returned; a reference light beam adjusting module for receiving the reference light generated by the light beam splitting module, generating different reference light beams based on different voltage forces, and generating different reference light beams after different brightening and increasing; a lens imaging system for receiving the object light beam generated by the light beam splitting module and performing light beam amplification; a second polarization beam splitter for receiving the different reference light beams generated by the reference light beam adjusting module and the amplified object light beam of the lens imaging system, and performing light beam combination; a linear polaroid for respectively interfering a series of light beams after combination; an image acquisition module for acquiring a series of interference images; and a computer for receiving the series of interference images transmitted by the image acquisition module, extracting phase information of the object light by using a phase shift algorithm, and realizing measurement of the three-dimensional appearance of the surface of the measured object.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of optical precision measurement, and relates to a phase shift digital holographic three-dimensional measurement method and device for vibration of a measured object. BACKGROUND

[0002] In recent years, digital holography has been widely concerned and studied due to its strong application potential in three-dimensional topography measurement. According to the hologram generation mode, digital holography can be divided into off-axis and on-axis digital holography. Among them, the off-axis mode filters out the interference of the zero-order image and the conjugate image from the obtained single carrier frequency hologram by introducing an included angle between the object light and the reference light, but this mode cannot fully utilize the space-bandwidth product of the CCD / CMOS optical-electrical device. In the on-axis recording mode, the object light and the reference light propagate in the same direction, which can fully utilize the space-bandwidth product of the CCD / CMOS, but it is necessary to introduce different phase shift amounts between the object light and the reference light, and then directly extract the object light information in the on-axis hologram by using the phase shift method. The phase shift digital holography technology is a high-precision, non-contact measurement method based on digital holography combined with phase shift technology, and is widely used in industrial detection, biomedicine and other fields. The phase shift digital holography not only has the advantages of digital holography, but also has higher phase measurement precision, higher spatial resolution and lower noise level.

[0003] The phase shift interferometric measurement records the interference patterns formed by introducing different phase shift amounts between the object light and the reference light, and reconstructs the amplitude and phase distribution of the measured sample from the phase shift interference patterns by using the corresponding phase shift algorithm and digital reconstruction algorithm. The reconstruction accuracy of the measured sample depends on the accurate phase shift amount information, and the phase shift amount is realized by the displacement of the piezoelectric ceramic, but the phase shift amount information cannot be accurately obtained due to the following factors: (1) the piezoelectric ceramic material has inherent hysteresis and nonlinear error in electrostriction, so that the piezoelectric ceramic phase shifter has random phase shift error, so that the actual phase shift value deviates from the set value; (2) the environmental vibration inevitably causes the vibration of the measured object and related components, and the vibration causes the introduction of distributed unknown phase shift amount between the reference light and the object light. Therefore, at present, there is an urgent need for a method for determining the distributed unknown phase shift amount caused by the vibration of the measured object to realize the high-precision measurement of the micro three-dimensional topography of the precision measured object surface. SUMMARY

[0004] In order to solve the above technical problems, the technical scheme adopted by the present application is: a precision surface three-dimensional topography measurement device based on phase shift digital holography, comprising:

[0005] a beam splitting module for generating an object light beam and a reference light beam irradiated to the surface of a measured object and returned;

[0006] The reference light beam adjustment module generates the reference light beam with different increased optical paths based on different applied voltage forces;

[0007] The lens imaging system receives the object light beam generated by the beam splitting module;

[0008] The second polarization beam splitter receives the reference light beam passing through the reference light beam adjustment module and the object light beam passing through the lens imaging system, and combines them;

[0009] The image acquisition module acquires a series of interference images formed by the combined light passing through the linear polarizer;

[0010] The computer receives a series of interference images transmitted by the image acquisition module, extracts the phase information of the object light using the phase shift algorithm, and realizes the measurement of the three-dimensional topography of the measured object surface.

[0011] The measured object is a rigid body model.

[0012] Further, the beam splitting module includes

[0013] The laser generates the light beam;

[0014] The attenuator attenuates the light beam;

[0015] The beam expander expands the attenuated light beam;

[0016] The first half-wave plate changes the polarization properties of the expanded light beam;

[0017] The first polarization beam splitter divides the light beam with changed polarization properties into two paths, and the first path is the reference light beam;

[0018] The second path of light passing through the first polarization beam splitter is irradiated onto the measured object through the quarter-wave plate, and the reflected light from the measured object passes through the quarter-wave plate and returns to the first polarization beam splitter, then is transmitted to form the object light beam.

[0019] Further, the reference light beam adjustment module includes

[0020] The mirror receives the reference light beam divided by the first polarization beam splitter and reflects the reference light beam;

[0021] The second half-wave plate changes the polarization properties of the reference light beam reflected by the mirror;

[0022] The piezoelectric ceramic phase shifter changes the optical path of the reference light beam transmitted by the second half-wave plate.

[0023] Further, the piezoelectric ceramic phase shifter receives different voltages applied by a computer to realize phase shift, when a driving voltage is applied to the piezoelectric ceramic, a plane mirror on the piezoelectric ceramic produces corresponding displacement along the optical axis direction, thereby obtaining holograms with different phase shift amounts.

[0024] A precision surface three-dimensional topography measurement method based on phase shift digital holography, comprising the following steps:

[0025] Suppose the complex amplitude distributions of the object light and the reference light reaching the CCD / CMOS detector plane of the camera are respectively:

[0026]

[0027] In formula (1), A o (x,y), A r (x,y), denoted as A o , A r is the amplitude of the object light and the reference light, represents the phase of the object light and the reference light;

[0028] The holographic interference pattern is:

[0029]

[0030] In formula (2), represents the phase difference between the object light and the reference light;

[0031] By controlling the displacement of the piezoelectric ceramic, a phase shift amount δ i is introduced into the reference light, and the holographic interference pattern under different phase shift amounts is represented as:

[0032]

[0033] In formula (3), δ i is the phase shift amount generated by the i-th relative to the first phase shift, if the reference light phase at the first measurement is taken as the reference, δ1=0;

[0034] The error distribution of the phase shift amount caused by the displacement along the optical axis Z axis under the vibration of the measured object is:

[0035] ε i (x,y)=a i x+b i y+c i (4)

[0036] Considering the vibration of the measured object, the interference pattern of formula (3) is updated as:

[0037]

[0038] Considering the phase shift error caused by the vibration of the measured object, the phase shift error distribution caused by the vibration is solved based on the idea of region blocking to determine the phase shift error ε i (x,y);

[0039] The phase shift error ε caused by the vibration of the measured object in any holographic interference figure i After the determination of (x,y), the phase information of each point (x,y) in the image can be calculated according to formula (5), as follows:

[0040]

[0041] In formula (13), σ i =σ i (x,y) = ε i (x,y) + δ i , A = A(x,y), I i =I i (x,y). Wherein, A(x,y), B(x,y), I i (x,y), ε i (x,y) and δ i are defined as formula (5);

[0042] According to formula (13), the u(x,y) and v(x,y) are calculated, and the phase difference between the object light and the reference light is calculated as:

[0043]

[0044] According to the phase difference information between the object light and the reference light calculated by formula (14), combined with the constant phase of the reference light, the phase information of the object light can be recovered, and the three-dimensional topography h(x,y) of the measured object surface can be obtained according to the phase of the object light:

[0045]

[0046] Further, the phase shift error distribution caused by the vibration is solved based on the idea of region blocking to determine the phase shift error ε i (x,y) is as follows:

[0047] S1: A series of phase shift interference images are divided into MxN small block division regions according to the same region division method,

[0048] S2: For each small block division region, it is assumed that the phase shift error caused by the vibration in the region is the same, and the average phase shift error is calculated by statistical analysis;

[0049] S3: After the phase shift error of all small block division areas is calculated, the center coordinates of each small block division area and the corresponding phase shift are used to fit the phase shift error distribution in the whole image according to the model of formula (4).

[0050] Further: for each small block division area, it is assumed that the phase shift error caused by vibration in the area is the same, and the average phase shift error is calculated by statistical analysis, which is realized by using the interference image information in the same small block division area with three different phase shifts, and the specific implementation is as follows:

[0051] Since it is assumed that the phase shift error caused by vibration in any small block division area is the same, the interference image information in the same small block division area with three different phase shifts is represented as:

[0052]

[0053] Where: δ 2, δ3 is the phase shift caused by the displacement of the second and third images relative to the first image, 0 < δ i <π; ε2, ε3 are the phase shift errors caused by vibration; δ'2 = δ2 + ε2, δ'3 = δ3 + ε3- δ'2;

[0054] Define a new variable composed of three phase shift interference intensity images:

[0055]

[0056] Where < > represents taking the average of the whole interference image, and it is assumed that A(x, y), are independent of each other, and the phase distribution of the original object light wave Fresnel diffraction field is considered randomly distributed in space, so the < |…| > term on the right side of the formula has the same approximate value c, and the following is obtained:

[0057]

[0058] From the above formula, we can get:

[0059] Then the two phase shifts are calculated:

[0060]

[0061] Using formula (9), combined with the known phase shift δ i corresponding to the piezoelectric ceramic control amount, the phase shift error ε i caused by the vibration of the measured body in each small block division area can be solved.

[0062] The phase shift error in each small block division area is calculated through the above steps, and the least square fitting data fitting is performed on the whole interference pattern:

[0063]

[0064] In formula (10), k represents the kth small block division area after area division, (x k ,y k ) represents the coordinates corresponding to the center of the small block division area in the whole image, and i represents the interference pattern number of different phase shifts.

[0065] The partial derivatives of the three unknowns a i ,b i ,c i in formula (10) are obtained as follows:

[0066]

[0067] In matrix form:

[0068]

[0069] The a i ,b i ,c i are obtained, and the phase shift error distribution ε i (x,y) caused by the vibration of the measured body is obtained according to formula (4).

[0070] The phase shift digital holographic three-dimensional measurement method and device of the measured body vibration provided by the application, when measuring the micro surface three-dimensional morphology by using the phase shift digital holographic method, a series of holographic interference images under different phase shifts are obtained by using the piezoelectric ceramic to generate displacement. However, during the measurement process, the vibration of the measured body is caused by environmental factors, thereby introducing a distributed unknown phase shift, and affecting the high-precision acquisition of the measurement result.

[0071] On the basis of the phase shift digital holographic method, the rigid body motion model of the vibration of the measured body is used to correct the distributed phase shift error caused by the vibration of the measured body, so as to determine the accurate phase shift information between the holographic interference images, realize the high-precision detection of the three-dimensional morphology of the surface of the measured body, and effectively promote the high-precision measurement technology based on the phase shift digital holographic method from the laboratory to the actual application of the industrial production line. BRIEF DESCRIPTION OF DRAWINGS

[0072] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or prior art description. Obviously, the drawings described in the following are only some embodiments of the present application, and not all embodiments. The following description of at least one exemplary embodiment is merely illustrative in nature and not intended to limit the present application and its applications or uses in any way. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0073] Figure 1 is a reflective digital phase shift holographic experimental optical path diagram;

[0074] Figure 2 (a) is a measured object along the X-axis rotation position change diagram, (b) is a measured object along the Y-axis rotation position change diagram, (c) is a measured object along the Z-axis rotation position change diagram;

[0075] Figure 3 (a) is the first interference diagram of the measured area division model, (b) is the second interference diagram of the measured area division model, (c) is the third interference diagram of the measured area division model.

[0076] The drawings show that: 1, laser, 2, attenuator, 3, beam expander, 4, first half-wave plate, 5, first polarization beam splitter prism, 6, quarter-wave plate, 7, three-dimensional moving platform, 8, lens imaging system, 9, first polarization beam splitter prism, 10, mirror, 11, second half-wave plate, 12, piezoelectric ceramic phase shifter, 13, linear polarizer, 14, camera, 15, computer. DETAILED DESCRIPTION

[0077] It should be noted that the embodiments in the present application and the features in the embodiments can be combined with each other without conflict, and the present application will be described in detail below with reference to the drawings and in combination with the embodiments.

[0078] In order to make the purpose, technical solutions and advantages of the embodiments of the present application more clear, the technical solutions in the embodiments of the present application will be described clearly and completely below in combination with the drawings in the embodiments of the present application. Obviously, the described embodiments are only some embodiments of the present application, not all embodiments. The following description of at least one exemplary embodiment is merely illustrative in nature and not intended to limit the present application and its applications or uses in any way. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0079] It is to be understood that the terms so far as the word "comprise" and / or "comprising", or "include" and / or "including" when used in this specification is / are used to express the inclusion of one or more steps, operations, elements, and / or components, but these are not mutually exclusive and the phrase can be accepted as equivalent to "consist of" and / or "consist essentially of".

[0080] The relative arrangement of parts and steps, numerical expressions, and numerical values set forth in the examples are not intended to limit the scope of the application unless otherwise specifically stated. It is also to be understood that the drawings are not necessarily drawn to scale of the actual proportions of the various parts and elements thereof. Techniques, methods, and apparatus known to those of ordinary skill in the relevant art can not be discussed in detail, but should be considered as part of the description of the application. In all examples shown and discussed herein, any specific numerical value should be interpreted as merely an example, and not as a limitation. Other examples of the exemplary embodiments can therefore have different values. It is to be noted that like numbers and letters refer to like elements throughout the several views of the drawings and, as such, no further discussion with regard thereto is deemed necessary.

[0081] In the description of the application, it is to be understood that the orientation or positional relationships indicated by orientation words such as "front, back, upper, lower, left, right", "transverse, vertical, perpendicular, horizontal", and "top, bottom" are generally based on the orientation or positional relationships shown in the drawings, and are only for the convenience of describing the application and simplifying the description. Without the opposite indication, these orientation words do not indicate and imply that the devices or elements referred to must have a particular orientation or be constructed and operated in a particular orientation, and therefore cannot be understood as a limitation on the scope of protection of the application: the orientation words "inner, outer" refer to the inner and outer relative to the contour of each component.

[0082] For purposes of the description hereinafter, spatially relative terms, such as "above", "below", "up", "down", "between", "within", "left", "right", "rear", "front", "upper", "lower", "horizontal", "vertical", "above", "below", "top", "bottom", "under", and the like, can be used for ease of description to describe one element's or feature's relationship to another element(s) or feature(s) as illustrated in the figures. It will be understood that the spatially relative terms are intended to encompass different orientations of the device in use or operation in addition to the orientations depicted in the figures. For example, if a device in the figures is inverted, elements described as "above" or "up" other elements or features would then be oriented "below" or "down" the other elements or features. Thus, the exemplary term "above" can encompass both an orientation of above and below. The devices can be otherwise oriented (rotated 90 degrees or at other orientations) and the spatially relative descriptors used herein interpreted accordingly. The terms "first", "second", "third", etc. do not necessarily indicate any ordinal, temporal, hierarchical or spatial relationship between the entities to which they are applied.

[0083] In addition, it should be noted that the use of "first", "second", etc. words to qualify parts, is only for the convenience of distinguishing the corresponding parts, and the above words have no special meaning unless otherwise stated, and therefore cannot be understood as limiting the scope of protection of the present application.

[0084] A precise surface three-dimensional appearance measurement device based on phase shift digital holography, comprising: a light beam splitting module, a reference light beam adjusting module, a lens imaging system 8, a second polarization beam splitter prism 9, a linear polarizer 13, an image acquisition module and a computer 15;

[0085] The light beam splitting module is used to generate an object light beam irradiated to the surface of a measured object and returned and to generate a reference light;

[0086] The measured object is a rigid body model;

[0087] The measured object is arranged on a three-dimensional moving platform 7; the three-dimensional moving platform 7 is used to control the three-dimensional movement of the measured object;

[0088] The reference light beam adjusting module receives the reference light generated by the light beam splitting module, applies different voltage forces based on the computer, and generates different reference light beams of the object light beam after different brightening and increasing ranges;

[0089] The lens imaging system 8 receives the object light beam generated by the light beam splitting module and amplifies the object light beam;

[0090] The second polarization beam splitter prism 9 receives the different reference light beams of the reference light beam adjusting module and the amplified object light beam of the lens imaging system, and respectively performs light beam merging;

[0091] The linear polarizer 13 respectively causes a series of light beams after merging to interfere;

[0092] The image acquisition module acquires a series of interference images; the image acquisition module uses a CCD / CMOS camera 14;

[0093] The computer 15 receives the series of interference images transmitted by the image acquisition module, uses a phase shift algorithm to extract the phase information of the object light, and realizes the measurement of the three-dimensional topography of the measured object surface.

[0094] Further, the light beam splitting module comprises:

[0095] A laser 1 for generating a light beam;

[0096] An attenuator 2 for attenuating the light beam;

[0097] A beam expander 3 for expanding the attenuated light beam;

[0098] A first half-wave plate 4 for changing the polarization characteristics of the expanded light beam;

[0099] A first polarization beam splitter prism 5 for splitting the light beam with changed polarization characteristics into two paths: a first light path and a second light path; the first light path is the reference light path;

[0100] A quarter-wave plate 6 for receiving the second light path split by the first polarization beam splitter prism 5 and changing the polarization characteristics of the light;

[0101] The light transmitted by the quarter-wave plate 6 is irradiated onto the measured object, and the light reflected by the measured object passes through the quarter-wave plate 6 and is transmitted after returning to the polarization beam splitter prism 5, forming an object light beam; the polarization beam splitter prism 5 reflects S-state light and transmits P-state light;

[0102] Further, the reference light beam adjustment module comprises:

[0103] A mirror 10 for receiving the reference light beam split by the first polarization beam splitter prism 5 and reflecting the reference light beam;

[0104] A second half-wave plate 11 for receiving the reference light beam reflected by the mirror 10 and adjusting the reference light energy by changing the polarization characteristics of the reference light;

[0105] A piezoelectric ceramic phase shifter 12 for receiving the reference light and changing the optical path of the reference light.

[0106] Further, the piezoelectric ceramic phase shifter 12 receives different voltages applied by the computer 15 to realize phase shifting; when a driving voltage is applied to the piezoelectric ceramic, the plane mirror on the piezoelectric ceramic produces a corresponding displacement along the optical axis direction, thereby obtaining holograms with different phase shift amounts.

[0107] Further, the process of extracting phase information of object light by using phase shift algorithm to realize three-dimensional topography of measured object surface from a series of interference images transmitted by image acquisition module (interference image formation mechanism as follows) is as follows:

[0108] Suppose the complex amplitude distribution of object light and reference light reaching the CCD / CMOS detector plane of camera is:

[0109]

[0110] In formula (1), A o (x,y), A r (x,y), denoted as A o , A r is the amplitude of object light and reference light, represents the phase of object light and reference light;

[0111] The holographic interference pattern is:

[0112]

[0113] In formula (2), represents the phase difference between object light and reference light;

[0114] By controlling the displacement of piezoelectric ceramic to introduce phase shift δ i into the reference light, the interference pattern of holographic image under different phase shift is:

[0115]

[0116] In formula (3), δ i is the phase shift generated by the i-th measurement relative to the first phase shift. If the phase of the reference light in the first measurement is taken as the reference, δ1=0;

[0117] During the measurement, due to the vibration of the experimental platform, the position of the measured object will randomly deviate, as shown in the attached Figure 2 . Figure 2 (a) represents the rotation of the measured object along the X-axis, Figure 2 (b) represents the rotation of the measured object along the Y-axis, Figure 2 (c) represents the translation of the measured object along the Z-axis. If the measured object is regarded as a rigid body, the displacement generated by the vibration of the measured object belongs to the combination of the above three cases.

[0118] Therefore, the error distribution of phase shift caused by the displacement of the measured object along the optical axis Z-axis under the vibration condition is:

[0119] ε i (x,y)=a i x+b i y+ci (4)

[0120] Considering the vibration of the measured body, the interference pattern of formula (3) is updated as:

[0121]

[0122] Considering the influence of the phase shift error caused by the vibration of the measured body, the phase shift error distribution caused by the vibration is solved based on the idea of region blocking to determine the phase shift error ε i (x,y); the phase shift error distribution caused by the vibration is solved based on the idea of region blocking to determine the phase shift error ε i (x,y) is as follows:

[0123] S1: A series of phase shift interference images are divided into MxN small block regions according to the same region division method,

[0124] S2: For each small block region, it is assumed that the phase shift error caused by the vibration in the region is the same, and the average phase shift error is calculated by statistical analysis;

[0125] S3: After the phase shift error of all small block regions is calculated, the center coordinates of each small block region and the corresponding phase shift are used to fit the phase shift error distribution in the whole image according to the model of formula (4).

[0126] For each small block region, it is assumed that the phase shift error caused by the vibration in the region is the same, and the average phase shift error is calculated by statistical analysis, which is realized by using the interference image information of the same small block region with continuous three different phase shifts, which is as follows:

[0127] Since it is assumed that the phase shift error caused by the vibration in any small block region is the same, the interference image information of the same small block region with continuous three different phase shifts is represented as:

[0128]

[0129] Where: δ 2, δ3 is the phase shift caused by the displacement of the second and third images relative to the first image, 0 < δ i <π; ε2, ε3 are the phase shift errors caused by the vibration; δ'2 = δ2 + ε2, δ'3 = δ3 + ε3- δ'2;

[0130] Define a new variable composed of three phase shift interference intensity images:

[0131]

[0132] where < > represents the average of the whole interferogram, and A(x, y) is the original object wave field. The phase distribution of the original object wave field is considered to be independent of each other The phase distribution of the original object wave field is considered to be independent of each other

[0133]

[0134] From the above formula, we can get:

[0135] Then the phase shift amount of two times is calculated:

[0136]

[0137] Using formula (9), combined with the known phase shift amount δ i corresponding to the piezoelectric ceramic control amount, the phase shift amount error ε caused by the vibration of the measured object in each small divided area can be solved i ;

[0138] Through the above steps, the phase shift amount error in each small divided area is calculated, and the least square fitting data fitting is performed on the whole interferogram:

[0139]

[0140] In formula (10), k represents the kth small divided area after area division, (x k ,y k ) represents the coordinates corresponding to the center of the small divided area in the whole image, and i represents the label of the interferogram with different phase shift amount.

[0141] The partial derivative of the three unknown quantities a i ,b i ,c i in formula (10) is obtained:

[0142]

[0143] Written in matrix form:

[0144]

[0145] The a i ,b i ,c i are obtained, and the phase shift amount error distribution ε i (x, y) caused by the vibration of the measured object is obtained according to formula (4).

[0146] The phase shift amount error ε iAfter (x, y) is determined, phase information of each point (x, y) in the image can be calculated according to formula (5) as follows:

[0147]

[0148] In formula (13), σ i = σ i (x, y) = ε i (x, y) + δ i , A = A(x, y), I i = I i (x, y). Wherein, A(x, y), B(x, y), I i (x, y), ε i (x, y) and δ i are defined as formula (5);

[0149] According to formula (13), u(x, y) and v(x, y) are calculated, and phase difference between the object light and the reference light is calculated as:

[0150]

[0151] According to the phase difference between the object light and the reference light calculated by formula (14), and the phase of the reference light being constant, phase information of the object light can be recovered, and three-dimensional topography h(x, y) of the measured surface can be obtained according to the phase of the object light:

[0152]

[0153] In formula (15), λ is the wavelength of the laser.

[0154] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present application, and not to limit them; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: it can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement to part or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present application.

Claims

1. A precise method for measuring three-dimensional surface topography based on phase-shifting digital holography, characterized in that: Includes the following steps: The holographic interferogram is as follows: (2) In equation (2), 、 , recorded as , , where is the amplitude of the object beam and the reference beam. This indicates the phase difference between the object beam and the reference beam; , Indicates the phase of the object beam and the reference beam; A phase shift is introduced into the reference light by controlling the displacement of the piezoelectric ceramic. Then, the holographic interferograms under different phase shifts are represented as follows: (3) In formula (3) δ i For the first i The phase shift relative to the first phase shift, if taken as a reference light phase during the first measurement, then δ 1 = 0; The phase shift error distribution caused by the displacement along the optical axis Z-axis under the condition of vibration of the measured object is as follows: (4) Considering the vibration of the measured object, the interferogram of equation (3) is updated as follows: (5) Considering the influence of phase shift error caused by the vibration of the measured object, the distribution of phase shift error caused by vibration is solved based on the idea of ​​region partitioning, and the phase shift error is determined. ε i ( x,y ); Phase shift error caused by vibration of the measured object in any holographic interferogram Once determined, each point in the image can be calculated according to equation (5). x, y The phase information is as follows: (13) In equation (13), , A = A ( x , y ), u = B ( x , y cos( φ ( x , y )), v =- B ( x , y sin( φ ( x , y )), ; Calculated according to formula (13) u ( x , y )and v ( x , y The phase difference between the object light and the reference light is calculated as follows: (14) Based on the phase difference information between the object beam and the reference beam calculated using equation (14), and considering that the phase of the reference beam is constant, the phase information of the object beam can be recovered. The three-dimensional morphology of the surface of the object under test can then be obtained based on the phase of the object beam. h ( x , y ): (15) Specifically, the phase shift error distribution caused by vibration is solved based on the idea of ​​regional segmentation, thus determining the phase shift error. The process is as follows: S1: Divide a series of phase-shifting interferometric images into M×N small blocks according to the same region division method; S2: Divide each small block into regions, assuming that the phase shift error caused by vibration in the region is the same, and use statistical analysis to obtain the average phase shift error; S3: After calculating the phase shift error of all small-block division regions, use the center coordinates of each small-block division region and its corresponding phase shift to fit the phase shift error distribution in the entire image according to the model of Equation (4).

2. A method for measuring the precise three-dimensional surface topography based on phase-shifting digital holography according to claim 1, characterized in that: For each small segmented region, assuming that the phase shift error caused by vibration within that region is the same, the average phase shift error is calculated using statistical analysis. This is achieved by using interference image information from the same segmented region with three consecutive steps of different phase shifts, as detailed below: Since it is assumed that the phase shift error caused by vibration is the same in any small segmented region, the interference image information of three consecutive small segmented regions with different phase shifts is represented as follows: (6) in: , The phase shifts of the second and third frames relative to the first frame, 0 < δ i <π; , This refers to the phase shift error caused by vibration. , ; Define a new variable consisting of three phase-shifted interferometric intensity maps: (7) in: The representative takes the average of the entire interferogram, assuming A ( x , y ), φ ( x , y They are independent of each other, considering the phase distribution of the Fresnel diffraction field of the original object's light wave. φ ( x , y The distribution is random in space, therefore the right side of the formula... The terms have the same approximation. c Therefore, we get: (8) From the above formula, we can obtain: ; The phase shifts are then calculated twice: (9) Using equation (9), combined with the known phase shift corresponding to the piezoelectric ceramic control quantity... δ i This allows us to solve for the phase shift error caused by the vibration of the measured object within each small divided region. ; The phase shift error within each small segment is calculated using the above steps, and then least-squares fitting is performed on the entire interferogram. (10) In equation (10), k Indicates the first after regional division k Divide the area into small blocks, ( x k , y k () indicates the coordinates of the center of the small segmented region within the entire image. i Interference icon symbols representing different phase shifts; For the three unknowns in equation (10) a i ,b i ,c i Taking the partial derivative, we get: (11) Written in matrix form: (12) Seeking , , The phase shift error distribution caused by the vibration of the measured body is obtained according to equation (4). .

3. A precision surface three-dimensional topography measurement device based on phase-shifting digital holography, adapted to the measurement method described in any one of claims 1-2, characterized in that: include: A beam splitter module that generates an object beam and a reference beam that illuminate the surface of the object being measured and return to it. A reference beam adjustment module receives the reference light generated by the beam splitting module and produces reference beams with different optical path lengths based on different applied voltage forces. A lens imaging system that receives the product beam generated by a beam splitting module; A second polarizing beam splitter that receives the reference beam after passing through the reference beam adjustment module and the object beam after passing through the lens imaging system and combines them; An image acquisition module that acquires a series of interference images formed by the combined beam of light passing through a linear polarizer; A computer that receives a series of interferometric images transmitted by an image acquisition module and uses a phase-shifting algorithm to extract the phase information of the light to measure the three-dimensional morphology of the surface of the object under test.

4. A precision surface three-dimensional topography measurement device based on phase-shifting digital holography according to claim 3, characterized in that: The object being measured is a rigid body model.

5. A precision surface three-dimensional topography measurement device based on phase-shifting digital holography according to claim 3, characterized in that: The beam splitter module includes: A laser that generates a light beam; An attenuator that reduces the beam size; A beam expander that expands a weakened beam; A first half-wave plate that alters the polarization characteristics of the expanded beam; The first polarization beam splitter splits the light beam, after altering its polarization characteristics, into two paths; the first path of light serves as the reference beam. The second beam, split by the first polarizing beam splitter, passes through a quarter-wave plate and illuminates the object under test. The light reflected from the object passes through the quarter-wave plate and returns to the first polarizing beam splitter, where it is transmitted to form an object beam.

6. A precision surface three-dimensional topography measurement device based on phase-shifting digital holography according to claim 3, characterized in that: The reference beam adjustment module includes: A reflector that receives the reference beam split by the first polarizing beam splitter and reflects the reference beam. A second half-wave plate that alters the polarization characteristics of the reference beam after reflection transmitted through the mirror; A piezoelectric ceramic phase shifter that changes the optical path of the reference beam transmitted by the second half-wave plate.

7. A precision surface three-dimensional topography measurement device based on phase-shifting digital holography according to claim 6, characterized in that: The piezoelectric ceramic phase shifter receives different voltages applied by the computer to achieve phase shift. When a driving voltage is applied to the piezoelectric ceramic, the plane mirror on the piezoelectric ceramic is displaced along the optical axis, thereby obtaining holograms with different phase shifts.

Images