A co-path shear interferometric imaging system and method with independent adjustable shear and carrier frequencies

Abstract

The application discloses a kind of shearing and carrier frequency independently adjustable common-path shearing interferometry imaging system and method, including coherent light source, the light beam of coherent light source is shot to the surface of measured object by beam expander, and measured object, lens one, diaphragm, lens two, Wollaston prism, polaroid, imaging lens, camera are sequentially arranged on the same axis with measured object.The application also discloses a kind of shearing and carrier frequency independently adjustable common-path shearing interferometry imaging method.The application uses the above-mentioned one kind of shearing and carrier frequency independently adjustable common-path shearing interferometry imaging system and method, the control of shear quantity and spatial carrier frequency in imaging system is distributed to different parts of imaging system, and adjustable near-zero shear quantity provides small enough shear force, to ensure that complex surface shape or deformation can be solved;When configuring the required near-zero shear quantity, the separate control of spatial carrier wave further ensures the well-distributed spatial spectrum.

Description

Technical Field

[0001] This invention relates to the field of optical interferometry technology, and in particular to a common-path shearing interferometry imaging system and method with independently adjustable shearing and carrier frequencies. Background Technology

[0002] Shearing interferometry uses a laser as the measuring tool. The laser beam is expanded and then irradiated onto the surface of an object. The reflected / diffuse light is collected by a detector after passing through the system. A shearing unit shears the collected object beam, forming two identical beams with lateral displacement. This results in a shearing interference pattern on the detector. After algorithm processing, a phase map of the shearing interference can be obtained, which characterizes the phase distribution of the surface under test. For optically smooth surfaces, this phase map characterizes their geometric morphology and is used to measure their surface geometric errors. For optically rough surfaces, the displacement gradient caused by the deformation can be obtained by subtracting the two phase maps obtained before and after deformation. This technique is a non-destructive testing technique commonly used in aerospace, mechanical manufacturing, and optical processing fields.

[0003] In shear interferometry, the "shear amount" is defined as the displacement between two transverse shear images. It is one of the characteristic parameters of a shear interferometric imaging system and, to a certain extent, determines the performance of the shear measurement system. In optically smooth surfaces with complex surface distributions, optically rough surfaces with complex deformation distributions, and in nondestructive testing with high rates of change, a sufficiently small shear amount (near-zero shear amount) is required and preferred. On the one hand, within the shear amount range, the surface undulations or deformation distribution can only have one extreme point, which requires the shear amount to be sufficiently small. On the other hand, a near-zero shear amount slows down the decorrelation process between the two shear beams, providing a large dynamic range, especially in applications with high rates of change.

[0004] Meanwhile, phase shifting in either time or space is an indispensable technique for realizing quantitative shearing interferometry imaging systems. For recent measurements, a large number of measurements require extremely high temporal resolution; therefore, the spatial carrier method is preferred because the phase map can be retrieved using only a single shearing interferogram.

[0005] Compared to shearing interferometry systems based on the Michelson and Mach-Zehnder configuration, collinear co-path systems offer advantages in system setup and further enhance robustness and stability. In a collinear co-path system, all optics are simultaneously concentric and collinear, and the two tangential object beams propagate along the same optical path, canceling out interference and noise in the optical path. However, in existing collinear co-path systems, the shearing magnitude is entangled with the spatial carrier frequency, making independent control impossible. In practice, small shearing magnitudes lead to high accuracy and a large measurement range. Furthermore, for effective measurements, only one extreme point of deformation or surface distribution within the shearing magnitude is required, necessitating a sufficiently small shearing magnitude. However, while collinear co-path shearing imaging systems possess unique collinear characteristics, achieving independent control of arbitrarily small, adjustable shearing magnitudes and carrier frequencies is typically challenging. Summary of the Invention

[0006] The purpose of this invention is to provide a common-path shearing interferometry imaging system and method with independently adjustable shearing and carrier frequency, thereby solving the problems mentioned in the background art.

[0007] To achieve the above objectives, the present invention provides a common-path shearing interferometric imaging system with independently adjustable shearing and carrier frequency, comprising a coherent light source, wherein the beam of the coherent light source is directed onto the surface of the object under test through a beam expander, and the object under test, lens one, aperture, lens two, Wollaston prism, polarizer, imaging lens, and camera are arranged sequentially on the same axis as the object under test.

[0008] This invention also provides a common-path shearing interferometry imaging method with independently adjustable shearing and carrier frequency, comprising the following steps:

[0009] Step 1: Adjust the imaging system to obtain the desired shearing amount and the desired spatial spectral distribution;

[0010] Step 2: A coherent light source illuminates the surface of the object under test, and the imaging system collects the light reflected from the surface of the object under test, forming an image on the camera.

[0011] Step 3: The camera acquires the sheared interferogram and performs a Fourier transform;

[0012] Step 4: Introduce a spatial carrier frequency, select components in the spatial spectrum after Fourier transform, and perform inverse Fourier transform on the components to obtain complex amplitude.

[0013] Step 5: Calculate the phase angle of the complex amplitude, remove the carrier frequency from the obtained phase angle, obtain the phase distribution, and obtain the surface undulation height gradient of the measured surface.

[0014] Step six: For surface displacement gradient measurement, perform steps one through five before and after deformation respectively to obtain the surface height gradient before and after the deformation and calculate the difference.

[0015] Preferably, in step one, the imaging system is adjusted to control the distance between the Wollaston prism and the intermediate real image plane in order to obtain the desired shearing amount; the image distance of the imaging system is adjusted to obtain the desired spatial spectrum distribution.

[0016] Preferably, in step two, the light emitted from the coherent light source is expanded by a beam expander and illuminates the surface of the object under test at a certain angle. The light returning from the surface of the object under test is collected by the imaging system and imaged onto the intermediate real image plane. This light is then split by a Wollaston prism to produce two misaligned object beams, which are then imaged onto the intermediate real image plane by an imaging lens. The resulting image is located on the camera's photosensitive surface. The wavefronts of the two sheared object beams are...

[0017] u1(x,y)=|u1(x,y)exp{i[φ(x,y)]}

[0018] u2(x,y)=|u1(x+δ x ,y)exp{i[φ(x+δ x ,y)+2πf0x]}

[0019] Where (x,y) describes the coordinates of the camera's photosensitive surface, φ is the phase from the surface of the object being measured, and δ x f0 is the applied shearing amount, and f0 is the introduced spatial carrier frequency.

[0020] Preferably, in step three, the camera acquires a shearing interferogram, the intensity of which is denoted as...

[0021]

[0022] The asterisk (*) indicates the complex conjugate operation.

[0023] Perform a Fourier transform on the shearing interferogram acquired by the camera, denoted as

[0024]

[0025] in The symbol represents the Fourier transform operation, DC represents the low-frequency spectrum of the background light intensity, and the uppercase letter U represents the Fourier transform of each complex amplitude in the formula of step two.

[0026] Preferably, in step four, by introducing spatial carrier frequencies, the three components in the spatial spectrum diagram shown in step three are discretely located at different positions in the spatial spectrum, and selection is made within the spectrum. Components; perform inverse Fourier transform on the selected components to obtain the complex amplitude. Recorded as

[0027]

[0028] in This represents the inverse Fourier transform operation.

[0029] Preferably, in step five, the phase angle of the obtained complex amplitude is calculated and denoted as...

[0030]

[0031] Where Im is the imaginary part operation and Re is the real part operation;

[0032] Remove the carrier frequency from the obtained phase angle to obtain the phase distribution φ(x,y). Calculate the surface undulation height gradient of the measured surface using the following formula, denoted as:

[0033]

[0034] Where θ is the angle between the incident light and the normal to the surface of the object being measured.

[0035] Therefore, the present invention employs the above-mentioned common-path shearing interferometry imaging system and method with independently adjustable shearing and carrier frequency, which has the following beneficial effects:

[0036] 1. The present invention adopts a common-path system to provide a convenient system installation method, and due to its excellent noise resistance, it has the potential to operate in industrial environments;

[0037] 2. The shearing interferometric imaging system proposed in this invention is particularly suitable for measuring complex surface distributions or those with complex deformations. The adjustable near-zero shear quantity provides a sufficiently small shear force to ensure that complex surface shapes or deformations can be addressed.

[0038] 3. In the imaging system of the present invention, the control of shearing amount and spatial carrier frequency is allocated to different parts of the imaging system. When the required near-zero shearing amount is configured, the individual control of the spatial carrier further ensures a well-distributed spatial spectrum.

[0039] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0040] Figure 1 This is a schematic diagram of the imaging system of the present invention;

[0041] Figure 2 This is a flowchart of the imaging method steps of the present invention;

[0042] Figure 3 This is a schematic diagram of the imaging system structure according to an embodiment of the present invention.

[0043] Figure Labels

[0044] 1. Coherent light source; 2. Beam expander; 3. Object under test; 4. Lens 1; 5. Aperture; 6. Lens 2; 7. Wollaston prism; 8. Polarizer; 9. Imaging lens; 10. Camera. Detailed Implementation

[0045] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0046] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. The terms "set," "install," and "connect" should be interpreted broadly; for example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal connection of two elements. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0047] Example

[0048] Figure 1 This is a schematic diagram of the imaging system of the present invention; Figure 2 This is a flowchart of the imaging method steps of the present invention; Figure 3 This is a schematic diagram of the imaging system structure according to an embodiment of the present invention.

[0049] like Figure 1 As shown, the present invention discloses a common-path shearing interferometric imaging system with independently adjustable shearing and carrier frequency, comprising a coherent light source 1, the beam of the coherent light source 1 being directed onto the surface of the object under test 3 through a beam expander 2, and arranged sequentially on the same axis as the object under test 3 are the object under test 3, lens 1 4, aperture 5, lens 2 6, Wollaston prism 7, polarizer 8, imaging lens 9, and camera 10.

[0050] according to Figure 3The optical system is constructed as shown, using a laser as the coherent light source 1. The laser is incident on the surface of the object under test 3 at an angle θ. Lens 4 is L1, lens 6 is L2, and imaging lens 9 is L3. Lenses L1 and L2 have the same focal length f, and the distance between the two lenses is maintained at 2f. In this case, the distance between the surface of the object under test 3 and the intermediate real image plane is 4f. The aperture 5 is placed at the common focal point of lenses L1 and L2, and L1, L2, and aperture 5 are kept as a whole, allowing them to slide freely within the 4f distance between the surface of the object under test 3 and the intermediate real image plane. A Wollaston prism 7 is placed near the intermediate real image plane, with a beam-splitting angle of α. Imaging lens L3 is placed behind the Wollaston prism 7 to image the intermediate real image plane RI onto the photosensitive surface of camera 10. A polarizer 8 is placed in front of camera 10, causing the two orthogonally polarized beams emitted from the Wollaston prism 7 to interfere on the surface of camera 10.

[0051] Adjust aperture 5 to its maximum opening and adjust the axial position of Wollaston prism 7 to obtain a suitable shearing amount in the plane of camera 10. Fix Wollaston prism 7, adjust aperture 5 appropriately, and move L1, L2, and aperture 5 as a whole, while observing the spatial frequency spectrum of the shearing interferogram acquired by camera 10, ensuring that the left and right side lobes in the spatial spectrum are completely separated from the central fundamental frequency. The imaging system adjustment is now complete; proceed with the measurement according to the steps.

[0052] like Figure 3 As shown, the shearing interferometry imaging system proposed in this invention has the following features: 1. Independent control of the spatial carrier frequency; 2. Adjustable near-zero shear; 3. Embedded 4f imaging system; 4. The 4f imaging system includes a movable aperture 5; 5. An intermediate real image plane RI exists in the imaging system; 6. All optical elements, except for the illumination path, are coaxially placed. The object beam is collected by a 4f imaging system (L1 and L2) and imaged onto the intermediate real image plane (RI). A Wollaston prism 7 is placed near the intermediate real image plane RI. After passing through the Wollaston prism 7, the beam is split into two object beams with symmetrical tilt angles, which are then imaged onto the photosensitive surface IP of the camera 10 by the imaging lens L3, producing adjustable near-zero shear. A 4f imaging system embeds an aperture 5 with a variable position and variable aperture size to provide independent control of the spatial carrier frequency. The control of the shear and the spatial carrier frequency is distributed to different parts of the imaging system. Collinear systems offer a convenient installation method and, due to their excellent noise immunity, have the potential to operate in industrial environments. The shearing interferometric imaging system proposed in this invention is particularly suitable for measuring complex surface distributions or those with complex deformations. The adjustable near-zero shear amount provides sufficiently small shear forces to ensure that complex surface shapes or deformations are solvable. Simultaneously, when configured with the desired near-zero shear amount, individual control of the spatial carrier further guarantees a well-distributed spatial spectrum.

[0053] The surface of the object under test 3 is illuminated by an extended coherent light source 1. The light reflected back from the object is collected by a set of lenses L1 and L2 to form an intermediate real image at plane RI, where the aperture controls the spatial carrier frequency. A Wollaston prism 7 (WP) is placed in an adjacent region of the intermediate real image plane RI to produce shearing, and two identical but laterally shifted twin images are formed on the photosensitive surface of camera 10 through imaging lens L3. A polarizer P is placed in front of camera 10 to cause interference from the orthogonal polarizations from Wollaston prism 7.

[0054] The generation of near-zero shear depends on the formation of the intermediate real image plane RI. Imaging the surface of the test object 3 onto the intermediate real image plane using the 4f imaging system can be considered as mapping the surface of the test object 3 onto the intermediate real image plane, and the formation of the intermediate real image plane provides sufficient operating space for the shearing device (i.e., the Wollaston prism 7). Assuming the shear is along the x-direction, as... Figure 3 The shearing quantity δ of the imaging system shown x It can be represented as

[0055]

[0056] Where α is the beam splitting angle provided by Wollaston prism 7, and f img Let q be the focal length of the imaging lens L3. r Let l be the image distance of the imaging lens L3. w The distance between the Wollaston prism 7 and the intermediate real image plane RI is given. As the Wollaston prism 7 slides towards the intermediate real image plane RI, the shearing decreases. When the Wollaston prism 7 is sufficiently close to the intermediate real image plane, near-zero shearing is achieved. In the extreme case, when the Wollaston prism 7 is exactly positioned on the intermediate real image plane RI, precise zero shearing is obtained. At this point, the two object beams overlap again on the photosensitive surface of the camera 10, making it possible to achieve white light interference using this imaging system.

[0057] To achieve independent carrier frequency control, it is assumed that the two lenses in the 4f imaging system have the same focal length f. The axial distance between the two lenses L1 and L2 is set to a constant value of 2f, and the aperture 5 is placed between them, at a distance l from L2. a The distance between the object and image is 4f. To keep the position of the intermediate real image plane RI fixed, the object-image distance of the 4f lens group is set to 4f. In this configuration, the lens group can slide within a distance of 4f while the object imaging relationship remains unchanged. The spatial carrier is characterized by its center frequency, which determines the position of the spatial carrier in the spatial spectrum.

[0058] In the imaging system proposed in this invention, the center frequency of the carrier frequency can be expressed as:

[0059]

[0060] Where λ is the laser wavelength used, p r and q r Let l be the object distance and image distance of the imaging lens L3. a The distance between aperture 5 and L2, l w q is the distance between Wollaston prism 7 and the intermediate real image plane. o This is the image distance (the distance between L2 and the intermediate real image plane) for the 4f imaging system. From the aforementioned shearing amount δ... x As can be seen from the formula, the shearing amount of the imaging system is determined by l w Control. Therefore, to achieve independent carrier frequency control, other imaging system parameters can be selected from the formula for the center frequency of the carrier frequency for control. Generally, this can be achieved by controlling the aperture position l. a Image distance q of 4f imaging system o Control the spatial carrier frequency. Note that when aperture 5 deviates from the midpoint between L1 and L2 (l... a When f) is not equal to f, aperture 5 itself becomes the field stop of the imaging system, causing aperture 5 to obstruct the field of view. Therefore, when the near-zero shear configuration is completed, it means that l w It has been fixed, and the distance q between lens groups L1 and L2 and the intermediate real image plane can be changed. o To control the space carrier frequency.

[0061] The present invention discloses a common-path shearing interferometric imaging method with independently adjustable shearing and carrier frequency, comprising the following steps:

[0062] Step 1: Adjust the imaging system and control the distance l between the Wollaston prism 7 and the intermediate real image plane. w To obtain the desired shearing amount; adjust the image distance q of the 4f imaging system. o In order to obtain the desired spatial spectrum distribution.

[0063] Step two: The coherent light source 1 is a laser. The emitted laser beam is expanded by the beam expander 2 and illuminates the surface of the object under test 3 at a certain angle. The light reflected from the surface of the object under test 3 is collected by the 4f imaging system and imaged onto the intermediate real image plane RI. Then, it is split by the Wollaston prism 7 to produce two misaligned object beams. These beams are then imaged onto the intermediate real image plane by the imaging lens L3. The resulting image is located on the photosensitive surface of the camera 10. The wavefronts of the two sheared object beams are...

[0064] u1(x,y)=|u1(x,y)|exp{i[φ(x,y)]}

[0065] u2(x,y)=|u1(x+δ x ,y)|exp{i[φ(x+δ x ,y)+2πf0x]}

[0066] Where (x,y) describes the coordinates of the photosensitive surface of camera 10, φ is the phase from the surface of the object under test 3, and δ x f0 is the applied shearing amount, and f0 is the introduced spatial carrier frequency.

[0067] Step 3: Camera 10 acquires the shearing interferogram and performs a Fourier transform.

[0068] Camera 10 acquires shear interference patterns, the intensity of which is denoted as

[0069]

[0070] The asterisk (*) indicates the complex conjugate operation.

[0071] Perform a Fourier transform on the shearing interferogram acquired by camera 10, denoted as

[0072]

[0073] in The symbol represents the Fourier transform operation, DC represents the low-frequency spectrum of the background light intensity, and the uppercase letter U represents the Fourier transform of each complex amplitude in the formula of step two.

[0074] Step four: By introducing spatial carrier frequencies, the three components in the spatial spectrum diagram shown by the Fourier transform formula in step three are discretely located at different positions in the spatial spectrum. Selecting from the spectrum... Components; perform inverse Fourier transform on the selected components to obtain the complex amplitude. Recorded as

[0075]

[0076] in This represents the inverse Fourier transform operation.

[0077] Step 5: Calculate the phase angle of the complex amplitude, remove the carrier frequency from the obtained phase angle, obtain the phase distribution, and obtain the surface undulation height gradient of the measured surface.

[0078] The phase angle of the obtained complex amplitude is calculated and denoted as .

[0079]

[0080] Where Im represents the imaginary part operation and Re represents the real part operation.

[0081] Remove the carrier frequency from the obtained phase angle to obtain the phase distribution φ(x,y). Calculate the surface undulation height gradient of the measured surface using the following formula, denoted as:

[0082]

[0083] Where θ is the angle between the incident light and the normal to the surface of the object under test 3.

[0084] Step six: For surface displacement gradient measurement, steps one through five are performed before and after deformation to obtain the surface height gradients before and after the deformation. The difference between the two gradients is then used to obtain the first derivative information of the out-of-surface displacement.

[0085] Therefore, this invention employs a common-path shearing interferometric imaging system and method with independently adjustable shearing and carrier frequencies. The control of the shearing amount and spatial carrier frequency in the imaging system is distributed to different parts of the system. The adjustable near-zero shearing amount provides a sufficiently small shearing force to ensure that complex surface shapes or deformations can be resolved. When the required near-zero shearing amount is configured, the individual control of the spatial carrier further guarantees a well-distributed spatial spectrum.

[0086] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method of shearing and carrier frequency independently adjustable co-path shearing interferometric imaging, characterized in that: The imaging system of the shearing and carrier frequency independently adjustable common-path shearing interferometry method comprises a coherent light source, a light beam of the coherent light source is shot to a surface of an object to be measured through an expander, and a lens one, an aperture, a lens two, a Wollaston prism, a polarizer, an imaging lens and a camera are arranged in sequence on the same axis as the object to be measured. The shearing and carrier frequency independently adjustable common-path shearing interferometry method comprises the following steps: Step one, adjusting the imaging system to obtain a desired shearing amount and a desired spatial frequency spectrum distribution; Step two, the surface of the object to be measured is irradiated by the coherent light source, the light returned by the surface of the object to be measured is collected by the imaging system, and imaging is performed on the camera; Step three, the shearing interferogram is collected by the camera and Fourier transform is performed; Step four, introducing a spatial carrier frequency, selecting a component in the spatial frequency spectrum after Fourier transform and performing inverse Fourier transform on the component to obtain a complex amplitude; Step five, the phase angle of the complex amplitude is obtained, the carrier frequency is removed from the obtained phase angle, the phase distribution is obtained, and the surface height gradient of the measured surface is obtained; Step six, for surface displacement gradient measurement, steps one to five are performed before and after deformation, respectively, to obtain the surface height gradients before and after deformation and to make a difference between the two. Amount of shear of an imaging system is represented as: wherein, is the splitting angle provided by the Wollaston prism, is the focal length of the imaging lens, is the image distance of the imaging lens, is the distance of the Wollaston prism 7 from the intermediate real image plane RI; as the Wollaston prism is slid towards the intermediate real image plane RI, the shear decreases, and when the Wollaston prism is close to the intermediate real image plane, a near zero shear is produced; in the extreme case, when the Wollaston prism is located at the intermediate real image plane RI, a zero shear will be obtained, at which point the two beams of object light recombine on the camera's photosurface; In order to obtain the carrier frequency independent control, it is assumed that the lens one and the lens two in the imaging system have the same focal length f, the axial distance between the lens one and the lens two is set as a constant value of 2f, and the aperture is placed between the lens one and the lens two, and the distance from the lens two In order to keep the position of the intermediate real image plane RI fixed, the object-image distance of the lens group composed of the lens one and the lens two is set as 4f, in this configuration, the lens group slides within the distance of 4f, and the object imaging relationship remains unchanged, and the spatial carrier is characterized by the center frequency, and the center frequency determines the position of the spatial carrier in the spatial spectrum; In the imaging system, the center frequency of the spatial carrier frequency is represented as: in, The laser wavelength used. and The object distance and image distance of the imaging lens, This is the distance between the aperture and lens 2. This is the distance between the Wollaston prism and the intermediate real image plane. The distance between lens two and the intermediate real image plane; determined by the aforementioned shearing amount. As the formula shows, the shearing amount of the imaging system is determined by... Control, by controlling the aperture position Image distance in imaging systems Controlling the spatial carrier frequency; when the aperture deviates from the midpoint between lens one and lens two. At this time, the aperture becomes the field stop of the imaging system, and the aperture blocks the field of view. When the near-zero shear configuration is completed, Fixed, by changing the distance between lens one and lens two and the intermediate real image plane. To control the space carrier frequency.

2. The method of claim 1, wherein the method is a common-path shear interferometric imaging method with independent adjustable shear and carrier frequencies. In step one, the imaging system is adjusted, the distance between the Wollaston prism and the intermediate real image plane is controlled, and a desired shearing amount is obtained; and the image distance of the imaging system is adjusted to obtain a desired spatial frequency spectrum distribution.

3. The co-routed shear interferometric imaging method with independent adjustable shear and carrier frequencies of claim 2, wherein: In step two, the light emitted by the coherent light source is expanded by the expander and illuminates the surface of the object to be measured at a certain angle, the light returned by the surface of the object to be measured is collected by the imaging system, and imaging is performed on the intermediate real image plane, then the Wollaston prism is used to split the light to produce two beams of object light with a displacement, the intermediate real image plane is imaged by the imaging lens, and the image formed is located on the light-sensitive surface of the camera, the wave fronts of the two beams of sheared object light are wherein, Camera image plane coordinates are described, is the phase from the surface of the object under test, is the amount of shear applied, is the spatial carrier frequency introduced.

4. The co-routed shear interferometric imaging method of claim 3, wherein: In step three, the camera collects the shearing interferogram, and the intensity is denoted as Wherein, the asterisk represents the complex conjugate operation; The Fourier transform is performed on the shearing interferogram collected by the camera, and is denoted as where represents the Fourier transform operation, DC represents the low frequency spectrum of the background light intensity, and the capital letters represent the Fourier transforms of the complex amplitudes in the equations of step two.

5. The method of claim 4, wherein the shear and carrier frequency are independently adjustable. In step four, by introducing the spatial carrier frequency, the three components in the spatial spectrum shown in the formula in step three are separated in different positions in the spatial spectrum. In the spectrum, the three components are selected components; The inverse Fourier transform is applied to the selected components to obtain complex amplitudes denoted by wherein represents an inverse Fourier transform operation.

6. The method of claim 5, wherein the method is a common-path shear interferometric imaging method with independently adjustable shear and carrier frequencies. In step five, the phase angle of the obtained complex amplitude is obtained, and is denoted as wherein is a take imaginary operation, is a take real operation; The phase angle is removed from the obtained carrier frequency to obtain a phase distribution The surface relief height gradient of the measured surface is calculated as wherein is the angle between the incident light and the surface normal of the object under test.

Images