Grating sensor preparation method, displacement measurement method and grating sensor

Abstract

The invention discloses a grating sensor preparation method, a displacement measurement method and a grating sensor, and belongs to the technical field of measuring instruments. The grating sensor only needs one grating, a plurality of stripes are arranged on the grating in parallel, and the extending direction of the stripes is perpendicular to the length direction of the grating. The grating adjacent stripe distance array D is a K-order unique sliding window array, that is, a sub-array obtained by traversing the array through a sliding window with the length of K only appears once in the array. Images of K + 1 stripes are collected at each measurement position through an optical conversion element, the distance between the central positions of the adjacent stripe images is calculated, and the distance is compared with a distance array D of the adjacent stripes of the grating, so that the absolute position corresponding to each measurement position can be calculated, and the displacement is calculated. Due to the fact that extremely high precision can be guaranteed in the center positions of the stripes, the requirement for the machining precision of the stripes is not high, the machining difficulty and the machining cost of the stripes are reduced, and the machining efficiency and the product yield are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of measuring instruments, and in particular to a grating sensor preparation method, a displacement measurement method, and a grating sensor. Background Art

[0002] Grating sensor is a sensor that uses the optical properties of grating to achieve high-precision measurement of physical quantities such as displacement, speed, and angle. It is widely used in CNC machine tools, precision instruments, automation equipment and other fields. Grating sensor mainly consists of two parts: main grating and indicator grating: Main grating: It is a transparent sheet or metal sheet engraved with uniform parallel lines. The spacing between the lines is called the "grating constant", usually 0.01mm~0.1mm. The length is consistent with the measurement range and is fixed on the object being measured.

[0003] Indicator grating: The line density is the same as that of the main grating, the line direction is slightly inclined, it is fixed on the reading head of the sensor, and does not move with the object being measured.

[0004] When the main grating overlaps with the indicator grating and the lines form a small angle, light passing through the grating will form alternating light and dark stripes, namely moiré fringes, which is the basis for the grating sensor to achieve measurement.

[0005] To improve the grating accuracy, you can reduce the "grating constant" or increase the "subdivision multiple".

[0006] Reducing the grating constant directly depends on line accuracy. As the line spacing decreases, the requirements for processing equipment and processes increase exponentially. Grating lines must maintain uniform line width, parallelism, and depth consistency. When the grating constant is reduced to the micron or even submicron level, the line width may be as little as 0.25μm. At this point, any slight processing vibration, temperature fluctuation, or tool / laser beam drift will cause line shape distortion. For long-travel measurement, reducing the grating constant while maintaining a cumulative error of less than 1μm across the entire length of the line spacing requires extremely high levels of linearity in the guideways and positioning accuracy of the drive system. Even the slightest deformation of mechanical components can disrupt this consistency. Reducing the grating constant reduces the contrast of the moiré fringes, which can lead to unstable fringe signals. This also increases processing cycles and scrap rates, leading to a sharp increase in costs: high-precision ruling machines can cost millions of dollars per unit and can only produce gratings a few centimeters long per hour. The time and cost of material screening and post-processing inspections increase significantly, making mass production extremely difficult.

[0007] The accuracy of subdivision directly depends on the sinusoidality and symmetry of the Moiré fringes, but actual signals often have distortion. The higher the subdivision multiple, the more stringent the requirements for signal quality. In addition, the slight impact of environmental factors on the signal will be amplified by high subdivision, resulting in unstable subdivision results. Slight drift of the signal will also cause fluctuations in the subdivision results.

[0008] In short, whether reducing the "grating constant" or increasing the "subdivision multiple", it requires exponentially increasing precision of materials or hardware, which undoubtedly brings huge challenges to processing difficulty, production costs and subsequent maintenance. Summary of the Invention

[0009] The technical problem to be solved by the present invention is: in view of the above-mentioned defects of the prior art, a method for preparing a grating sensor, a displacement measurement method, and a grating sensor are provided.

[0010] To achieve the above objectives, in a first aspect, the present invention provides a method for preparing a grating sensor, the method comprising the following steps: Step A1, determining the width of the grating stripes according to the width of a single pixel of the optical conversion element; Step A2, determining the minimum spacing between adjacent grating stripes according to the width of the grating stripes; Step A3: Generate an array D of distances between adjacent grating stripes according to the minimum spacing between adjacent stripes, the preset sliding window order K, the size of the optical conversion element, and the range, which is recorded as D=[d1, d2, ..., d M ]; the grating adjacent stripe distance array D is a K-order unique sliding window array, that is, the subarray obtained by traversing the sliding window with a length of K appears only once in the grating adjacent stripe distance array D; Step A4, determining the center position of each stripe in the grating according to the array D of distances between adjacent stripes of the grating; Step A5: Processing all the stripes on the grating according to the center position of each stripe, the width value of the grating stripe and the preset grating stripe length value.

[0011] In the grating sensor preparation method of the present invention, in step A1, the width of the grating stripes is 3 to 20 times the width of a single pixel of the optical conversion element; In step A2, the minimum spacing between adjacent grating stripes is 1.2-2.5 times the width of the grating stripes; In step A3, the generated array D of distances between adjacent grating stripes needs to satisfy the following requirement: the sum of any consecutive K elements is less than the length of the optical conversion element.

[0012] In a second aspect, the present invention provides a method for measuring displacement of a grating sensor, which is applied to a grating sensor prepared by the grating sensor preparation method described above, and the method for measuring displacement of the grating sensor comprises the following steps: Step B1: At the first measurement position, determine a target area from the grating image captured by the optical conversion element 3, wherein the target area includes images of at least K+1 stripes; select images of K+1 consecutive stripes as a first calculation area, and calculate a first offset value do and a first index value r of the first calculation area; the first offset value do is the distance between the center position of the first stripe image in the first calculation area and the starting point of the target area; the first index value r is the index value of the first element in the first distance array D1 between the center positions of adjacent stripe images in the first calculation area in the grating adjacent stripe distance array D; Step B2: At the second measurement position, select an image of K+1 consecutive stripes in the target area as a second calculation area, and calculate a second offset value do and a second index value u of the second calculation area; Step B3, calculating the displacement value d according to the first offset value do, the second offset value ds, the first index value r, the second index value u, and the grating adjacent stripe distance array D. total and displacement direction; the specific method is: d total =ds-do+dv; When r>u, dv= ; When r=u, dv=0; When r<u, dv= .

[0013] In the grating sensor displacement measurement method of the present invention, in step B1, the specific method of selecting an image with K+1 consecutive stripes as the first calculation area is: Determine a brightness threshold according to the brightness of the center position of each stripe image in the target area or the global area, and select images of K+1 consecutive stripes in the target area whose brightness at the center position of the stripes exceeds the brightness threshold as the first calculation area; The target area includes a first calculation area and at least one first correction area, the first correction area includes at least one fringe image, and the first correction area is used to correct the first index value r.

[0014] In the grating sensor displacement measurement method of the present invention, in step B1, the method for calculating the first offset value do and the first index value r of the first calculation area is: Calculate the centroid position coordinates of K+1 fringe images in the first calculation area, and obtain a first offset value do according to the centroid position coordinates of the first fringe image and the starting point coordinates of the target area; Calculate the distances between the center positions of adjacent fringe images in sequence based on the coordinates of the centroid positions, combine them in order to obtain a first distance array D1, compare the first distance array D1 with the grating adjacent fringe distance array D, and determine the index value of the first element in the first distance array D1 in the grating adjacent fringe distance array D as the first index value r; The method for calculating the second offset value ds and the second index value u of the second calculation area is the same as the method for calculating the first offset value do and the first index value r of the first calculation area in step B1.

[0015] In the grating sensor displacement measurement method of the present invention, the method for comparing the first distance array D1 with the grating adjacent stripe distance array D to determine the index value of the first element in the first distance array D1 in the grating adjacent stripe distance array D is: Traverse the grating adjacent stripe distance array D, and take K consecutive values ​​from it each time as a temporary array. If the value of the temporary array is exactly the same as the first distance array D1, return the index value of the first element in the temporary array in the grating adjacent stripe distance array D.

[0016] In the grating sensor displacement measurement method of the present invention, the method for comparing the first distance array D1 with the grating adjacent stripe distance array D to determine the index value of the first element in the first distance array D1 in the grating adjacent stripe distance array D is: Traverse the grating adjacent stripe distance array D, take K consecutive values ​​from it each time as a temporary array, calculate the overall error between the temporary array and the first distance array D1, and return the index value of the first element in the temporary array corresponding to the minimum overall error in the grating adjacent stripe distance array D.

[0017] In the grating sensor displacement measurement method of the present invention, after step B3, the displacement correction factor W is calculated based on the first distance array D1, the first index value r, the first distance array D2, the first index value u, and the grating adjacent stripe distance array D, and the displacement value d is corrected according to the correction factor W. total , the specific formula is as follows: D1=[dt1,dt2,...,dt K ], D2=[ds1,ds2,...,ds K ], W1=(dt1+dt2+...+dt K ) / (d r +d r+1 +...+d r+K-1 ), Or W1=Sqrt((dt1 2 +dt22 +...+dt K 2 ) / (d r 2 +d r+1 2 +...+d r+K-1 2 )), W2=(ds1+ds2+...+ds K ) / (d u +d u+1 +...+d u+K-1 ), Or W2=Sqrt((ds1 2 +ds2 2 +...+ds K 2 ) / (d u 2 +d u+1 2 +...+d u+K-1 2 ))、 W=W1, or W=(W1+W2) / 2, or W=Sqrt((W1 2 +W2 2 ) / 2), or W=Min(W1, W2), or W=Max(W1, W2); Corrected total displacement of the object d total =ds-do+W*dv.

[0018] In a third aspect, the present invention further provides a grating sensor, comprising a light emitting device, a grating, an optical conversion element, a hardware circuit board, a housing, a control device, and an input / output device; The grating is provided with a plurality of stripes in parallel, and the extending direction of the stripes is perpendicular to the length direction of the grating; The grating adjacent stripe distance array D is a K-order unique sliding window array, that is, the subarray obtained by traversing the array with a sliding window of length K only appears once in the array; The light emitting device is fixed on the housing; The optical conversion element is fixed on the hardware circuit board, and the hardware circuit board is fixed on the housing; the optical conversion element is arranged along a direction perpendicular to the optical axis of the light-emitting device after reflection or transmission by the grating and parallel to the length of the grating; The light emitted by the light emitting device forms a grating image in the optical conversion element after passing through the grating; The hardware circuit board is used to receive the raster image data output by the optical conversion element and transmit it to the control device; The control device calculates the displacement amount based on the grating image data; The input and output devices are used to set parameters and display displacement calculation results.

[0019] In the grating sensor of the present invention, the light emitting device and the optical conversion element are located on the same side of the grating, the stripes on the grating are reflective stripes or non-reflective stripes, and the parallel light emitted by the light emitting device is reflected by the grating and received by the optical conversion element on the same side to form a grating image; or: The light emitting device and the optical conversion element are respectively located on both sides of the grating, and the stripes on the grating are light-transmitting stripes or light-opaque stripes.

[0020] The present invention has the following beneficial effects: The grating sensor provided by the present invention only requires a grating, which is provided with a plurality of parallel stripes, and the extension direction of the stripes is perpendicular to the length direction of the grating on which they are located. The spacing between adjacent stripes constitutes a K-order unique sliding window array D, that is, all sub-arrays obtained by traversing the spacing array with a sliding window of length K are unique in the array. During the measurement process, the optical conversion element collects images of K+1 consecutive stripes at different measurement positions, calculates the center spacing of adjacent stripe images, forms a local spacing sequence, and matches it with the preset grating stripe spacing array D, thereby determining the absolute position of the sensor on the grating and further calculating the displacement. Compared with traditional grating sensors, the present invention utilizes a stripe encoding pattern with a unique sliding window characteristic to achieve direct identification of the absolute position without relying on high-precision subdivision circuits or complex signal processing algorithms. Since the requirements for stripe edge clarity and geometric dimensional accuracy are significantly reduced, high-precision displacement measurement can be achieved under conditions where the stripes are wide and the processing accuracy is relatively low, effectively reducing the grating manufacturing cost.

[0021] In summary, the grating sensor of the present invention has a simple structure, a simple fabrication process, and low precision requirements for processing equipment. It has high practicality and scalability, making it suitable for cost-sensitive industrial applications that require high measurement accuracy. The displacement calculation method of the present invention is simple, efficient, and robust, requiring no complex signal processing algorithms, making it suitable for high-speed, real-time applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] The drawings described herein are used to provide further understanding of the present invention and constitute a part of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0023] Figure 1 This is a schematic diagram of the grating sensor structure provided in Example 1 of the present invention.

[0024] Figure 2 This is a schematic diagram of the steps of the method for preparing a grating sensor provided in Example 1 of the present invention.

[0025] Figure 3 This is a schematic diagram of the steps of the grating sensor displacement measurement method provided in Example 1 of the present invention.

[0026] Figure 4-6 A schematic diagram of a grating image provided in the first embodiment of the present invention.

[0027] Figure 7 This is a schematic diagram of the grating sensor structure provided in Example 4 of the present invention.

[0028] In the accompanying drawings: 1. Light-emitting device; 2. Grating; 3. Optical conversion element; 4. Hardware circuit board; 5. Housing; 6. Control device; 7. Input and output device. DETAILED DESCRIPTION

[0029] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0030] The embodiments of the present invention are described in further detail below in conjunction with the accompanying drawings. It should be understood that the embodiments described herein are only used to illustrate and explain the present invention and are not intended to limit the present invention.

[0031] Example 1 like Figure 1As shown, this embodiment provides a grating sensor, comprising a light-emitting device 1, a grating 2, an optical conversion element 3, a hardware circuit board 4, a housing 5, a control device 6, and an input / output device 7. The grating 2 is provided with a plurality of parallel stripes, the stripes extending in a direction perpendicular to the length direction of the grating 2. An array D of distances between adjacent grating stripes is a K-order unique sliding window array, i.e., a subarray obtained by traversing the array with a sliding window of length K appears only once in the array. The light-emitting device 1 is fixed to the housing 5. The optical conversion element 3 is fixed to the hardware circuit board 4, which is also fixed to the housing 5. The optical conversion element 3 is arranged in a direction perpendicular to the optical axis of the light-emitting device 1 after reflection or transmission by the grating 2 and parallel to the length direction of the grating 2. Light emitted by the light-emitting device 1 forms a grating image in the optical conversion element 3 after passing through the grating 2. The hardware circuit board 4 is used to receive grating image data output by the optical conversion element 3 and transmit it to the control device 6. The control device 6 calculates displacement based on the grating image data. The input / output device 7 is used to set parameters and display the displacement calculation results.

[0032] In this embodiment, the light emitting device 1 is an LED or laser light source.

[0033] like Figure 1 As shown, in this embodiment, the light-emitting device 1 and the optical conversion element 3 are located on the same side of the grating 2. The stripes on the grating 2 are either reflective or non-reflective. Light emitted by the light-emitting device 1 is reflected by the grating 2 and received by the optical conversion element 3 on the same side, forming a grating image. The arrangement of the light-emitting device 1 and the optical conversion element 3 on the same side of the grating 2 is suitable for single-sided installation where the mounting position is limited. Compared with arrangements where the light-emitting device 1 and the optical conversion element 3 are located on either side of the grating 2, the device is more resistant to environmental interference such as dust and oil.

[0034] There is no need for an additional collimating lens for generating parallel light between the light emitting device 1 and the grating 2 , or a collimating lens for generating parallel light may be placed.

[0035] The grating 2 is typically made of a metal material or a base material coated with a metal film. It is provided with reflective and / or non-reflective stripes arranged in a predetermined pattern. For example, reflective stripes may be present in the grooved areas, while non-reflective stripes may be present in the non-grooved areas, or vice versa. Light emitted by the light-emitting device 1 enters the grating 2 from one side. After the light strikes the surface of the grating 2, the reflective stripes reflect the light, forming a light spot on the optical conversion element 3. The non-reflective stripes absorb or scatter the light, forming a shadow on the optical conversion element 3.

[0036] In particular, the grating adjacent stripe distance array D is a K-order unique sliding window array, that is, the subarray obtained by traversing the array with a sliding window of length K appears only once in the array. Assuming that the total number of stripes on grating 2 is M+1, then the grating adjacent stripe distance array D=[d1, d2, ..., d M ], where d1 is the distance between the center of the first stripe and the center of the second stripe, d2 is the distance between the center of the second stripe and the center of the third stripe, and so on. M is the distance between the center position of the Mth stripe and the center position of the M+1th stripe. When a sliding window of length K is used to traverse the array D of distances between adjacent stripes of the grating, each result is a subarray containing K elements, and each subarray appears only once in the array D of distances between adjacent stripes of the grating. Therefore, by calculating the distance between the centers of adjacent stripes using images of K+1 consecutive stripes, the absolute positions of these stripes on the grating 2 can be determined, thereby enabling displacement measurement. To reduce the difficulty of manufacturing the grating 2, the widths of all stripes on the grating 2 are equal. Because the determination of absolute position relies on the distance between the centers of adjacent stripes, and during the stripe processing process, the center position of each stripe is first determined, and then stripes of a preset width are processed based on these center positions, even if there are large processing errors in the stripe width or the size of the stripe edge burrs is large, as long as the center position of each stripe is accurately positioned, the accuracy of the displacement measurement can be guaranteed. In addition, in this embodiment of the present invention, there is no specific requirement for the stripe length, as long as the stripe forms a clear image on the optical conversion element 3, that is, the stripe length needs to be greater than the pixel height of the optical conversion element 3. The pixel height of the optical conversion element 3 is typically 50-150 micrometers.

[0037] Compared with traditional grating sensors that use moiré fringes, the grating sensor of this embodiment only requires a grating scale with a cleverly designed fringe spacing to achieve accurate calculation of displacement. The fringe width value can be designed to be larger, and the processing accuracy requirements for the fringes are not high. This significantly improves the yield of grating sensor products, reduces the processing difficulty and cost of the fringes, shortens the quality inspection process, and improves processing efficiency.

[0038] In this embodiment, the width of the grating stripes is 3 to 20 times the width of a single pixel of the optical conversion element. The width of a single pixel of an optical conversion element, i.e., the pixel size, is a key parameter with a wide range of values ​​and is determined after the element is selected. If the grating stripe width is too small, it is difficult to accurately calculate the centroid coordinates of a single stripe image. If the grating stripe width is too large, the stripe image captured by the optical conversion element lacks distinct peaks and valleys, affecting measurement accuracy. Experimental verification has shown that a grating stripe width of 3 to 20 times the width of a single pixel of the optical conversion element can produce a relatively ideal grating image, ensuring measurement accuracy.

[0039] If the distance between adjacent stripes in grating 2 is too small, light emitted by the light-emitting device will diffract after passing through adjacent stripes, illuminating the entire optical conversion element 3 and preventing the acquisition of an image of grating 2. If the distance between adjacent stripes is too large, the number of stripes per unit area of ​​optical conversion element 3 will decrease, hindering product miniaturization and increasing manufacturing costs. In this embodiment, the minimum spacing between adjacent stripes of the grating is 1.2-2.5 times the width of the grating stripes.

[0040] The grating sensor of this embodiment can be used as a grating ruler. For example, the grating 2 is fixed to the guide rail of a machine tool, and the light emitting device 2, optical conversion element 3, hardware circuit board 4 and housing 5 are made into a reading head, which moves along the length direction of the grating 2.

[0041] The grating sensor of this embodiment can also be used as a contact displacement meter. In this case, the grating 2 is moved in a predetermined direction via a structural member such as a bearing. Its distal end is connected to a probe, which can be extended from the housing 5. An elastic member such as a spring or pneumatic valve can be interposed between the grating 2 and the housing 5 to deflect the probe in the extension direction.

[0042] In this embodiment, the optical conversion element 3 is an image sensor comprising optical conversion units arranged at predetermined intervals, such as a complementary metal oxide semiconductor image sensor or a charge-coupled device image sensor. The multiple optical conversion units comprising the optical conversion element 3 are arranged perpendicular to the optical path and parallel to the length of the grating 2. The optical conversion element 3 is attached to the hardware circuit board 4 via patching or soldering and is electrically connected to the hardware circuit board 4. Light from the light-emitting device 1 passes through the grating 2 having a specific pattern, forming a corresponding grating pattern on the optical conversion element 3.

[0043] like Figure 2 As shown, this embodiment further provides a method for preparing a grating sensor, wherein the method for preparing a grating sensor includes the following steps: Step A1: determining the width of the grating stripes according to the width of a single pixel of the optical conversion element.

[0044] In an embodiment of the present invention, in step A1, the width of the grating stripes is 3 to 20 times the width of a single pixel of the optical conversion element.

[0045] Step A2: determining the minimum spacing between adjacent grating stripes according to the width of the grating stripes.

[0046] In this embodiment, in step A2, the minimum spacing between adjacent grating stripes is 1.2-2.5 times the width of the grating stripes.

[0047] Step A3: Generate an array D of distances between adjacent grating stripes according to the minimum spacing between adjacent stripes, the preset sliding window order K, the size of the optical conversion element, and the range, which is recorded as D=[d1, d2, ..., d M ]; The grating adjacent stripe distance array D is a K-order unique sliding window array, that is, the subarray obtained by traversing the sliding window with a length of K appears only once in the grating adjacent stripe distance array D.

[0048] This embodiment imposes no particular restrictions on the specific algorithm used to generate the grating adjacent fringe distance array D, as long as the generated array is a K-order unique sliding window array. To obtain a sufficient number of fringe images for accurate displacement calculation, the generated grating adjacent fringe distance array D must satisfy the following conditions: the sum of any K consecutive elements is less than the length of the optical conversion element. The grating range is approximately equal to the sum of all elements in the grating adjacent fringe distance array D.

[0049] Step A4, determining the center position of each stripe in the grating according to the array D of distances between adjacent stripes of the grating; Step A5: Processing all the stripes on the grating according to the center position of each stripe, the width value of the grating stripe and the preset grating stripe length value.

[0050] In a specific implementation of this embodiment, the width of a single pixel of the optical conversion element is 10 microns, the width of the grating stripes is 180 microns, K=3, M=6, D=[270, 300, 330, 290, 350, 310], the sliding window subarray is: [270, 300, 330], [300, 330, 290], [330, 290, 350], [290, 350, 310], and the center positions corresponding to the 7 stripes are 90 μm, 540 μm, 1020 μm, 1530 μm, 2000 μm, 2530 μm, and 3020 μm, respectively.

[0051] In another specific implementation of this embodiment, the width of a single pixel of the optical conversion element is 6 microns, the width of the grating stripes is 150 microns, K=4, M=9, D=[225,250,280,300,240,260,290,310,230], and the sliding window subarrays are: [225,250,280,300], [250,280,300,240], [280 ,300,240,260], [300,240,260,290], [240,260,290,310], [260,290,310,230], and the center positions corresponding to the 10 stripes are 75μm, 450μm, 850μm, 1280μm, 1730μm, 2120μm, 2530μm, 2970μm, 3430μm, and 3810μm respectively.

[0052] In this embodiment, after calculating the array D of distances between adjacent grating stripes, the center position of each stripe can be determined. Then, combined with the stripe width value determined in step A1 and the preset grating stripe length value, all stripes can be processed. Once the stripe center position is determined, if there are processing errors, the errors are generally symmetrical about the center position. For example, if the width on one side of the center position is 5% smaller than the designed value, the width on the other side will also be 5% smaller than the designed value. Therefore, even if there are processing errors in the stripe width or length, the displacement can still be accurately calculated based on the stripe center position.

[0053] The grating sensor of this embodiment has a simple structure, a simple preparation process, low requirements for the precision of processing equipment, high practicality and scalability, and is suitable for industrial application scenarios that are cost-sensitive and require high measurement accuracy.

[0054] In this embodiment, the information such as the preset sliding window order K of the grating sensor, the size of the optical conversion element, the distance array D between adjacent grating stripes, and the stripe width is stored in the non-volatile memory on the hardware circuit board 4 or in the control device 6. The control device 6 can perform displacement measurement based on this information. Specifically, Figure 3 As shown, the grating sensor displacement measurement method includes the following steps: Step B1, at the first measurement position, determine a target area from the grating image captured by the optical conversion element 3, wherein the target area includes images of at least K+1 stripes; select images of K+1 consecutive stripes as the first calculation area, and calculate a first offset value do and a first index value r of the first calculation area; the first offset value do is the distance between the center position of the first stripe image in the first calculation area and the starting point of the target area, and the first index value r is the index value of the first element in the first distance array D1 between the center positions of adjacent stripe images in the first calculation area in the grating adjacent stripe distance array D.

[0055] The first measurement position is the starting point of the displacement and can be any position on the grating 2. First, it is necessary to determine the target area from the grating image collected by the optical conversion element 3, and calculate the absolute position corresponding to the first measurement position based on the fringe image of the first measurement position in the target area. Figure 4 The figure shows a schematic diagram of a grating image obtained by an optical conversion element, wherein the X-axis represents the pixel position on the optical conversion element 3 and the Y-axis represents the pixel brightness at that position. The width Dt of the target area needs to satisfy: Dt≥Max , that is, the width of the target area is no less than the maximum sum of K+1 consecutive distances in the array D of distances between adjacent grating stripes, ensuring that at least K+1 stripes can be found within the target area. The starting point of the target area can be flexibly determined based on the distribution of peaks in the grating image, ensuring that the target area covers the K+1 consecutive stripes with the highest brightness value. Typically, the center of the optical conversion element 3 is selected as the target area.

[0056] After the target area is determined, it is necessary to select the area within the target area where the K+1 fringe images are located as the first calculation area. In some embodiments of the present invention, in step B1, at the first measurement position, the target area includes a first calculation area and at least one first correction area, wherein the first correction area includes at least one fringe image, and the first correction area is used to correct the first index value r.

[0057] In this embodiment, in step B1, the specific method of selecting an image having K+1 consecutive stripes as the first calculation area is: A brightness threshold is determined based on the brightness of the center of each stripe image in the target region or global region. Within the target region, images of K+1 consecutive stripes whose center brightness exceeds the brightness threshold are selected as the first calculation region. The global region refers to the entire coverage area along the x-axis. Figure 5The diagram is a schematic diagram of the grating image at the first measurement position. The box represents the target area, which includes five fringe images (numbers 1, 2, 3, 4, and 5 in the box correspond to one fringe image each). Assume that the X-axis coordinate range of the target area is [600, 800], the X-axis coordinate range of the global area is [0, 1350], the unit is um, and K=3. Assume that the minimum brightness value gmin=950 and the maximum brightness gmax=2450 at the center of each fringe image in the global area, and assume that the brightness threshold gs=(gmin+gmax) / 2=1550. Find the first K+1=4 consecutive sub-areas whose brightness exceeds the specific value gs as the main calculation area. For example, select Figure 5 The four continuous stripe image regions 1, 2, 3, and 4 are used as the first calculation region, and 5 is used as the correction region.

[0058] In this embodiment, in step B1, the method for calculating the first offset value do and the first index value r of the first calculation area is: Calculate the centroid position coordinates of K+1 fringe images in the first calculation area, and obtain a first offset value do according to the centroid position coordinates of the first fringe image and the starting point coordinates of the target area; The distances between the center positions of adjacent fringe images are calculated in sequence according to the coordinates of the centroid position, and a first distance array D1 is obtained by combining them in sequence. The first distance array D1 is compared with the grating adjacent fringe distance array D, and the index value of the first element in the first distance array D1 in the grating adjacent fringe distance array D is determined as the first index value r.

[0059] by Figure 5 For example, the centroid coordinates of stripe images 1, 2, 3, and 4 are calculated, and the X coordinates of the centroid coordinates are recorded as xo1, xo2, xo3, and xo4, respectively. The distances between the centers of adjacent stripes are: dt1 = xo2 - xo1, dt2 = xo3 - xo2, and dt3 = xo4 - xo3, respectively. The first offset value do = xo1 - x0, where x0 is the starting position coordinate of the selected target area. This can be recorded in the control device 6 during the initialization of the grating sensor, or can be specified as needed, such as by specifying the target area's position coordinates, including the starting position x0 of the target area, through the input and output device 7. The first distance array D1 is recorded as D1 = [dt1, dt2, dt3]. D1 is then compared with the elements in the grating adjacent stripe distance array D to determine the index value r of dt1 in D.

[0060] In this embodiment, the method for comparing the first distance array D1 with the grating adjacent stripe distance array D to determine the index value of the first element in the first distance array D1 in the grating adjacent stripe distance array D is: Traverse the grating adjacent stripe distance array D, and take K consecutive values ​​from it each time as a temporary array. If the value of the temporary array is exactly the same as the first distance array D1, return the index value of the first element in the temporary array in the grating adjacent stripe distance array D.

[0061] by Figure 5 For example, the first distance array D1 is numerically compared with all temporary arrays one by one. The comparison is considered successful only when the order and value of each element are exactly the same. For example, dt1=d r ,dt2=d r+1 ,dt3=d r+2 , the first index value can be determined as r. If the first index value r cannot be obtained from the fringe image of the first calculation area, the first index value r is determined by combining the partial fringe image of the first calculation area with the partial image of the correction area that is continuous with it. For example, Figure 5 In the example, if the first index value r cannot be determined using fringe images 1, 2, 3, and 4, you can try to determine the first index value r using consecutive fringe images 2, 3, 4, and 5. Alternatively, even if the first index value r is determined using fringe images 1, 2, 3, and 4, you can determine a new index value using fringe images 2, 3, 4, and 5 to verify whether the first index value r is correct.

[0062] Step B2: At the second measurement position, select an image of K+1 consecutive stripes in the target area as a second calculation area, and calculate a second offset value do and a second index value u of the second calculation area.

[0063] The second measurement position is the end point of the displacement. At this second measurement position, the target area selected at the first measurement position is still used. However, due to the uneven spacing of the fringe patterns, the number of fringe patterns within the target area is likely to be different from the first measurement position, and the positions of the fringe patterns relative to the starting point of the target area are also likely to be different. Therefore, at the second measurement position, K+1 fringe patterns must be reselected as the second calculation area.

[0064] The specific method for selecting images of K+1 consecutive stripes in the target area as the second calculation area is the same as the method for selecting images of K+1 consecutive stripes in step B1 as the first calculation area. At the second measurement position, the target area includes the second calculation area and at least one second correction area. The second correction area includes at least one stripe image, and the second correction area is used to correct the second index value u. The method for calculating the second offset value ds and the second index value u for the second calculation area is the same as the method for calculating the first offset value do and the first index value r for the first calculation area in step B1.

[0065] Figure 6 The diagram below is a schematic diagram of the grating image at the second measurement position. The box represents the target area, which includes six fringe images. The brightness difference at the center of each fringe image is not significant. 1-4 consecutive fringe images, 2-5 consecutive fringe images, or 3-6 consecutive fringe images can be selected as the second calculation area. The fringe image area outside the second calculation area serves as the second correction area. Taking 2-5 consecutive fringe images as the second calculation area as an example, the centroid coordinates of areas 2, 3, 4, and 5 are calculated, with the X coordinates of the centroid coordinates being denoted as xs1, xs2, xs3, and xs4, respectively. The distances between the centers of adjacent fringe images are ds1 = xs2 - xs1, ds2 = xs3 - xs2, and ds3 = xs4 - xs3, respectively. The second offset value, ds, is xs1 - x0. The second distance array D2 is recorded as D2=[ds1, ds2, ds3], and then D2 is compared with the elements in the grating adjacent stripe distance array D to determine the index value u of ds1 in D.

[0066] Step B3, calculating the displacement value d according to the first offset value do, the second offset value ds, the first index value r, the second index value u, and the grating adjacent stripe distance array D. total and displacement direction. The specific method is: d total =ds-do+dv; When r>u, dv= ; When r=u, dv=0; When r<u, dv=

[0067] When d total > 0, the object moves in the positive direction. total When <0, the object moves in the opposite direction, d total = 0, the object does not move. The terms forward and reverse here simply refer to two relative directions, not specific directions. In practical applications, either grating 2 or housing 5 may be fixed, while grating 2 and housing 5 are in relative motion.

[0068] The grating sensor displacement measurement method provided in this embodiment first determines the target area from the grating image captured by the optical conversion element at a first measurement position. Images of at least K+1 stripes are selected from these images, and the distances between the centers of adjacent images are calculated. This is compared with the grating adjacent stripe distance array D to obtain a first offset value and a first index value. Next, a second offset value and a second index value are obtained at a second measurement position. The displacement is then calculated based on the data obtained at the first and second measurement positions. This method is simple, efficient, and robust, requiring no complex signal processing algorithms and is suitable for high-speed, real-time applications.

[0069] In this embodiment, the absolute position is calculated based on the distance between the center positions of the fringe images. It should be understood that the stripes can be reflective or non-reflective (light-absorbing), so the fringe image can be either a light spot or a shadow. If the stripes are light spots, the center position of the fringe image is the point of highest brightness; if the stripes are shadows, the center position of the fringe image is the point of lowest brightness. For ease of calculation, the inverse light spot can be generated by subtracting the brightness of the shadow fringe image from a specific brightness value. The calculation method for this is the same as for light spot stripes. The selection of the first and second calculation areas and the determination of the center position of the fringe image need to be based on the type of fringe image.

[0070] The displacement measurement accuracy of the grating sensor of this embodiment is determined by the pixel width, fringe width, and fringe spacing of the optical conversion element 3. Given a fixed pixel width, the accuracy is typically between one-fifth and one-twentieth of the pixel width. Compared to traditional grating sensors, the grating sensor of this embodiment utilizes a self-modulated fringe grating. This eliminates the need for stringent requirements for fringe edges and dimensions, significantly reducing the cost of the grating sensor. In scenarios where the grating grating is wide and accuracy is low, overall calculation accuracy is improved without using a subdivision algorithm. For example, with a fringe width of 200 microns and a pixel width of 10 microns, an accuracy of 1 micron can be achieved.

[0071] Example 2 In the first embodiment, the first distance array D1, the second distance array D2, and the grating adjacent stripe distance array D are directly compared to determine the index value. However, if the X coordinate of the centroid of each stripe is not an integer due to various errors, the values ​​in the first distance array D1 and the second distance array D2 are not integers, or even if they are integers, the direct comparison of the values ​​cannot find an identical subarray in the grating adjacent stripe distance array D, and the index value cannot be obtained. Figure 5 、 Figure 6For example, based on Example 1, xo1, xo2, xo3, xo4 and xs1, xs2, xs3, xs4 may not be integers, which means that dt1, dt2, dt3 and ds1, ds2, ds3 may not be integers either. Therefore, the corresponding first index value r and second index value u may not be found in the grating adjacent stripe distance array D.

[0072] In this embodiment, the above problem is improved. Specifically, in this embodiment, the method for comparing the first distance array D1 with the grating adjacent stripe distance array D to determine the index value of the first element in the first distance array D1 in the grating adjacent stripe distance array D is: Traverse the grating adjacent stripe distance array D, take K consecutive values ​​from it each time as a temporary array, calculate the overall error between the temporary array and the first distance array D1, and return the index value of the first element in the temporary array corresponding to the minimum overall error in the grating adjacent stripe distance array D.

[0073] Taking K=3 as an example, because the grating adjacent stripe distance array D is a K-order unique sliding window array, it is not possible to match dt1 or ds1 individually. The overall similarity of the K-tuple must be used as the judgment basis to avoid mismatching due to approximation errors of individual elements. Set the error e(df, di) = df-di, where df is the actual distance difference between dt1, dt2, dt3 or ds1, ds2, ds3, and di is the temporary array of D. Then, use the sliding window to traverse all temporary arrays of length K in D and calculate the overall similarity: For the target triple (such as [dt1, dt2, dt3]), traverse all sliding windows of length 3 in D [d n , d n+1 ,d n+2 ] (n ranges from 1 to M-2), calculate the overall error between the subarray in the window and the target triplet, and select the window with the smallest overall error as the approximate match. You can choose any of the following methods to calculate the overall error: 1. Average error: En = {e (dt1, d n )+e(dt2,d n+1 )+e(dt3,d n+2 )} / 3 2. Root mean square error: En = Sqrt ({e (dt1, d n ) 2 +e(dt2,d n+1 ) 2 +e(dt3,d n+2 ) 2} / 3) 3. Maximum error: En = Max (e (dt1, d n), e(dt2,d n+1 ), e(dt3,d n+2 ) You can directly select the window with the smallest En as the optimal solution, or you can set a maximum acceptable overall error threshold T. If En ≤ T for a window, it is considered a valid approximate match. If there are multiple valid windows, the window with the smallest En is selected as the optimal solution. If En > T for all windows, an error is reported. Check whether grating 2 is damaged or whether the value of T is set correctly. Typically, T ≤ min (dm) / 2, where dm is any element in the array D of distances between adjacent grating stripes.

[0074] The grating sensor displacement measurement method provided in this embodiment further improves the robustness and measurement accuracy of the displacement measurement algorithm.

[0075] Example 3 Based on the second embodiment, this embodiment further corrects the displacement measurement result to improve the accuracy of displacement calculation.

[0076] Specifically, the displacement correction factor W is calculated based on the first distance array D1, the first index value r, the first distance array D2, the first index value u, and the grating adjacent stripe distance array D, and the displacement value d is corrected based on the correction factor W. total , the specific formula is as follows: D1=[dt1,dt2,...,dt K ], D2=[ds1,ds2,...,ds K ], W1=(dt1+dt2+...+dt K ) / (d r +d r+1 +...+d r+K-1 ), Or W1=Sqrt((dt1 2 +dt2 2 +...+dt K 2 ) / (d r 2 +d r+1 2 +...+d r+K-1 2 )), W2=(ds1+ds2+...+ds K ) / (d u +d u+1 +...+d u+K-1 ) Or W2=Sqrt((ds1 2 +ds22 +...+ds K 2 ) / (d u 2 +d u+1 2 +...+d u+K-1 2 )) W=W1, or W=(W1+W2) / 2, or W=Sqrt((W1 2 +W2 2 ) / 2), or W=Min(W1, W2), or W=Max(W1, W2); Corrected total displacement of the object d total =ds-do+W*dv.

[0077] In one specific implementation of this embodiment, the width of a single pixel in the optical conversion element is 10 microns, the width of the grating stripes is 180 microns, K = 3, M = 6, and D = [270, 300, 330, 290, 350, 310]. The target region is the center area of ​​the optical conversion element, within the X-axis coordinate range of [400 μm, 1600 μm]. Global grating image brightness analysis is performed, and the global brightness range is 950-2450. The mean is added to 100 to screen for clear stripes, resulting in a brightness threshold gs of 1600. The displacement correction factor is calculated as W = (W1 + W2) / 2. The target region includes stripes 2, 3, 4, and 5. The first calculation region is determined to be the image region of stripes 2-5, and stripes 1 and 6 are used as the first correction region.

[0078] Through the brightness weighted algorithm, the X coordinates of the centroids of stripes 2 to 5 are 542 μm, 1018 μm, 1531 μm, and 2002 μm, respectively; the first offset value do = 542-400 = 142 μm; dt1 = 1018-542 = 276 μm, dt2 = 1531-1018 = 313 μm, dt3 = 2002-1531 = 471 μm, so D1 = [276, 313, 471].

[0079] The method for matching the first index value r is: traverse the grating adjacent stripe distance array D, take 3 consecutive elements as sub-arrays, and calculate the root mean square error (En) between each sub-array and D1. The results are: En≈82.3 for the sub-array [270,300,330]; En≈138.5 for the sub-array [300,330,290]; En≈105.1 for the sub-array [330,290,350]; En≈121.7 for the sub-array [290,350,310]; the sub-array corresponding to the minimum En is [270,300,330], whose first element has an index of 1 in D, so the first index value r=1.

[0080] After the object is moved, the grating image of the second measurement position is collected. The target area is still [400 μm, 1600 μm]. At this time, the area is covered by stripes 4, 5, 6, and 7, and stripe 3 is used as the second correction area.

[0081] Through the brightness weighted algorithm, the X coordinates of the centroids of stripes 4 to 7 are 1529 μm, 2001 μm, 2533 μm, and 3019 μm, respectively; the second offset value ds = 1129 μm; ds1 = 2001-1529 = 472 μm, ds2 = 2533-2001 = 532 μm, and ds3 = 3019-2533 = 486 μm, so D2 = [472, 532, 486].

[0082] The method for matching the second index value u is to traverse the grating adjacent stripe distance array D, take 3 consecutive elements as subarrays, and calculate the root mean square error (En) between each subarray and D2. Among them, En≈178.2 corresponding to the subarray [290,350,310] is the smallest, so the second index value u=4.

[0083] Because the first index value r = 1 < the second index value u = 4, dv = -900 μm. W ≈ 1.373. dtotal = -248.7 μm. Displacement Direction: dtotal < 0. The measured object is determined to be moving in the opposite direction, resulting in an actual displacement of 248.7 μm.

[0084] Example 4 like Figure 7 As shown, this is a structural diagram of the grating sensor provided in this embodiment. The difference from the grating sensor in Example 1 is that the light-emitting device 1 and the optical conversion element 3 are respectively located on both sides of the grating 2, and the stripes on the grating 2 are translucent stripes or opaque stripes.

[0085] In this embodiment, the stripes can be light-transmitting or opaque (light-absorbing), so the fringe image can be a light spot or a shadow. If the stripes are light spots, the center of the fringe image is the point of highest brightness. If the stripes are shadows, the center of the fringe image is the point of lowest brightness. The first and second calculation areas must be selected based on the type of fringe image to determine the center of the fringe image.

[0086] The above is only a specific embodiment of the present invention and cannot be used to limit the scope of the present invention. Equal changes made by ordinary technicians in this technical field based on this creation, as well as changes well known to technicians in this field, should still fall within the scope of the present invention.

Claims

1. A method for preparing a grating sensor, characterized in that: The grating sensor preparation method comprises the following steps: Step A1, determining the width of the grating stripes according to the width of a single pixel of the optical conversion element; Step A2, determining the minimum spacing between adjacent grating stripes according to the width of the grating stripes; Step A3: Generate an array D of distances between adjacent grating stripes according to the minimum spacing between adjacent stripes, the preset sliding window order K, the size of the optical conversion element, and the range, which is recorded as D=[d1, d2, ..., d M ]; the grating adjacent stripe distance array D is a K-order unique sliding window array, that is, the subarray obtained by traversing the sliding window with a length of K appears only once in the grating adjacent stripe distance array D; Step A4, determining the center position of each stripe in the grating according to the array D of distances between adjacent stripes of the grating; Step A5: Processing all the stripes on the grating according to the center position of each stripe, the width value of the grating stripe and the preset grating stripe length value.

2. The method for preparing a grating sensor according to claim 1, wherein: In step A1, the width of the grating stripes is 3 to 20 times the width of a single pixel of the optical conversion element; In step A2, the minimum spacing between adjacent grating stripes is 1.2-2.5 times the width of the grating stripes; In step A3, the generated array D of distances between adjacent grating stripes needs to satisfy the following requirement: the sum of any consecutive K elements is less than the length of the optical conversion element.

3. A grating sensor displacement measurement method, characterized in that: The grating sensor displacement measurement method comprises the following steps: Step B1: At a first measurement position, determine a target area from a grating image captured by the optical conversion element, wherein the target area includes images of at least K+1 stripes; select images of K+1 consecutive stripes as a first calculation area, and calculate a first offset value do and a first index value r of the first calculation area; the first offset value do is the distance between the center position of the first stripe image in the first calculation area and the starting point of the target area; the first index value r is the index value of the first element in a first distance array D1 between the center positions of adjacent stripe images in the first calculation area, in the grating adjacent stripe distance array D; Step B2: At the second measurement position, select an image of K+1 consecutive stripes in the target area as a second calculation area, and calculate a second offset value ds and a second index value u of the second calculation area; Step B3, calculating the displacement value d according to the first offset value do, the second offset value ds, the first index value r, the second index value u, and the grating adjacent stripe distance array D. total ; The specific method is: d total =ds-do+dv; When r>u, dv= ; When r=u, dv=0; When r<u, dv= .

4. The grating sensor displacement measurement method according to claim 3, characterized in that: In step B1, the specific method of selecting an image with K+1 consecutive stripes as the first calculation area is: Determine a brightness threshold according to the brightness of the center position of each stripe image in the target area or the global area, and select images of K+1 consecutive stripes in the target area whose brightness at the center position of the stripes exceeds the brightness threshold as the first calculation area; The target area includes a first calculation area and at least one first correction area, the first correction area includes at least one fringe image, and the first correction area is used to correct the first index value r.

5. The grating sensor displacement measurement method according to claim 4, characterized in that: In step B1, the method for calculating the first offset value do and the first index value r of the first calculation area is: Calculate the centroid position coordinates of K+1 fringe images in the first calculation area, and obtain a first offset value do according to the centroid position coordinates of the first fringe image and the starting point coordinates of the target area; Calculate the distances between the center positions of adjacent fringe images in sequence based on the coordinates of the centroid positions, combine them in order to obtain a first distance array D1, compare the first distance array D1 with the grating adjacent fringe distance array D, and determine the index value of the first element in the first distance array D1 in the grating adjacent fringe distance array D as the first index value r; The method for calculating the second offset value ds and the second index value u of the second calculation area is the same as the method for calculating the first offset value do and the first index value r of the first calculation area in step B1.

6. The grating sensor displacement measurement method according to claim 5, characterized in that: The method of comparing the first distance array D1 with the grating adjacent stripe distance array D to determine the index value of the first element in the first distance array D1 in the grating adjacent stripe distance array D is: Traverse the grating adjacent stripe distance array D, and take K consecutive values ​​from it each time as a temporary array. If the value of the temporary array is exactly the same as the first distance array D1, return the index value of the first element in the temporary array in the grating adjacent stripe distance array D.

7. The grating sensor displacement measurement method according to claim 5, characterized in that: The method of comparing the first distance array D1 with the grating adjacent stripe distance array D to determine the index value of the first element in the first distance array D1 in the grating adjacent stripe distance array D is: Traverse the grating adjacent stripe distance array D, take K consecutive values ​​from it each time as a temporary array, calculate the overall error between the temporary array and the first distance array D1, and return the index value of the first element in the temporary array corresponding to the minimum overall error in the grating adjacent stripe distance array D.

8. The grating sensor displacement measurement method according to claim 7, characterized in that: After step B3, the displacement correction factor W is calculated based on the first distance array D1, the first index value r, the first distance array D2, the first index value u, and the grating adjacent stripe distance array D, and the displacement value d is corrected based on the correction factor W. total , the specific formula is as follows: D1=[dt1,dt2,...,dt K ], D2=[ds1,ds2,...,ds K ], W1=(dt1+dt2+...+dt K ) / (d r +d r+1 +...+d r+K-1 ), Or W1=Sqrt((dt1 2 +dt2 2 +...+dt K 2 ) / (d r 2 +d r+1 2 +...+d r+K-1 2 )), W2=(ds1+ds2+...+ds K ) / (d u +d u+1 +...+d u+K-1 ), Or W2=Sqrt((ds1 2 +ds2 2 +...+ds K 2 ) / (d u 2 +d u+1 2 +...+d u+K-1 2 ))、 W=W1, or W=(W1+W2) / 2, or W=Sqrt((W1 2 +W2 2 ) / 2), or W=Min(W1, W2), or W=Max(W1, W2); Corrected total displacement of the object d total =ds-do+W*dv.

9. A grating sensor, characterized in that: It includes a light emitting device (1), a grating (2), an optical conversion element (3), a hardware circuit board (4), a housing (5), a control device (6), and an input / output device (7); The grating (2) has a plurality of stripes arranged in parallel, and the extension direction of the stripes is perpendicular to the length direction of the grating (2); The grating adjacent stripe distance array D is a K-order unique sliding window array, that is, the subarray obtained by traversing the array with a sliding window of length K only appears once in the array; The light-emitting device (1) is fixed on the housing (5); The optical conversion element (3) is fixed on the hardware circuit board (4), and the hardware circuit board (4) is fixed on the housing (5); the optical conversion element (3) is arranged along a direction perpendicular to the optical axis of the light-emitting device (1) after reflection or transmission by the grating (2) and parallel to the length of the grating (2); The light emitted by the light emitting device (1) passes through the grating (2) and forms a grating image in the optical conversion element (3); The hardware circuit board (4) is used to receive the grating image data output by the optical conversion element (3) and transmit the data to the control device (6); The control device (6) calculates the displacement amount according to the grating image data; The input and output device (7) is used to set parameters and display displacement calculation results.

10. The grating sensor according to claim 9, characterized in that The light emitting device (1) and the optical conversion element (3) are located on the same side of the grating (2); the stripes on the grating (2) are reflective stripes or non-reflective stripes; the parallel light emitted by the light emitting device (1) is reflected by the grating (2) and then received by the optical conversion element (3) on the same side to form a grating image; or: The light emitting device (1) and the optical conversion element (3) are respectively located on both sides of the grating (2), and the stripes on the grating (2) are light-transmitting stripes or light-opaque stripes.

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