Quantitative detection method of ring zone error using knife-edge method based on digital aperture modulation

Abstract

A digital aperture modulation-based knife-edge annular error quantitative detection method first moves the knife-edge instrument along the principal optical axis of the optical component under test while simultaneously capturing a knife-edge shadow detection image. The multiple axial knife-edge shadow detection images produced by the mirror under test are then segmented into sub-annular zones. The axial evolution characteristics of the grayscale corresponding to each annular zone are used to determine the corresponding axial focus position, thereby achieving a quantitative solution for the entire surface shape. This digital aperture addition method improves the problem of traditional physical apertures being limited to fixed positions, resulting in inflexible use and increased system complexity. It provides a new approach to quantitative detection for optical workshop inspections and optimizes the efficiency of optical processing and inspection.

Description

Technical field:

[0001] The invention relates to the fields of optical workshop detection and digital image processing, and in particular to a knife-edge annular zone error quantitative detection method based on digital aperture modulation. Background technology:

[0002] The knife-edge method is a traditional optical inspection method. It uses a point light source to emit spherical light onto the optical component under test. The returned light spot contains the optical component's wavefront surface machining errors. A shadow pattern containing this error information can be observed by cutting the knife-edge across the surface. In optical workshops, the knife-edge method has a good response to rough-machined and pre-machined optical mirrors, allowing qualitative detection of machining errors. Traditional quantitative inspection methods, which involve cutting the knife-edge horizontally at the focal point, do provide good quantitative inspection results, but they still require manual operation, resulting in low inspection efficiency and an inability to quantitatively determine the surface shape of the mirror under test. Existing patents related to the knife-edge method primarily focus on improvements to the knife-edge instrumentation used in the method, such as CN210375623U, CN214163177U, and CN116164664A. While these patents have optimized the use of the knife-edge instrument and facilitated its execution to some extent, they have not fundamentally addressed the knife-edge method's reliance on experience and difficulty in quantitative measurement. Although the traditional method of adding an aperture optimizes the detection of annular errors, it is limited by factors such as the shape of the aperture and image processing. In addition, the traditional physical aperture cannot be used flexibly and can only be slit at a fixed position. The edges of the aperture slit will produce some hard-edge diffraction effects, which is not conducive to the accuracy of the detection results and increases the complexity of the system. The knife-edge method for quantitative detection of annular errors based on digital aperture modulation uses a device system of a previously published patent, patent publication number CN114001676A. The patent proposes a method for automatically aligning the optical axis in a knife-edge method detection system, but it still cannot enable the knife-edge method to effectively perform quantitative detection. For this reason, we propose a knife-edge method for quantitative detection of annular errors based on digital aperture modulation, which can enable the knife-edge method to better implement detection, improve detection efficiency, and provide quantitative reference detection results. Summary of the invention:

[0003] The present invention aims to overcome the above-mentioned shortcomings of the prior art and provide a knife-edge method for quantitative detection of annular zone errors based on digital aperture modulation. This method can significantly improve the efficiency of knife-edge instrument quantitative detection.

[0004] The technical solutions of the present invention are as follows:

[0005] A method for quantitatively detecting annular errors using the knife-edge method based on digital aperture modulation is disclosed. The experimental system for this method includes a knife-edge instrument and its displacement system, a CCD camera and lens, an optical element to be measured, and a computer. The knife-edge instrument and its displacement system consist of a knife-edge instrument and a two-dimensional electric adjustment mechanism. The knife-edge instrument is mounted on the two-dimensional electric adjustment mechanism. The imaging system, consisting of the CCD camera and lens, is located behind the knife-edge instrument's blade. The imaging system and the knife-edge instrument are relatively fixed and perform subsequent two-dimensional movement as a whole. The knife-edge is placed near the center of curvature of the optical element. The output of the CCD camera is connected to the input of the computer, and the output of the computer is connected to the control terminal of the two-dimensional electric adjustment mechanism.

[0006] Its characteristic is that the method comprises the following steps:

[0007] (1) Move the knife-edge gauge along the optical axis of the optical element to be measured, and use CCD to collect the knife-edge shadow detection image, which is recorded as P(z1), P(z2)…P(z m ).

[0008] (2) Let the annular aperture function be f n (x), the conditions are as follows:

[0009]

[0010] Where N is the number of annular zones divided equally into the full aperture, n is the nth exposed annular zone, and R is the radius of the component to be tested. By dividing the full aperture of the knife edge shadow detection image into equal parts and exposing different annular zones from the outside to the inside, the annular aperture f is obtained. n (x).

[0011] (3) Using the annular aperture f1(x), mask each knife-edge shadow detection image and expose the target annulus, obtaining the knife-edge shadow images Pδ1(z1), Pδ1(z2)…Pδ1(zm) after annular filtering. If the image with the smallest grayscale variance in this series of images is Pδ1(zR1), it means that the focal point corresponding to the R1 annulus is at zR1 on the optical axis. Similarly, after filtering with an aperture that exposes different annulus from the outside to the inside, the knife-edge shadow image is processed. For a total of n×m, the focus zRn corresponding to the different annulus Rn on the axis can be obtained.

[0012] (4) The theoretical radius of curvature R of the mirror to be measured is known, and the r value of the position of the annular zone on the mirror to be measured can be converted from the relative position of the annular zone on the shadow diagram and the diameter of the mirror to be measured. Therefore, the distance L from the theoretical center of curvature to the corresponding position of the annular zone on the main optical axis can be solved by the relative position of the annular zone on the mirror surface and the surface shape function of the mirror to be measured.

[0013]

[0014] (5) The true center of curvature of the defective annulus can be obtained by the light-dark conversion position zRn corresponding to the annulus on the shadow map. Since the shadow map is automatically collected by the CCD camera at equal intervals while the displacement stage moves at a constant speed, each shadow map is accompanied by position information zRn. Therefore, the distance L' from the actual center of curvature of the annulus to the mirror to be tested can also be known. Therefore, the true error θ of the annulus to be tested can be calculated.

[0015]

[0016] θ represents the true extent of the defect, or the angle between the normal line at the defect location and the ideal surface normal. Multiplying tanθ by the true width of the ring zone gives the specific height of the ring zone defect. Finally, integrating the height values ​​of all defect locations from the outer ring zone to the inner ring zone yields the surface shape of the mirror being measured.

[0017] Compared with the existing technology, the present invention improves the efficiency of knife-edge optical detection, reduces the high requirements for the experience of the implementer during the manual implementation of the knife-edge detection, reduces the complexity of the detection system, and can achieve highly efficient and accurate knife-edge quantitative optical detection. Description of the drawings:

[0018] Figure 1 This is a schematic diagram of the structure of the digital aperture modulation knife-edge method annular zone error quantitative detection device in the prior art.

[0019] Figure 2 This is a schematic diagram of the principle of adding a mask aperture to a series of shadow images collected along the optical axis and finding the shadow image located at the center of curvature of the target annulus.

[0020] Figure 3 This is a logic block diagram of the method steps of the present invention

[0021] Figure 4 It is the surface shape result of the optical component under test under the commercial Twyman-Green interferometer test.

[0022] Figure 5 The surface shape result of the optical element to be tested under the method of the present invention is Specific implementation method:

[0023] The present invention will be further described below with reference to the embodiments and drawings, but the scope of protection of the present invention should not be limited thereto.

[0024] See Figure 1A method for quantitatively detecting annular band errors using the knife-edge method based on digital aperture modulation is disclosed. The experimental system includes a knife-edge instrument and its displacement system 3, a CCD camera 5 and a lens 4, an optical element 1 to be measured, and a computer 6. The knife-edge instrument and its displacement system 3 consist of a knife-edge instrument and a two-dimensional electric adjustment mechanism. The knife-edge instrument is mounted on the two-dimensional electric adjustment mechanism. The image plane of the imaging system composed of the CCD camera 5 and the lens 4 falls on the knife-edge surface. The imaging system and the knife-edge instrument are relatively fixed and perform subsequent two-dimensional movement as a whole. The knife-edge is placed near the center of curvature of the optical element 1. The output end of the CCD camera 5 is connected to the input end of the computer, and the output end of the computer is connected to the control end of the two-dimensional electric adjustment mechanism. The optical path of this device can be applied to a method for quantitatively detecting annular band errors using the knife-edge method based on digital aperture modulation.

[0025] The point light source 2 used in the present invention is a white light source.

[0026] The optical element 1 has a curvature radius of 482 mm and an aperture of 50 mm.

[0027] The resolution of the CCD camera 5 is 2048 pixels×2048 pixels, and the side length of each pixel is 4 μm.

[0028] The motor of the knife-edge displacement system 3 has 200 step intervals per revolution, and the control card of the computer 6 has 16 subdivisions.

[0029] like Figure 2 As shown, first adjust the knife-edge gauge to the optical axis and cut the knife-edge gauge's blade longitudinally along the optical axis. A series of knife-edge shadow images with varying light and dark will be obtained. Depending on the position of the annular error, the knife-edge shadow image will also have different changes, as shown in the first row of shadow images. The entire aperture of the mirror to be measured is evenly divided into 1, 2, 3 and so on to n areas using an annular aperture. Here, area 1 is exposed first, so the series of shadow images collected along the optical axis after adding the mask will be as follows Figure 2 The changes shown in the second row of shadow diagrams are that the axial position corresponding to the center of curvature of the ring is b; then areas 2 to n are exposed in sequence, showing the changes in the shadow diagram with the addition of the mask, and also showing the positions of the centers of curvature corresponding to this series of rings.

[0030] If a shadow map is observed directly, the brightness variations at the location of the annular band will be affected by the brightness relationships elsewhere in the shadow map. However, if an algorithm is used to manually add a mask, focusing only on the brightness variations at the annular band location in the shadow map, the annular band error at that specific location can be effectively distinguished. Specifically, in a series of shadow maps with a digital aperture mask added, the annular band corresponding to the center of curvature is closest to pure gray, resulting in the smallest overall variance. Before calculating the variance of a shadow map, the shadow map can be denoised for more reliable and accurate results. The formula for calculating the variance of a shadow map is shown below, where a represents the grayscale value of a single pixel, n represents the total number of pixels, and the result, S, represents the variance of the shadow map.

[0031]

[0032] The definition formula of the annular mask aperture is as follows, where f n (x) represents the transmittance function, R is the radius of the mirror to be measured, N is the number of ring zones divided equally into the full aperture, and n is the nth exposed ring zone.

[0033]

[0034] The quantitative detection of the annular zone error by the knife-edge method based on digital aperture modulation requires the following steps:

[0035] 1. Move the knife-edge gauge along the optical axis of the optical element to be measured, and use CCD to collect the knife-edge shadow detection image, which is recorded as P(z1), P(z2)…P(z m ).

[0036] 2. Let the annular aperture function be f n (x), the conditions are as follows:

[0037]

[0038] Where N is the number of annular zones divided equally into the full aperture, n is the nth exposed annular zone, and R is the radius of the component to be tested. By dividing the full aperture of the knife edge shadow detection image into equal parts and exposing different annular zones from the outside to the inside, the annular aperture f is obtained. n (x).

[0039] 3. Using the annular aperture f1(x), mask each knife-edge shadow detection image and expose the target annulus, obtaining the annularly filtered knife-edge shadow images Pδ1(z1), Pδ1(z2), …Pδ1(zm). If the image with the smallest grayscale variance in this series is Pδ1(zR1), then the focal point corresponding to the R1 annulus is at zR1 on the optical axis. Similarly, after filtering with the aperture that exposes different annulus zones from the outside inward, the knife-edge shadow images are processed. For a total of n×m annulus zones, the on-axis focal points zRn corresponding to the different annulus zones Rn can be obtained.

[0040] 4. The theoretical radius of curvature R of the mirror to be measured is known, and the r value of the position of the annular zone on the mirror to be measured can be converted from the relative position of the annular zone on the shadow diagram and the diameter of the mirror to be measured. Therefore, the distance L from the theoretical center of curvature to the corresponding position of the annular zone on the main optical axis can be solved by the relative position of the annular zone on the mirror surface and the surface shape function of the mirror to be measured.

[0041]

[0042] 5. The true center of curvature of the defective annulus can be obtained by the light-dark conversion position zRn corresponding to the annulus on the shadow map. Since the shadow map is automatically captured by the CCD camera at equal intervals while the translation stage moves at a constant speed, each shadow map is accompanied by position information zRn. Therefore, the distance L' from the actual center of curvature of the annulus to the mirror to be tested can also be known. Therefore, the true error θ of the annulus to be tested can be calculated.

[0043]

[0044] θ represents the true extent of the defect, or the angle between the normal line at the defect location and the ideal surface normal. Multiplying tanθ by the true width of the ring zone gives the specific height of the ring zone defect. Finally, integrating the height values ​​of all defect locations from the outer ring zone to the inner ring zone yields the surface shape of the mirror being measured.

Claims

1. A quantitative detection method for annular zone errors using a knife-edge method based on digital aperture modulation, wherein the experimental setup and data acquisition include the following features: a quantitative detection system for annular zone errors using a knife-edge method is used, the system comprising a knife-edge gauge and its displacement system, a CCD camera and a lens, and a computer; the knife-edge gauge and its displacement system are composed of a knife-edge gauge and a two-dimensional electric adjustment mechanism; the knife-edge gauge is mounted on the two-dimensional electric adjustment mechanism; the imaging system composed of the CCD camera and the lens is located at the rear side of the knife-edge gauge blade; the imaging system and the knife-edge gauge are relatively fixed and perform subsequent two-dimensional movement as a whole; the knife-edge is placed near the center of curvature of the optical element; the output end of the CCD camera is connected to the input end of the computer; the output end of the computer is connected to the control end of the two-dimensional electric adjustment mechanism; using this series of equipment, the knife-edge gauge is first adjusted to the principal optical axis of the optical element to be measured, so that the knife-edge gauge and its displacement system can move along the principal optical axis of the optical element to be measured; The data processing process includes the following steps: S1. Move the knife-edge gauge along the main optical axis of the optical element to be measured, and use the CCD camera to collect the knife-edge shadow detection image, which is recorded as P(z1), P(z2)…P(z m ); S2. Let the annular aperture function be f n (x), the conditions are as follows: Where N is the number of annular zones divided equally into the full aperture, n is the nth exposed annular zone, and R is the radius of the optical element to be tested. The annular aperture f is obtained by dividing the full aperture of the knife-edge shadow detection image into equal parts and exposing different annular zones from the outside to the inside. n (x); S3. Using the annular aperture f1(x), mask each knife-edge shadow detection image and expose the target annulus to obtain annular-filtered knife-edge shadow detection images Pδ1(z1), Pδ1(z2)…Pδ1(zm). If the image with the smallest grayscale variance in this series of images is Pδ1(zR1), then the focal point corresponding to the R1 annulus is at position zR1 on the principal optical axis. Similarly, after using the aperture filter to expose different annular zones from the outside to the inside, the knife edge shadow detection image is processed, which is n×m in total. Then, the focus zRn corresponding to the different annular zones Rn on the axis can be obtained; S4. Calculate the distance L from the theoretical center of curvature to the corresponding position of the annulus on the principal optical axis using the following formula: Where R is the theoretical curvature radius of the mirror to be measured, and r is the position of the ring zone on the mirror surface; S5. The true center of curvature of the defective annulus is obtained by the light-dark transition position zRn corresponding to the annulus on the knife-edge shadow detection image. Since the knife-edge shadow detection images are automatically captured by the CCD camera at equal intervals while the translation stage moves at a constant speed, each knife-edge shadow detection image is accompanied by the position information zRn. The distance L' from the actual center of curvature of the annulus to the mirror surface to be tested is obtained; Calculate the true error θ of the ring to be measured, the formula is as follows: θ represents the true extent of the defect, that is, the angle between the normal line of the defect position and the normal line of the ideal surface; Multiplying tanθ by the true width of the annulus is the specific height of the annulus defect; Finally, the height values ​​of all defect positions are integrated from the outer ring to the inner ring to obtain the surface shape of the mirror to be measured.

2. The method for quantitative detection of annular zone errors using a knife-edge method based on digital aperture modulation according to claim 1, wherein: The knife-edge gauge and its displacement system emit a spherical wave through a point light source on the main optical axis, which is reflected by the optical element to be measured and returned to the knife-edge position of the knife-edge gauge and its displacement system. The knife-edge shadow detection image is imaged on the receiving surface of the CCD camera through the lens.

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