Apparatus for measuring the clamping deformation of thin-walled free-form optical elements and method of using the same

Abstract

The application discloses a kind of thin-walled free-form optical element clamping deformation measuring devices and its use method, including work stand, sample stage is installed in the inside of the work stand, image generating mechanism, laser generating mechanism, image acquisition mechanism and lifting mechanism;The image generating mechanism, the laser generating mechanism and the image acquisition mechanism are all located above the sample stage, and the sample stage is installed with the clamping structure for clamping thin-walled free-form optical element;The clamping structure includes first clamping part, second clamping part, pivot and the driving part of driving pivot rotation, first clamping part and second clamping part are respectively hinged with pivot, and reset elastic member is arranged between second clamping part and pivot.The measuring device of the application can be suitable for testing and analyzing the influence of the clamping mode and clamping load of concave curved surface thin-walled optical element / convex curved surface thin-walled optical element on optical element surface type and position accuracy.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of product surface profile detection, in particular to a thin-walled free-form optical element clamping deformation measurement and analysis device and a use method thereof. BACKGROUND

[0002] With the continuous research and development of modern optical systems, various optical elements are needed in various fields in today's society, from cameras on mobile phones, glasses, to various microscopes used in various microscopes. Further, with the increasing demand of modern optical systems for the volume and weight of optical systems, free-form optical elements are increasingly widely used. From the free-form prism on the increasingly concerned augmented reality device, to the free-form mirror used in the head-up display of the car, to the 6.5-meter main mirror composed of several free-form mirrors in the new generation James Webb space telescope.

[0003] Free-form optical element manufacturing technology has made great progress, however, the three-dimensional profile measurement technology of free-form optical elements and related molds is still a technical bottleneck. In particular, free-form optical elements are often thin-walled elements, and many thin-walled free-form elements will inevitably deform in the clamping position and surface profile during assembly and clamping, resulting in deviations in the final imaging quality. Therefore, it is necessary to carry out online measurement of the clamping deformation of optical free-form elements, and then optimize the design of the clamping method and load of the optical free-form element.

[0004] When the free-form optical element is clamped and deformed online, the following difficulties exist:

[0005] 1. Different extrusions will cause a certain degree of deformation to the free-form surface, and the deformation of the surface may only be tens of microns. This small deformation is very difficult to measure online, but it will have a non-negligible impact on the subsequent system imaging;

[0006] 2. In the clamping process, the clamping force can cause not only the deformation of the element, but also the small position change of the element. The pose change and surface deformation of the optical element are mixed together, and the decoupling of the two information is difficult to achieve;

[0007] 3. The existing measuring instruments on the market, such as three coordinates, have slow measurement speed and few sampling positions, and cannot accurately output the deformation data of the free-form surface during clamping, making it difficult to measure online. SUMMARY

[0008] The technical problem solved by the present application is to provide a measuring device for clamping deformation of a thin-walled free-form optical element and a use method thereof.

[0009] To solve the above technical problem, the present application adopts a technical solution of a measuring device for clamping deformation of a thin-walled free-form optical element, comprising a workbench, wherein a sample stage, an image generating mechanism, a laser generating mechanism, an image collecting mechanism and a lifting mechanism for driving the sample stage to move up and down are installed inside the workbench; the image generating mechanism, the laser generating mechanism and the image collecting mechanism are located above the sample stage, and a clamping structure for clamping a thin-walled free-form optical element is installed on the sample stage.

[0010] The clamping structure comprises a first clamping part, a second clamping part, a rotating shaft and a driving member for driving the rotating shaft to rotate, the first clamping part and the second clamping part are hingedly connected with the rotating shaft, and a reset elastic member is arranged between the second clamping part and the rotating shaft, and the reset elastic member is sleeved on the rotating shaft.

[0011] A first clamping groove is arranged on one side of the first clamping part relative to the second clamping part, a second clamping groove is arranged on one side of the second clamping part relative to the first clamping part, the opening direction of the first clamping groove is parallel to the width direction of the first clamping part, and the opening direction of the second clamping groove is parallel to the width direction of the second clamping part.

[0012] The image generating mechanism, the laser generating mechanism, the image collecting mechanism, the lifting mechanism and the driving member are electrically connected with a mobile terminal.

[0013] Further, the lifting mechanism comprises a gas cylinder and a guide rod, the gas cylinder is fixedly connected with the workbench, an output shaft of the gas cylinder is connected with one end of the guide rod, and the other end of the guide rod is connected with the sample stage.

[0014] Further, the first clamping part and the second clamping part are both arc-shaped clamping parts.

[0015] Further, the reset elastic member is a reset spring.

[0016] Further, the driving member is a torque motor.

[0017] Further, the image generating mechanism is a display screen generating a bar image, and the image collecting mechanism is a camera.

[0018] Further, the laser generating mechanism is a semiconductor-pumped microchip solid-state laser.

[0019] According to the method for using the thin-wall free-form optical element clamping deformation measuring device, the method comprises the following steps:

[0020] S1, placing a to-be-measured free-form optical element in a clamping structure, the to-be-measured free-form optical element being in a zero clamping force state;

[0021] S2, generating a periodic sinusoidal fringe pattern on the surface of the to-be-measured free-form optical element through an image generating mechanism, capturing a fringe image reflected by the to-be-measured free-form optical element through an image collecting mechanism, and transmitting the fringe image to a mobile terminal installed with an image processing system, demodulating the surface profile information of the to-be-measured free-form optical element from the collected fringe image, and saving initial surface profile information;

[0022] S3, projecting laser onto the surface of the to-be-measured free-form optical element through a laser generating mechanism, obtaining initial position information of the corresponding point on the surface of the to-be-measured free-form optical element in the direction, combining the position information of the measured points in other positions, transmitting the position information to the mobile terminal, and saving the initial position information of the to-be-measured free-form optical element;

[0023] S4, adjusting the driving current of the torque motor to adjust the torque between the first clamping part and the second clamping part, and giving the to-be-measured free-form optical element a certain clamping force to make the to-be-measured free-form optical element deform;

[0024] S5, repeating S2 and S3 to measure the deformed surface profile information and the deformed position information of the to-be-measured free-form optical element under the action of a certain clamping force;

[0025] S6, calculating the displacement and the surface deformation degree of the to-be-measured free-form optical element in the clamping process in the mobile terminal according to the initial surface profile information, the initial position information, the deformed surface profile information and the deformed position information.

[0026] Further, the calculation method of the surface change amount of the to-be-measured free-form optical element in the clamping process is specifically: selecting a plurality of sampling points on the surface of the to-be-measured free-form optical element, and the calculation formula of the surface normal of each sampling point is:

[0027]

[0028] Wherein, n is the surface normal of a sampling point.

[0029] i is an incident light ray;

[0030] r is a reflected light ray;

[0031] [(r-i) / (||r-i||)]x is a component in the x direction, [(r-i) / (||r-i||)] y is a component in the y direction,

[0032] [(r-i) / (||r-i||)]z is a component in the z direction;

[0033] At the same time, the normal vector of any point on the to-be-measured free-form optical element is calculated according to the following formula:

[0034]

[0035] Definition

[0036] According to the formulas 1-1 and 1-2, the curvature information of any point on the to-be-measured free-form optical element is obtained:

[0037]

[0038] Based on the curvature information of each point on the to-be-measured free-form optical element, the initial surface profile information and the deformed surface profile information of the to-be-measured free-form optical element can be reconstructed by an integral method. By comparing the deformed surface profile information with the initial surface profile information, the surface profile change amount of the to-be-measured free-form optical element during clamping can be obtained.

[0039] Further, the calculation method of the displacement change amount of the to-be-measured free-form optical element during clamping is as follows: the output light of the laser generator is first divided into two parts by a beam splitter: a projection light and a reflection light. The transmission light is irradiated onto the to-be-measured free-form optical element after passing through an acousto-optic frequency shifter, and generates a laser feedback light, which causes the fluctuation of the laser output signal. The reflection light is used for photoelectric detection and demodulation. The laser output signal (laser feedback fringe) detected by the photoelectric detector is as follows:

[0040]

[0041] Where, ΔI(2Ω) is the fluctuation value of the laser output power, I s is the steady-state output power of the laser, Ω is the frequency shift of the acousto-optic frequency shifter, κ is the reflectivity of the to-be-measured free-form optical element, G is the laser feedback gain of light modulation, t is time, and Δφ = φ s- φ is the change amount of the laser external cavity phase; the phase change amount Δφ = 2nΔL / λ, n is the refractive index, and λ is the laser wavelength. Therefore, the heterodyne synchronous demodulation is performed on the above formula (2-3), so that the change amount Δφ of the external cavity phase is obtained, and the external cavity length ΔL (i.e. the distance change between the laser generating mechanism and the free-form optical element to be measured) can be demodulated and obtained.

[0042] The beneficial effects of the present application are as follows:

[0043] 1、The measuring device of the present application comprises a clamping mechanism, which comprises a first clamping part, a second clamping part, a rotating shaft and a driving part for driving the rotating shaft to rotate, wherein the driving part is a torque motor. When the torque motor is reversely powered, the rotating shaft will rotate in a certain direction, causing the first clamping part to rotate away from the second clamping part, so that the clamping mechanism is in an open state, facilitating the placement of the concave curved optical element. When the torque motor is forwardly powered, the rotating shaft will rotate back under the action of a return spring, causing the first clamping part to rotate towards the second clamping part, so that the clamping mechanism is in a closed state. In addition, a first clamping groove is arranged on one side of the first clamping part relative to the second clamping part, and a second clamping groove is arranged on one side of the second clamping part relative to the first clamping part. When the clamping mechanism is in an open state, the convex curved optical element can be clamped through the first clamping groove and the second clamping groove. By adjusting the current of the torque motor, the torque between the first clamping part and the second clamping part can be adjusted, and a certain clamping force can be applied to the concave curved optical element / convex curved optical element to cause the deformation of the concave curved thin-walled optical element / convex curved thin-walled optical element.

[0044] 2、The present application can quickly measure and analyze various changes in the surface profile and position attitude of the free-form curved element during clamping through the respective functions of the image generating mechanism and the laser generating mechanism, and finally obtain the deformation degree of the free-form curved element during clamping. BRIEF DESCRIPTION OF DRAWINGS

[0045] Figure 1 is a schematic diagram of the overall structure of the present application;

[0046] Figure 2 is a schematic diagram of the structure of the clamping mechanism of the present application;

[0047] Figure 3 is an exploded schematic diagram of the clamping mechanism of the present application;

[0048] Figure 4 is a schematic diagram of the projection and reflection principle of the image generating mechanism, the image collecting mechanism and the free-form optical element to be measured of the present application;

[0049] The markings of the various parts in the drawings are as follows:

[0050] The working frame 1, the sample table 2, the image generating mechanism 3, the laser generating mechanism 4, the image collecting mechanism 5, the lifting mechanism 6, the air cylinder 61, the guide rod 62, the clamping structure 7, the first clamping part 71, the second clamping part 72, the rotating shaft 73, the driving part 74, the first clamping groove 75, the second clamping groove 76 and the free curved surface optical element 8 to be measured. DETAILED DESCRIPTION

[0051] The advantages and features of the present application can be more easily understood by those skilled in the art from the preferred embodiments of the present application described in detail below in conjunction with the accompanying drawings, so that the scope of protection of the present application can be more clearly defined.

[0052] Embodiment: A kind of thin-walled free curved surface optical element clamping deformation measuring device, as shown in Figures 1-3 The working frame 1, the sample table 2, the image generating mechanism 3, the laser generating mechanism 4, the image collecting mechanism 5 and the lifting mechanism 6 for driving the sample table to move up and down are installed inside the working frame; the image generating mechanism, the laser generating mechanism and the image collecting mechanism are all located above the sample table, and the clamping structure 7 for clamping thin-walled free curved surface optical element is installed on the sample table.

[0053] The clamping structure includes the first clamping part 71, the second clamping part 72, the rotating shaft 73 and the driving part 74 for driving the rotating shaft to rotate; the first clamping part and the second clamping part are respectively hinged with the rotating shaft, and a reset elastic member is arranged between the second clamping part and the rotating shaft, and the reset elastic member is sleeved on the rotating shaft.

[0054] A first clamping groove 75 is arranged on one side of the first clamping part relative to the second clamping part, and a second clamping groove 76 is arranged on one side of the second clamping part relative to the first clamping part; the opening direction of the first clamping groove is parallel to the width direction of the first clamping part, and the opening direction of the second clamping groove is parallel to the width direction of the second clamping part.

[0055] The image generating mechanism, the laser generating mechanism, the image collecting mechanism, the lifting mechanism and the driving part are electrically connected with the mobile terminal.

[0056] The lifting mechanism includes the air cylinder 61 and the guide rod 62; the air cylinder is fixedly connected with the working frame, the output shaft of the air cylinder is connected with one end of the guide rod, and the other end of the guide rod is connected with the sample table. The distance between the sample table and the image generating mechanism can be adjusted according to the size of the free curved surface optical element to be measured, so that the image collecting mechanism can clearly collect the fringe image on the surface of the free curved surface optical element to be measured.

[0057] The first clamping part and the second clamping part are both arc-shaped clamping parts.

[0058] The reset elastic member is a reset spring. When the force moment motor is reversely powered, the rotation of the rotating shaft will cause the first clamping part to rotate away from the second clamping part, so that the clamping structure is in an open state, facilitating the placement of the concave curved thin-wall optical element; when the force moment motor is powered in the positive direction, the rotating shaft will rotate back under the action of the reset spring, causing the first clamping part to rotate towards the second clamping part, so that the clamping structure is in a closed state; in addition, since the first clamping part is provided with a first clamping groove on one side relative to the second clamping part, and the second clamping part is provided with a second clamping groove on one side relative to the first clamping part, when the clamping structure is in an open state, the convex curved thin-wall optical element can be clamped through the first clamping groove and the second clamping groove. By adjusting the current of the force moment motor, the torque between the first clamping part and the second clamping part is adjusted, and a certain clamping force is applied to the concave curved thin-wall optical element / convex curved thin-wall optical element to cause the concave curved thin-wall optical element / convex curved thin-wall optical element to deform.

[0059] The driving member is a force moment motor.

[0060] The image generating mechanism is a display screen generating a bar-shaped image, and the image collecting mechanism is a camera.

[0061] The laser generating mechanism is a semiconductor-pumped microchip solid-state laser. The laser generating mechanism is provided with five, which are uniformly distributed above the to-be-measured free-form optical element.

[0062] According to the use method of the thin-wall free-form optical element clamping and deforming measuring device, the following steps are included:

[0063] S1, placing the to-be-measured free-form optical element in the clamping structure, and the to-be-measured free-form optical element is in a zero clamping force state;

[0064] S2, generating a periodic sinusoidal fringe pattern on the surface of the to-be-measured free-form optical element 8 through the image generating mechanism, capturing the fringe image reflected by the to-be-measured free-form optical element through the image collecting mechanism, and transmitting the fringe image to the mobile terminal installed with the image processing system, demodulating the surface profile information of the to-be-measured free-form optical element from the collected fringe image, and saving the initial surface profile information;

[0065] S3, projecting laser to the surface of the to-be-measured free-form optical element through the laser generating mechanism, obtaining the initial position information of the corresponding point on the surface of the to-be-measured free-form optical element in this direction, combining the position information of other measured points, sending the position information to the mobile terminal, and saving the initial position information of the to-be-measured free-form optical element;

[0066] S4, adjusting the torque between the first clamping part and the second clamping part by adjusting the torque motor driving current, so as to give the to-be-tested free-form optical element a certain clamping force to make the to-be-tested free-form optical element deform;

[0067] S5, repeating S2 and S3 to measure the deformed surface profile information and the deformed position information of the to-be-tested free-form optical element under the action of a certain clamping force;

[0068] S6, calculating the displacement and the surface deformation degree of the to-be-tested free-form optical element in the clamping process in the mobile terminal according to the initial surface profile information, the initial position information, the deformed surface profile information and the deformed position information.

[0069] As Figure 4 shown, according to the use method of the thin-walled free-form optical element clamping deformation measuring device, the calculation method of the surface change amount of the to-be-tested free-form optical element in the clamping process is specifically: selecting a plurality of sampling points on the surface of the to-be-tested free-form optical element, and the calculation formula of the surface normal of each sampling point is:

[0070]

[0071] Wherein: n is the surface normal of a sampling point;

[0072] i is the incident light;

[0073] r is the reflected light;

[0074] [(r-i) / (||r-i||)]x is the component in the x direction, [(r-i) / (||r-i||)] y is the component in the y direction,

[0075] [(r-i) / (||r-i||)]z is the component in the z direction;

[0076] At the same time, the calculation formula of the normal vector of any point on the to-be-tested free-form optical element is:

[0077]

[0078] Definition

[0079] According to the formula 1-1 and 1-2, the curvature information of any point on the to-be-tested free-form optical element is obtained:

[0080]

[0081] Based on the curvature information of each point on the to-be-measured free-form optical element, the initial surface profile information and the deformed surface profile information of the to-be-measured free-form optical element can be reconstructed by the integral method, and the surface profile change amount of the to-be-measured free-form optical element in the clamping process can be obtained by comparing the deformed surface profile information and the initial surface profile information.

[0082] The calculation method of the displacement change amount of the to-be-measured free-form optical element in the clamping process is specifically as follows: the output light of the laser generator is first divided into two parts by a beam splitter: projection light and reflection light. The transmission light irradiates the to-be-measured free-form optical element after passing through an acousto-optic frequency shifter, and generates laser feedback light, which causes the fluctuation of the laser output signal. The reflection light is used for photoelectric detection and demodulation. The laser output signal (laser feedback fringe) detected by the photoelectric detector is as follows:

[0083]

[0084] Wherein, △I(2Ω) is the fluctuation value of the laser output power, I s is the steady-state output power of the laser, Ω is the frequency shift amount of the acousto-optic frequency shifter, κ is the reflectivity of the to-be-measured free-form optical element, G is the laser feedback gain of light modulation, t is time, and △φ = φ s -φ is the change amount of the laser external cavity phase. The phase change amount △φ = 2n△L / λ, n is the refractive index, and λ is the laser wavelength. Therefore, the change amount △φ of the external cavity phase can be obtained by the above-mentioned 2-3 formula heterodyne synchronous demodulation, and the external cavity length △L (i.e. the distance change between the laser generator and the to-be-measured free-form optical element) can be obtained by demodulation.

[0085] The phase demodulation accuracy of the heterodyne synchronous demodulation can reach 0.01°, and the corresponding resolution is 0.03 nm, which is sufficient to meet the nanometer precision measurement requirement.

[0086] In addition, for formula (2-3), the expression form is very similar to the traditional heterodyne interference, but there is an additional coefficient G(2Ω) related to the frequency shift. When appropriate parameters are selected, G(2Ω) can be as high as 1 million. This means that when the reflectivity κ of the to-be-measured free-form optical element is 10 -6 , due to the amplification effect of G(2Ω), the modulation depth of the laser feedback fringe can reach 100%, which is equivalent to the interference fringe modulation depth under the condition that the reflectivity of the measured object in the traditional interference is 100%. Therefore, due to this feature, the laser feedback interference principle can be used for non-contact and non-cooperative nanometer measurement of extremely low reflectivity measured objects, realizing the "pointing and measuring" of the laser beam.

[0087] The above merely illustrates the embodiments of the present application, and is not intended to limit the patent scope of the present application, and any equivalent structural transformation or direct or indirect application in other related technical fields based on the content of the present application specification and drawings are also included in the patent protection scope of the present application.

Claims

1. A measuring device for clamping deformation of a thin-walled free-form optical element, characterized in that: The workbench (1) is internally provided with a sample table (2), an image generating mechanism (3), a laser generating mechanism (4), an image collecting mechanism (5) and a lifting mechanism (6) for driving the sample table to move up and down; the image generating mechanism, the laser generating mechanism and the image collecting mechanism are all located above the sample table, and the sample table is provided with a clamping structure (7) for clamping a thin-walled free-form optical element; The clamping structure comprises a first clamping part (71), a second clamping part (72), a rotating shaft (73) and a driving member (74) for driving the rotating shaft to rotate, the first clamping part and the second clamping part are respectively hinged to the rotating shaft, and a reset elastic member is arranged between the second clamping part and the rotating shaft and is sleeved on the rotating shaft; One side of the first clamping part relative to the second clamping part is provided with a first clamping groove (75), and one side of the second clamping part relative to the first clamping part is provided with a second clamping groove (76), the opening direction of the first clamping groove is parallel to the width direction of the first clamping part, and the opening direction of the second clamping groove is parallel to the width direction of the second clamping part; The image generating mechanism, the laser generating mechanism, the image collecting mechanism, the lifting mechanism and the driving member are all electrically connected with a mobile terminal; The first clamping part and the second clamping part are both arc-shaped clamping parts; The reset elastic member is a reset spring; The driving member is a torque motor; When the torque motor is reversely powered, the rotating shaft will rotate in a certain direction, causing the first clamping part to rotate away from the second clamping part, so that the clamping structure is in an open state, facilitating the placement of a concave curved thin-walled optical element; when the torque motor is powered in a normal direction, the rotating shaft will rotate back under the action of the reset spring, causing the first clamping part to rotate towards the second clamping part, so that the clamping structure is in a closed state; when the clamping structure is in an open state, the convex curved thin-walled optical element can be clamped through the first clamping groove and the second clamping groove, and the torque between the first clamping part and the second clamping part can be adjusted by adjusting the current of the torque motor, so as to give the concave curved thin-walled optical element / convex curved thin-walled optical element a certain clamping force to deform the concave curved thin-walled optical element / convex curved thin-walled optical element.

2. The apparatus for measuring the deformation of a thin-walled free-form optical element according to claim 1, wherein: The lifting mechanism comprises a gas cylinder (61) and a guide rod (62), the gas cylinder is fixedly connected with the workbench, the output shaft of the gas cylinder is connected with one end of the guide rod, and the other end of the guide rod is connected with the sample table.

3. The apparatus for measuring the deformation of a thin-walled free-form optical element according to claim 1, wherein: The image generating mechanism is a display screen for generating a bar-shaped image, and the image collecting mechanism is a camera.

4. The apparatus for measuring the deformation of a thin-walled free-form optical element according to claim 1, wherein: The laser generating mechanism is a microchip solid-state laser pumped by a semiconductor.

5. The method of claim 1, wherein the thin-walled freeform optical element is a lens. The method comprises the following steps: S1, placing a to-be-tested free-form optical element in the clamping structure, and the to-be-tested free-form optical element is in a zero clamping force state; S2, generating a periodic sinusoidal fringe pattern on the surface of the free-form optical element to be measured by an image generating mechanism, capturing the fringe image reflected by the free-form optical element to be measured by an image capturing mechanism, and transmitting the fringe image to a mobile terminal installed with an image processing system, demodulating the surface profile information of the free-form optical element to be measured from the captured fringe image by the mobile terminal, and saving the initial surface profile information; S3, projecting laser light onto the surface of the free-form optical element to be measured by a laser light generating mechanism, obtaining the initial position information of the corresponding point on the surface of the free-form optical element to be measured in the direction, and sending the position information to the mobile terminal, and saving the initial position information of the free-form optical element to be measured; S4, adjusting the torque between the first clamping part and the second clamping part by adjusting the driving current of the torque motor, and giving the free-form optical element to be measured a certain clamping force to deform the free-form optical element to be measured; S5, repeating S2 and S3 to measure the deformed surface profile information and the deformed position information of the free-form optical element to be measured under the action of a certain clamping force; S6, calculating the displacement and the surface deformation degree of the free-form optical element to be measured in the clamping process in the mobile terminal according to the initial surface profile information, the initial position information, the deformed surface profile information and the deformed position information.

6. The method of claim 5, wherein the thin-walled freeform optical element is a lens. The calculation method of the surface change amount of the free-form optical element to be measured in the clamping process is as follows: a plurality of sampling points are selected on the surface of the free-form optical element to be measured, and the calculation formula of the surface normal of each sampling point is: （1-1） Wherein: n is the surface normal of a sampling point; i is the incident light; r is the reflected light; is a component in the x direction, is a component in the y direction, is a component in the z direction; At the same time, the calculation formula of the normal vector of any point on the free-form optical element to be measured is: （1-2）； Definitions , , ; According to formula 1-1 and 1-2, the curvature information of any point on the free-form optical element to be measured is obtained: ； Based on the curvature information of each point on the free-form optical element to be measured, the initial surface profile information and the deformed surface profile information of the free-form optical element to be measured can be reconstructed by integral method, and the deformed surface profile information and the initial surface profile information are compared to obtain the surface change amount of the free-form optical element to be measured in the clamping process.

7. The method of claim 5, wherein the method further comprises: The calculation method of the displacement change amount of the free-form optical element to be measured in the clamping process is as follows: the output light of the laser generator is first divided into two parts by the beam splitter: the projection light and the reflected light; the transmitted light is irradiated to the free-form optical element to be measured after passing through the acousto-optic frequency shifter, and the laser feedback light is generated; the reflected light passing through the beam splitter is used for photoelectric detection and phase demodulation; the laser output signal detected by the photoelectric detector is: （2-3） Wherein, is the fluctuation value of the laser output power, is the steady-state output power of the laser, is the frequency shift amount of the acousto-optic frequency shifter, is the reflectivity of the free-form optical element to be measured, G is the laser feedback gain of light modulation, and t is time, is the phase change amount of the laser external cavity; the phase change amount =2n L / , wherein n is the refractive index, is the laser wavelength; by heterodyne synchronous demodulation of the above 2-3 formula, the phase change amount of the laser external cavity , from which the external cavity length change amount L, L is the distance change between the laser generating mechanism and the free-form optical element to be measured.

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