{"id":11153,"date":"2022-11-19T03:26:11","date_gmt":"2022-11-19T03:26:11","guid":{"rendered":"https:\/\/www.szlaser.com\/?page_id=11153"},"modified":"2022-11-20T04:37:11","modified_gmt":"2022-11-20T04:37:11","slug":"off-axis-paraboloid-mirror","status":"publish","type":"page","link":"https:\/\/www.szlaser.com\/index.php\/wiki\/off-axis-paraboloid-mirror\/","title":{"rendered":"Manufacture of \u03a6420mm off-axis paraboloid mirror"},"content":{"rendered":"<div class=\"fusion-fullwidth fullwidth-box fusion-builder-row-1 fusion-flex-container has-pattern-background has-mask-background nonhundred-percent-fullwidth non-hundred-percent-height-scrolling\" style=\"--awb-border-radius-top-left:0px;--awb-border-radius-top-right:0px;--awb-border-radius-bottom-right:0px;--awb-border-radius-bottom-left:0px;--awb-flex-wrap:wrap;\" ><div class=\"fusion-builder-row fusion-row fusion-flex-align-items-flex-start fusion-flex-content-wrap\" style=\"max-width:1331.2px;margin-left: calc(-4% \/ 2 );margin-right: calc(-4% \/ 2 );\"><div class=\"fusion-layout-column fusion_builder_column fusion-builder-column-0 fusion_builder_column_1_1 1_1 fusion-flex-column\" style=\"--awb-bg-size:cover;--awb-width-large:100%;--awb-margin-top-large:0px;--awb-spacing-right-large:1.92%;--awb-margin-bottom-large:20px;--awb-spacing-left-large:1.92%;--awb-width-medium:100%;--awb-order-medium:0;--awb-spacing-right-medium:1.92%;--awb-spacing-left-medium:1.92%;--awb-width-small:100%;--awb-order-small:0;--awb-spacing-right-small:1.92%;--awb-spacing-left-small:1.92%;\"><div class=\"fusion-column-wrapper fusion-column-has-shadow fusion-flex-justify-content-flex-start fusion-content-layout-column\"><div class=\"fusion-title title fusion-title-1 fusion-sep-none fusion-title-text fusion-title-size-one\"><h1 class=\"fusion-title-heading title-heading-left fusion-responsive-typography-calculated\" style=\"margin:0;--fontSize:32;line-height:1.3;\"><h1>Manufacture of \u03a6420mm off-axis paraboloid mirror<\/h1><\/h1><\/div><div class=\"fusion-text fusion-text-1\"><p>off axis paraboloid mirror, vertical testing of sub-aperture<\/p>\n<\/div><div class=\"fusion-title title fusion-title-2 fusion-sep-none fusion-title-text fusion-title-size-three\"><h3 class=\"fusion-title-heading title-heading-left fusion-responsive-typography-calculated\" style=\"margin:0;--fontSize:24;line-height:1.3;\"><h3>Abstract<\/h3><\/h3><\/div><div class=\"fusion-text fusion-text-2\"><p>A manufacture and testing technology of \u03a6420mm off axis paraboloid mirror are reported. The determination principle of manufacture scheme, the choice of start sphere, the calculation of the asphericity of the off axis paraboloid are given. The vertical testing method of sub-aperture of the off-axis surface are on the mother mirror is discussed. The requirement of position accuracy for the testing configuration is analysed. The separating method of the off-axis mirror from the mother mirror is reported. Testing result is given\uff0e<\/p>\n<\/div><div class=\"fusion-title title fusion-title-3 fusion-sep-none fusion-title-text fusion-title-size-three\"><h3 class=\"fusion-title-heading title-heading-left fusion-responsive-typography-calculated\" style=\"margin:0;--fontSize:24;line-height:1.3;\"><h3>Introduction<\/h3><\/h3><\/div><div class=\"fusion-text fusion-text-3\"><p>The aberration-free characteristics of the quadratic aspheric geometric focus make it widely used in large-aperture optical systems. It not only reduces the structure, but also reduces the cost. Because of the unique optical properties of aberration-free collimated beams, parabolic mirrors are often used as collimators as basic optical calibration tools.<\/p>\n<p>The off-axis parabolic mirror reflective collimator is the most simple collimator. Because its central area is not blocked, it has advantages that other forms of collimators cannot match. However, the fabrication of large-aperture, high-precision off-axis parabolic mirrors is very difficult. To a certain extent, its application is limited. There are few reports on the development of large off-axis mirrors with a diameter of more than 200mm in China.<\/p>\n<p>In recent years, we have developed three \u03a6420mm off-axis parabolic mirrors for a laboratory, and have made useful attempts and explorations on the manufacturing technology of large-diameter, high-precision off-axis parabolic mirrors. In the implementation, the sub-aperture inspection is boldly used to control the parent parabolic mirror shape, thus finally guaranteeing a new method of \u03a6420mm off-axis mirror shape. The P-V value of the final inspection result of the off-axis parabolic mirror is \u03bb\/8.4, which is better than the design index.<\/p>\n<\/div><div class=\"fusion-title title fusion-title-4 fusion-sep-none fusion-title-text fusion-title-size-three\"><h3 class=\"fusion-title-heading title-heading-left fusion-responsive-typography-calculated\" style=\"margin:0;--fontSize:24;line-height:1.3;\"><h3>The determination of the processing method<\/h3><\/h3><\/div><div class=\"fusion-text fusion-text-4\"><p>1. Basic parameters of \u03a6420mm off-axis parabolic mirror<\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>Diameter: D=420mm<\/li>\n<li>Focal length: F=5000\u00b15 (mm)<\/li>\n<li>Off-axis angle: \u03b1=3.6\u00b0<\/li>\n<li>Surface accuracy: P-V \u2264\u03bb\/6 (\u03bb=0.6328\u03bcm)<\/li>\n<\/ol>\n<p>2. Determination of process plan Usually, there are two methods for processing off-axis parabolic mirrors<\/p>\n<ul>\n<li>Single-piece processing: make the glass blank size to the required diameter of the off-axis paraboloid, and then grind it into the required surface by hand or supplemented by a machine shape. It is mainly suitable for off-axis mirror processing with low surface shape accuracy. Only when the technology for computer-controlled optical processing matures, can single-piece machining of high-precision off-axis mirrors become feasible and generally accepted.<\/li>\n<li>Cut out from a large axisymmetric paraboloid: Grind a large axisymmetric paraboloid (mother mirror) by ordinary methods. Then, dig out the required off-axis parabolic mirror from the casing with a dig round tool. This method is relatively mature in technology, and it is generally believed that it is suitable for mirrors with a diameter of about 100mm and a small off-axis amount.<\/li>\n<\/ul>\n<p>After repeated demonstrations, we finally chose the processing method of cutting a \u03a6420mm off-axis paraboloid from a large axisymmetric paraboloid. Obviously, the implementation of this processing scheme on the \u03a6420mm caliber is a breakthrough to the traditional concept. The basic basis for choosing this processing scheme is:<br \/>\n\u2460 Comprehensive analysis The technical index requirements are reasonable and moderate;<br \/>\n\u2461 We have the technical conditions and ability to process parabolic primary mirrors above \u03a61m;<br \/>\n\u2462 With a vertical inspection tower, vertical inspection can be carried out;<br \/>\n\u2463 Provide users with three off-axis mirrors at the same time, which is economically feasible for both users and manufacturers.<\/p>\n<ul>\n<li>Calculation of the diameter of the parent paraboloid The parent paraboloid equation is:<\/li>\n<\/ul>\n<p><img decoding=\"async\" class=\"lazyload aligncenter wp-image-11155 size-fusion-400\" src=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/y2-400x80.png\" data-orig-src=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/y2-400x80.png\" alt=\"\" width=\"400\" height=\"80\" srcset=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27400%27%20height%3D%2780%27%20viewBox%3D%270%200%20400%2080%27%3E%3Crect%20width%3D%27400%27%20height%3D%2780%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-srcset=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/y2-200x40.png 200w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/y2-300x60.png 300w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/y2-400x80.png 400w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/y2.png 538w\" data-sizes=\"auto\" data-orig-sizes=\"(max-width: 400px) 100vw, 400px\" \/><\/p>\n<p>As shown in Figure 1, if the height of the optical axis of the off-axis parabolic mirror is h, then<\/p>\n<p><img decoding=\"async\" class=\"lazyload aligncenter wp-image-11156 size-fusion-400\" src=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/h-400x79.png\" data-orig-src=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/h-400x79.png\" alt=\"\" width=\"400\" height=\"79\" srcset=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27400%27%20height%3D%2779%27%20viewBox%3D%270%200%20400%2079%27%3E%3Crect%20width%3D%27400%27%20height%3D%2779%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-srcset=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/h-200x39.png 200w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/h-300x59.png 300w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/h-400x79.png 400w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/h.png 528w\" data-sizes=\"auto\" data-orig-sizes=\"(max-width: 400px) 100vw, 400px\" \/><\/p>\n<p>F is the parabolic focal length, and \u03b1 is the off-axis angle.<\/p>\n<p>Therefore<\/p>\n<p><img decoding=\"async\" class=\"lazyload aligncenter wp-image-11157 size-fusion-800\" src=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/h2-800x67.png\" data-orig-src=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/h2-800x67.png\" alt=\"\" width=\"800\" height=\"67\" srcset=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27800%27%20height%3D%2767%27%20viewBox%3D%270%200%20800%2067%27%3E%3Crect%20width%3D%27800%27%20height%3D%2767%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-srcset=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/h2-200x17.png 200w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/h2-300x25.png 300w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/h2-400x34.png 400w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/h2-600x50.png 600w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/h2-768x64.png 768w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/h2-800x67.png 800w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/h2-1024x86.png 1024w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/h2.png 1194w\" data-sizes=\"auto\" data-orig-sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<p>The effective aperture of the off-axis mirror parent is<\/p>\n<p><img decoding=\"async\" class=\"lazyload aligncenter wp-image-11158\" src=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-D-600x79.png\" data-orig-src=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-D-600x79.png\" alt=\"\" width=\"700\" height=\"92\" srcset=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27700%27%20height%3D%2792%27%20viewBox%3D%270%200%20700%2092%27%3E%3Crect%20width%3D%27700%27%20height%3D%2792%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-srcset=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-D-200x26.png 200w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-D-300x40.png 300w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-D-400x53.png 400w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-D-600x79.png 600w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-D-768x101.png 768w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-D-800x106.png 800w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-D-1024x135.png 1024w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-D.png 1136w\" data-sizes=\"auto\" data-orig-sizes=\"(max-width: 700px) 100vw, 700px\" \/><\/p>\n<div id=\"attachment_11160\" style=\"width: 610px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" aria-describedby=\"caption-attachment-11160\" class=\"lazyload size-fusion-600 wp-image-11160\" src=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Fig.-1-Basic-parameter-diagram-600x394.jpg\" data-orig-src=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Fig.-1-Basic-parameter-diagram-600x394.jpg\" alt=\"\" width=\"600\" height=\"394\" srcset=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27600%27%20height%3D%27394%27%20viewBox%3D%270%200%20600%20394%27%3E%3Crect%20width%3D%27600%27%20height%3D%27394%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-srcset=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Fig.-1-Basic-parameter-diagram-200x131.jpg 200w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Fig.-1-Basic-parameter-diagram-300x197.jpg 300w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Fig.-1-Basic-parameter-diagram-400x262.jpg 400w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Fig.-1-Basic-parameter-diagram-600x394.jpg 600w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Fig.-1-Basic-parameter-diagram-768x504.jpg 768w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Fig.-1-Basic-parameter-diagram-800x525.jpg 800w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Fig.-1-Basic-parameter-diagram.jpg 907w\" data-sizes=\"auto\" data-orig-sizes=\"(max-width: 600px) 100vw, 600px\" \/><p id=\"caption-attachment-11160\" class=\"wp-caption-text\">Fig. 1 Basic parameter diagram<\/p><\/div>\n<\/div><div class=\"fusion-title title fusion-title-5 fusion-sep-none fusion-title-text fusion-title-size-three\"><h3 class=\"fusion-title-heading title-heading-left fusion-responsive-typography-calculated\" style=\"margin:0;--fontSize:24;line-height:1.3;\"><h3>Selection of starting spherical surface, calculation of asphericity<\/h3><\/h3><\/div><div class=\"fusion-text fusion-text-5\"><p>The rationality of the selection of the starting spherical surface is related to the size of the asphericity in the processing of the parabolic mirror, and directly determines the processing cycle and cost. Therefore, the selection of the starting sphere and the size of the asphericity play a very important role in the process design.<\/p>\n<\/div><div class=\"fusion-title title fusion-title-6 fusion-sep-none fusion-title-text fusion-title-size-four\"><h4 class=\"fusion-title-heading title-heading-left fusion-responsive-typography-calculated\" style=\"margin:0;--fontSize:22;--minFontSize:22;line-height:1.34;\"><h4>1. Selection of starting spherical surface<\/h4><\/h4><\/div><div class=\"fusion-text fusion-text-6\"><p>For a paraboloid without a central occlusion, the starting sphere should be a sphere that passes through the edge band and touches the vertex, as shown in Figure 2(a). However, the inner edge of the off-axis mirror (sub-aperture on the parent) to the center of the geometric axis of the parent mirror is the non-working area (blind area), and there is no need to identify it during inspection. Therefore, when the starting sphere is selected, the outer band can be in contact with the edge of the blind zone, as shown in Figure 2(b). The center of the starting sphere must be on the axis of symmetry.<\/p>\n<div id=\"attachment_11163\" style=\"width: 810px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" aria-describedby=\"caption-attachment-11163\" class=\"lazyload wp-image-11163 size-fusion-800\" src=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Fig.-2-Starting-spherical-selection-diagram-800x415.png\" data-orig-src=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Fig.-2-Starting-spherical-selection-diagram-800x415.png\" alt=\"\" width=\"800\" height=\"415\" srcset=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27800%27%20height%3D%27415%27%20viewBox%3D%270%200%20800%20415%27%3E%3Crect%20width%3D%27800%27%20height%3D%27415%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-srcset=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Fig.-2-Starting-spherical-selection-diagram-200x104.png 200w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Fig.-2-Starting-spherical-selection-diagram-300x156.png 300w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Fig.-2-Starting-spherical-selection-diagram-400x208.png 400w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Fig.-2-Starting-spherical-selection-diagram-600x312.png 600w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Fig.-2-Starting-spherical-selection-diagram-768x399.png 768w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Fig.-2-Starting-spherical-selection-diagram-800x415.png 800w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Fig.-2-Starting-spherical-selection-diagram.png 853w\" data-sizes=\"auto\" data-orig-sizes=\"(max-width: 800px) 100vw, 800px\" \/><p id=\"caption-attachment-11163\" class=\"wp-caption-text\">Fig. 2 Starting spherical selection diagram<\/p><\/div>\n<p>Let its radius be R, its vertex coordinates are not (0, 0), but (\u03b5, 0), so the coordinates of the center of the sphere are (c, 0), not (R, 0), \u03b5=c-R . From the distance formula it can be written<\/p>\n<p><img decoding=\"async\" class=\"lazyload aligncenter size-fusion-600 wp-image-11164\" src=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/distance-formula-600x58.png\" data-orig-src=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/distance-formula-600x58.png\" alt=\"\" width=\"600\" height=\"58\" srcset=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27600%27%20height%3D%2758%27%20viewBox%3D%270%200%20600%2058%27%3E%3Crect%20width%3D%27600%27%20height%3D%2758%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-srcset=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/distance-formula-200x19.png 200w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/distance-formula-300x29.png 300w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/distance-formula-400x39.png 400w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/distance-formula-600x58.png 600w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/distance-formula-768x75.png 768w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/distance-formula-800x78.png 800w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/distance-formula-1024x100.png 1024w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/distance-formula.png 1028w\" data-sizes=\"auto\" data-orig-sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/p>\n<p>Solutions have to formula C as below<\/p>\n<p><img decoding=\"async\" class=\"lazyload aligncenter size-fusion-600 wp-image-11165\" src=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-C-600x113.png\" data-orig-src=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-C-600x113.png\" alt=\"\" width=\"600\" height=\"113\" srcset=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27600%27%20height%3D%27113%27%20viewBox%3D%270%200%20600%20113%27%3E%3Crect%20width%3D%27600%27%20height%3D%27113%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-srcset=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-C-200x38.png 200w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-C-300x57.png 300w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-C-400x76.png 400w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-C-600x113.png 600w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-C-768x145.png 768w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-C-800x151.png 800w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-C.png 974w\" data-sizes=\"auto\" data-orig-sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/p>\n<p>thereby, formula R is<\/p>\n<p><img decoding=\"async\" class=\"lazyload aligncenter size-fusion-600 wp-image-11166\" src=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-R-1-600x87.png\" data-orig-src=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-R-1-600x87.png\" alt=\"\" width=\"600\" height=\"87\" srcset=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27600%27%20height%3D%2787%27%20viewBox%3D%270%200%20600%2087%27%3E%3Crect%20width%3D%27600%27%20height%3D%2787%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-srcset=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-R-1-200x29.png 200w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-R-1-300x43.png 300w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-R-1-400x58.png 400w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-R-1-600x87.png 600w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-R-1-768x111.png 768w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-R-1-800x115.png 800w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-R-1-940x138.png 940w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-R-1.png 956w\" data-sizes=\"auto\" data-orig-sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/p>\n<p>When calculating off-axis parabolic asphericity, \u03b5=c-R must be added. Substitute the coordinate values of the inner and outer edges of the \u03a6420mm off-axis mirror into equations (1) and (2) to obtain:<\/p>\n<p>Off-axis mirror starting spherical radius<\/p>\n<p><img decoding=\"async\" class=\"lazyload aligncenter wp-image-11167 size-fusion-400\" src=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Off-axis-mirror-starting-spherical-radius-400x58.png\" data-orig-src=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Off-axis-mirror-starting-spherical-radius-400x58.png\" alt=\"\" width=\"400\" height=\"58\" srcset=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27400%27%20height%3D%2758%27%20viewBox%3D%270%200%20400%2058%27%3E%3Crect%20width%3D%27400%27%20height%3D%2758%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-srcset=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Off-axis-mirror-starting-spherical-radius-200x29.png 200w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Off-axis-mirror-starting-spherical-radius-300x43.png 300w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Off-axis-mirror-starting-spherical-radius-400x58.png 400w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Off-axis-mirror-starting-spherical-radius-600x87.png 600w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Off-axis-mirror-starting-spherical-radius.png 732w\" data-sizes=\"auto\" data-orig-sizes=\"(max-width: 400px) 100vw, 400px\" \/><\/p>\n<p>The coordinates of the center of the starting radius are (10007.1075, 0) The starting radius selected in this way can minimize the amount of grinding during processing.<\/p>\n<\/div><div class=\"fusion-title title fusion-title-7 fusion-sep-none fusion-title-text fusion-title-size-four\"><h4 class=\"fusion-title-heading title-heading-left fusion-responsive-typography-calculated\" style=\"margin:0;--fontSize:22;--minFontSize:22;line-height:1.34;\"><h4>2. Calculation of asphericity<\/h4><\/h4><\/div><div class=\"fusion-text fusion-text-7\"><p>After the initial spherical radius is determined, in order to effectively guide the processing, the grinding amount \u03c3 of each belt of the mirror surface must also be calculated. As shown in Fig. 2(b), the off-axis paraboloid in the meridional section ranges from p1 to p2, and the equation of the parent paraboloid is y=2R\u00b0x. Therefore, the asphericity \u03c3 of each band of the paraboloid (along the X axis) is<\/p>\n<p><img decoding=\"async\" class=\"lazyload aligncenter size-fusion-600 wp-image-11168\" src=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/asphericity-\u03c3-600x80.png\" data-orig-src=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/asphericity-\u03c3-600x80.png\" alt=\"\" width=\"600\" height=\"80\" srcset=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27600%27%20height%3D%2780%27%20viewBox%3D%270%200%20600%2080%27%3E%3Crect%20width%3D%27600%27%20height%3D%2780%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-srcset=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/asphericity-\u03c3-200x27.png 200w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/asphericity-\u03c3-300x40.png 300w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/asphericity-\u03c3-400x53.png 400w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/asphericity-\u03c3-600x80.png 600w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/asphericity-\u03c3-768x102.png 768w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/asphericity-\u03c3-800x107.png 800w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/asphericity-\u03c3-1024x137.png 1024w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/asphericity-\u03c3-1200x160.png 1200w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/asphericity-\u03c3.png 1290w\" data-sizes=\"auto\" data-orig-sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/p>\n<p>The \u03c3 values calculated by this formula are all negative numbers, indicating that the starting spherical surface is to the left of the off-axis mirror. For the concave mirror surface, it is necessary to &#8220;repair&#8221; the glass instead of wearing it, so the starting sphere needs to be shifted to the right by an amount &#8211; The maximum value of all \u03c3 values is \u03c3<sub>max<\/sub>. In actual processing, the belt corresponding to \u03c3<sub>max<\/sub> is not ground, and the grinding amount is the largest at points p1 and p2. That is, the real grinding amount \u03c3<\/p>\n<p><img decoding=\"async\" class=\"lazyload aligncenter wp-image-11169 size-fusion-400\" src=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/the-real-grinding-amount-\u03c3-400x73.png\" data-orig-src=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/the-real-grinding-amount-\u03c3-400x73.png\" alt=\"\" width=\"400\" height=\"73\" srcset=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27400%27%20height%3D%2773%27%20viewBox%3D%270%200%20400%2073%27%3E%3Crect%20width%3D%27400%27%20height%3D%2773%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-srcset=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/the-real-grinding-amount-\u03c3-200x37.png 200w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/the-real-grinding-amount-\u03c3-300x55.png 300w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/the-real-grinding-amount-\u03c3-400x73.png 400w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/the-real-grinding-amount-\u03c3.png 600w\" data-sizes=\"auto\" data-orig-sizes=\"(max-width: 400px) 100vw, 400px\" \/><\/p>\n<p>\u03c3<sub>max<\/sub> can be obtained by taking the derivative of above formula asphericity \u03c3, formula y<\/p>\n<p><img decoding=\"async\" class=\"lazyload aligncenter wp-image-11170 size-fusion-400\" src=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-y-400x102.png\" data-orig-src=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-y-400x102.png\" alt=\"\" width=\"400\" height=\"102\" srcset=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27400%27%20height%3D%27102%27%20viewBox%3D%270%200%20400%20102%27%3E%3Crect%20width%3D%27400%27%20height%3D%27102%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-srcset=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-y-200x51.png 200w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-y-300x76.png 300w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-y-400x102.png 400w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-y-600x153.png 600w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-y-669x172.png 669w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-y.png 676w\" data-sizes=\"auto\" data-orig-sizes=\"(max-width: 400px) 100vw, 400px\" \/><\/p>\n<p>The maximum grinding amount is \u03c3<sub>max<\/sub>=0.00133mm.<\/p>\n<div id=\"attachment_11171\" style=\"width: 610px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" aria-describedby=\"caption-attachment-11171\" class=\"lazyload size-fusion-600 wp-image-11171\" src=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Fig.-3-Grinding-Amount-Diagram-600x401.png\" data-orig-src=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Fig.-3-Grinding-Amount-Diagram-600x401.png\" alt=\"\" width=\"600\" height=\"401\" srcset=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27600%27%20height%3D%27401%27%20viewBox%3D%270%200%20600%20401%27%3E%3Crect%20width%3D%27600%27%20height%3D%27401%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-srcset=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Fig.-3-Grinding-Amount-Diagram-200x134.png 200w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Fig.-3-Grinding-Amount-Diagram-300x200.png 300w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Fig.-3-Grinding-Amount-Diagram-400x267.png 400w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Fig.-3-Grinding-Amount-Diagram-600x401.png 600w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Fig.-3-Grinding-Amount-Diagram-768x513.png 768w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Fig.-3-Grinding-Amount-Diagram-800x534.png 800w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Fig.-3-Grinding-Amount-Diagram.png 933w\" data-sizes=\"auto\" data-orig-sizes=\"(max-width: 600px) 100vw, 600px\" \/><p id=\"caption-attachment-11171\" class=\"wp-caption-text\">Fig. 3 Grinding Amount Diagram<\/p><\/div>\n<p>Table 1 shows the relevant quantities of each belt and the final asphericity and grinding quantity according to formula\u00a0asphericity \u03c3 and the formula of the real grinding amount \u03c3, and translation requirements. Figure 3 is a graph of the amount of grinding drawn according to the \u03c3 value in Table 1.<\/p>\n<p style=\"text-align: center;\"><strong>Table 1<\/strong><\/p>\n<p><img decoding=\"async\" class=\"lazyload aligncenter wp-image-11172 size-fusion-800\" src=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Table-1-800x337.png\" data-orig-src=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Table-1-800x337.png\" alt=\"\" width=\"800\" height=\"337\" srcset=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27800%27%20height%3D%27337%27%20viewBox%3D%270%200%20800%20337%27%3E%3Crect%20width%3D%27800%27%20height%3D%27337%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-srcset=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Table-1-200x84.png 200w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Table-1-300x126.png 300w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Table-1-400x168.png 400w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Table-1-600x252.png 600w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Table-1-768x323.png 768w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Table-1-800x337.png 800w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Table-1-1024x431.png 1024w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Table-1-1200x505.png 1200w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Table-1-1536x646.png 1536w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Table-1.png 1740w\" data-sizes=\"auto\" data-orig-sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<\/div><div class=\"fusion-title title fusion-title-8 fusion-sep-none fusion-title-text fusion-title-size-three\"><h3 class=\"fusion-title-heading title-heading-left fusion-responsive-typography-calculated\" style=\"margin:0;--fontSize:24;line-height:1.3;\"><h3>Vertical inspection of sub-aperture<\/h3><\/h3><\/div><div class=\"fusion-text fusion-text-8\"><p>Accurate inspection is the premise of guiding processing. In a sense, the effective and accurate inspection of the mirror surface in polishing is more important than the processing itself.<\/p>\n<\/div><div class=\"fusion-title title fusion-title-9 fusion-sep-none fusion-title-text fusion-title-size-four\"><h4 class=\"fusion-title-heading title-heading-left fusion-responsive-typography-calculated\" style=\"margin:0;--fontSize:22;--minFontSize:22;line-height:1.34;\"><h4>1. Sub-aperture vertical inspection<\/h4><\/h4><\/div><div class=\"fusion-text fusion-text-9\"><p>Usually during manual grinding, a plane mirror matched with a parabolic parent is used to form a self-aligning inspection, or a collimator is used to generate a parallel beam, and knife-edge inspection or interference inspection is performed at the focus. Obviously, it is unrealistic to realize self-calibration inspection in the range of caliber up to 1050mm. It is a relatively mature method to use offner compensation method to perform compensation test on paraboloids. However, because the diameter of the paraboloid parent body is too large, it is not easy to turn over during processing, and it is not convenient to form a horizontal detection optical path, but only vertical inspection can be performed. In the vertical inspection, the installation and adjustment of the compensator are extremely difficult and forced to give up.<\/p>\n<p>To this end, we boldly adopted a new inspection method &#8211; sub-aperture vertical inspection method. The part of the off-axis sub-aperture required in the paraboloid matrix is listed as the inspection area, and a \u03a6420mm standard plane mirror is used for self-collimating reflection, and the sub-aperture shadow star point vertical inspection is realized by the knife edge on the geometric focus of the paraboloid matrix. Figure 4 is a vertical inspection light path diagram.<\/p>\n<div id=\"attachment_11173\" style=\"width: 610px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" aria-describedby=\"caption-attachment-11173\" class=\"lazyload size-fusion-600 wp-image-11173\" src=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Fig.-4-Optical-path-diagram-of-vertical-inspection-600x414.jpg\" data-orig-src=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Fig.-4-Optical-path-diagram-of-vertical-inspection-600x414.jpg\" alt=\"\" width=\"600\" height=\"414\" srcset=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27600%27%20height%3D%27414%27%20viewBox%3D%270%200%20600%20414%27%3E%3Crect%20width%3D%27600%27%20height%3D%27414%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-srcset=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Fig.-4-Optical-path-diagram-of-vertical-inspection-200x138.jpg 200w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Fig.-4-Optical-path-diagram-of-vertical-inspection-300x207.jpg 300w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Fig.-4-Optical-path-diagram-of-vertical-inspection-400x276.jpg 400w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Fig.-4-Optical-path-diagram-of-vertical-inspection-600x414.jpg 600w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Fig.-4-Optical-path-diagram-of-vertical-inspection-768x530.jpg 768w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Fig.-4-Optical-path-diagram-of-vertical-inspection-800x552.jpg 800w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Fig.-4-Optical-path-diagram-of-vertical-inspection.jpg 819w\" data-sizes=\"auto\" data-orig-sizes=\"(max-width: 600px) 100vw, 600px\" \/><p id=\"caption-attachment-11173\" class=\"wp-caption-text\">Fig. 4 Optical path diagram of vertical inspection<\/p><\/div>\n<\/div><div class=\"fusion-title title fusion-title-10 fusion-sep-none fusion-title-text fusion-title-size-four\"><h4 class=\"fusion-title-heading title-heading-left fusion-responsive-typography-calculated\" style=\"margin:0;--fontSize:22;--minFontSize:22;line-height:1.34;\"><h4>2. Analysis of inspection accuracy<\/h4><\/h4><\/div><div class=\"fusion-text fusion-text-10\"><p>The vertical inspection of sub-apertures during processing is asymmetric inspection. The wavefront deformation caused by the defocusing of the geometric focus and the wavefront deformation caused by the inclination of the standard plane mirror relative to the optical axis will seriously affect the recognition and judgment of the surface shape of the processed mirror. . The following discusses the positioning accuracy between the detection elements in the inspection. The defocusing of the knife-edge star point to the geometric focus can be divided into two cases: axial defocusing and lateral defocusing. According to D. \u0422. Priyaev&#8217;s theoretical formula.<\/p>\n<p>(1) when only the axial defocus<\/p>\n<p><img decoding=\"async\" class=\"lazyload aligncenter wp-image-11174\" src=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-N-400x125.png\" data-orig-src=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-N-400x125.png\" alt=\"\" width=\"300\" height=\"94\" srcset=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27300%27%20height%3D%2794%27%20viewBox%3D%270%200%20300%2094%27%3E%3Crect%20width%3D%27300%27%20height%3D%2794%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-srcset=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-N-200x63.png 200w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-N-300x94.png 300w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-N-400x125.png 400w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-N.png 550w\" data-sizes=\"auto\" data-orig-sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>In the formula,<br \/>\nN \u2013 defocusing wavefront deformation;<br \/>\n\u0394x \u2013 axial defocusing;<br \/>\nA = 2y\/f \u2013 is the relative diameter of the paraboloid.<\/p>\n<p>(2) When only laterally defocused<\/p>\n<p><img decoding=\"async\" class=\"lazyload aligncenter wp-image-11175 size-fusion-400\" src=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-N-2-400x109.png\" data-orig-src=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-N-2-400x109.png\" alt=\"\" width=\"400\" height=\"109\" srcset=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27400%27%20height%3D%27109%27%20viewBox%3D%270%200%20400%20109%27%3E%3Crect%20width%3D%27400%27%20height%3D%27109%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-srcset=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-N-2-200x54.png 200w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-N-2-300x82.png 300w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-N-2-400x109.png 400w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-N-2-600x163.png 600w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-N-2.png 668w\" data-sizes=\"auto\" data-orig-sizes=\"(max-width: 400px) 100vw, 400px\" \/><\/p>\n<p>Assuming that the maximum wavefront error allowed by defocusing is \u03bb\/8 during inspection, then the maximum allowable axial focus adjustment of the knife-edge star point.<\/p>\n<p><img decoding=\"async\" class=\"lazyload aligncenter size-fusion-600 wp-image-11176\" src=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-\u0394x-600x95.png\" data-orig-src=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-\u0394x-600x95.png\" alt=\"\" width=\"600\" height=\"95\" srcset=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27600%27%20height%3D%2795%27%20viewBox%3D%270%200%20600%2095%27%3E%3Crect%20width%3D%27600%27%20height%3D%2795%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-srcset=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-\u0394x-200x32.png 200w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-\u0394x-300x47.png 300w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-\u0394x-400x63.png 400w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-\u0394x-600x95.png 600w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-\u0394x-768x121.png 768w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-\u0394x-800x126.png 800w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-\u0394x-1024x162.png 1024w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-\u0394x.png 1102w\" data-sizes=\"auto\" data-orig-sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/p>\n<p>The maximum allowable amount of lateral focus adjustment of knife-edge star point<\/p>\n<p><img decoding=\"async\" class=\"lazyload aligncenter size-fusion-600 wp-image-11177\" src=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-\u0394y-600x96.png\" data-orig-src=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-\u0394y-600x96.png\" alt=\"\" width=\"600\" height=\"96\" srcset=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27600%27%20height%3D%2796%27%20viewBox%3D%270%200%20600%2096%27%3E%3Crect%20width%3D%27600%27%20height%3D%2796%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-srcset=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-\u0394y-200x32.png 200w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-\u0394y-300x48.png 300w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-\u0394y-400x64.png 400w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-\u0394y-600x96.png 600w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-\u0394y-768x123.png 768w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-\u0394y-800x128.png 800w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-\u0394y-1024x164.png 1024w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-\u0394y.png 1134w\" data-sizes=\"auto\" data-orig-sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/p>\n<p>(3) The allowable amount of the inclination angle error of the plane mirror, according to the precise analytical formula<\/p>\n<p><img decoding=\"async\" class=\"lazyload aligncenter wp-image-11178 size-medium\" src=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-N-3-300x90.png\" data-orig-src=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-N-3-300x90.png\" alt=\"\" width=\"300\" height=\"90\" srcset=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27300%27%20height%3D%2790%27%20viewBox%3D%270%200%20300%2090%27%3E%3Crect%20width%3D%27300%27%20height%3D%2790%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-srcset=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-N-3-200x60.png 200w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-N-3-300x90.png 300w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-N-3-400x120.png 400w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-N-3.png 494w\" data-sizes=\"auto\" data-orig-sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Assuming that the maximum wavefront error allowed by the tilt of the plane mirror is \u03bb\/8, then the maximum tilt angle of the plane mirror is<\/p>\n<p><img decoding=\"async\" class=\"lazyload aligncenter size-fusion-400 wp-image-11179\" src=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-\u03c9-400x97.png\" data-orig-src=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-\u03c9-400x97.png\" alt=\"\" width=\"400\" height=\"97\" srcset=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27400%27%20height%3D%2797%27%20viewBox%3D%270%200%20400%2097%27%3E%3Crect%20width%3D%27400%27%20height%3D%2797%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-srcset=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-\u03c9-200x49.png 200w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-\u03c9-300x73.png 300w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-\u03c9-400x97.png 400w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-\u03c9-600x146.png 600w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-\u03c9-768x187.png 768w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/formula-\u03c9.png 774w\" data-sizes=\"auto\" data-orig-sizes=\"(max-width: 400px) 100vw, 400px\" \/><\/p>\n<p>It can be seen that during the inspection, the adjustment of the star point of the knife edge and the placement of the plane mirror are very strict.<\/p>\n<\/div><div class=\"fusion-title title fusion-title-11 fusion-sep-none fusion-title-text fusion-title-size-three\"><h3 class=\"fusion-title-heading title-heading-left fusion-responsive-typography-calculated\" style=\"margin:0;--fontSize:24;line-height:1.3;\"><h3>Process<\/h3><\/h3><\/div><div class=\"fusion-text fusion-text-11\"><p>The entire process technology implementation process, including: rough grinding, forming, fine grinding, polishing and digging off-axis mirrors and other processes are all carried out on a \u03a61.6m mirror grinding machine.<\/p>\n<\/div><div class=\"fusion-title title fusion-title-12 fusion-sep-none fusion-title-text fusion-title-size-four\"><h4 class=\"fusion-title-heading title-heading-left fusion-responsive-typography-calculated\" style=\"margin:0;--fontSize:22;--minFontSize:22;line-height:1.34;\"><h4>1. Coarse grinding, fine grinding<\/h4><\/h4><\/div><div class=\"fusion-text fusion-text-12\"><p>The technical point of rough grinding and fine grinding is to strictly control the accuracy of the starting spherical radius and the uniformity of the radius on the same annular belt. Check after finishing grinding.<\/p>\n<p>Meridian radius deviation: \u0394R<sub>y<\/sub>=88mm;<br \/>\nSagittal radius deviation: \u0394R<sub>x<\/sub>=92mm;<br \/>\nAstigmatism deviation: \u0394R (x-y) <sub>max<\/sub>=8mm.<\/p>\n<p>The radial radius is large in the center and small on the side; the radii that are perpendicular to each other have good coincidence, and the deviation is small, that is, the mirror symmetry is good.<\/p>\n<\/div><div class=\"fusion-title title fusion-title-13 fusion-sep-none fusion-title-text fusion-title-size-four\"><h4 class=\"fusion-title-heading title-heading-left fusion-responsive-typography-calculated\" style=\"margin:0;--fontSize:22;--minFontSize:22;line-height:1.34;\"><h4>2. Polishing<\/h4><\/h4><\/div><div class=\"fusion-text fusion-text-13\"><p>Because the relative diameter D\/f of the parabolic parent body is small and the asphericity is not large, the polishing work is divided into two steps. First change the specular highlight to the starting aspheric radius (closest radius). Then on this basis, continue the light modification, that is, asphericization.<\/p>\n<p>The structure radius of each ring zone of the parabolic mirror is different. For the convenience and feasibility of changing the surface shape of the light, we have made 8 polishing pads with different diameters and shapes. First, use the large plate and the middle plate to modify the mirror surface, and then use various small plastic plates to shave the surface. After the spherical aberration is eliminated, a large-diameter plastic disc is finally used to smooth the entire mirror surface to the design surface shape accuracy requirements.<\/p>\n<\/div><div class=\"fusion-title title fusion-title-14 fusion-sep-none fusion-title-text fusion-title-size-four\"><h4 class=\"fusion-title-heading title-heading-left fusion-responsive-typography-calculated\" style=\"margin:0;--fontSize:22;--minFontSize:22;line-height:1.34;\"><h4>3. Quantitative final inspection<\/h4><\/h4><\/div><div class=\"fusion-text fusion-text-14\"><p>The timely inspection of the sub-aperture in the polishing process is a qualitative inspection and cannot provide quantitative inspection data. After the processing is completed, we use the method of chemical coating to coat the effective sub-aperture part of the paraboloid parent with chemical silver film to increase the reflectivity of the coated surface. Quantitative laser interferometry was then performed on the mirror surface. Figure 5 is the inspection light path diagram.<\/p>\n<p>The interference fringe sampling processing results, the surface shape accuracy reaches \u03bb\/8.4, and passes the user&#8217;s acceptance.<\/p>\n<div id=\"attachment_11180\" style=\"width: 810px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" aria-describedby=\"caption-attachment-11180\" class=\"lazyload wp-image-11180 size-fusion-800\" src=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Fig.-5-Inspection-light-path-diagram-800x514.jpg\" data-orig-src=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Fig.-5-Inspection-light-path-diagram-800x514.jpg\" alt=\"\" width=\"800\" height=\"514\" srcset=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27800%27%20height%3D%27514%27%20viewBox%3D%270%200%20800%20514%27%3E%3Crect%20width%3D%27800%27%20height%3D%27514%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-srcset=\"https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Fig.-5-Inspection-light-path-diagram-200x129.jpg 200w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Fig.-5-Inspection-light-path-diagram-300x193.jpg 300w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Fig.-5-Inspection-light-path-diagram-400x257.jpg 400w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Fig.-5-Inspection-light-path-diagram-460x295.jpg 460w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Fig.-5-Inspection-light-path-diagram-600x386.jpg 600w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Fig.-5-Inspection-light-path-diagram-768x494.jpg 768w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Fig.-5-Inspection-light-path-diagram-800x514.jpg 800w, https:\/\/www.szlaser.com\/wp-content\/uploads\/2022\/11\/Fig.-5-Inspection-light-path-diagram.jpg 823w\" data-sizes=\"auto\" data-orig-sizes=\"(max-width: 800px) 100vw, 800px\" \/><p id=\"caption-attachment-11180\" class=\"wp-caption-text\">Fig. 5 Inspection light path diagram<\/p><\/div>\n<\/div><div class=\"fusion-title title fusion-title-15 fusion-sep-none fusion-title-text fusion-title-size-four\"><h4 class=\"fusion-title-heading title-heading-left fusion-responsive-typography-calculated\" style=\"margin:0;--fontSize:22;--minFontSize:22;line-height:1.34;\"><h4>4. Set of digging<\/h4><\/h4><\/div><div class=\"fusion-text fusion-text-15\"><p>How to keep the mirror surface from being damaged and scratched in the sleeve excavation is the core problem of sleeve excavation off-axis mirror.<\/p>\n<p>To this end, before digging, first brush a pure glue layer with a thickness of about 5mm on the mirror surface to protect the mirror surface.<\/p>\n<p>It effectively blocks water and sand from immersing in the mirror surface during sleeve digging. The sleeve round tool is surrounded by three steel sheets with a thickness of about 3mm to form an open cylinder, and a 1.2m radial drilling machine is used as the rotational driving force for the sleeve digging.<\/p>\n<p>During sleeve digging, the speed is 60r\/min, and the manual micro-feed is used. The mirror cover was dug into a \u03a6420mm off-axis mirror and re-checked, and the surface shape accuracy did not change.<\/p>\n<\/div><div class=\"fusion-text fusion-text-16\"><p>We have completed the processing by adopting the method of trimming the tape of the small plate, smoothing the large plate, and gradually advancing. The processing of \u03a6300mm, \u03a6410mm, \u03a6470mm spherical light reflector and \u03a6630mm aspherical light reflector is completed by the above processing method. Figure 7 shows the shape of the \u03a6470mm light spherical fused silica reflecting mirror measured by ZYGO Mark IV laser interferometer, and the PV value is 0. 117\u03bb, the RMS value is 0.024\u03bb (\u03bb=632.8nm)<\/p>\n<\/div><div class=\"fusion-title title fusion-title-16 fusion-sep-none fusion-title-text fusion-title-size-three\"><h3 class=\"fusion-title-heading title-heading-left fusion-responsive-typography-calculated\" style=\"margin:0;--fontSize:24;line-height:1.3;\"><h3>Development of high-efficiency broadband reflective film<\/h3><\/h3><\/div><div class=\"fusion-text fusion-text-17\"><p>In order to ensure that the fused silica light reflector has a very high reflectivity at 3.8\u03bcm, and at the same time make the visible and infrared regions have a high reflectivity, Ag is selected as the reflective film material. In order to enhance the reflectivity of the silver film at 3.8\u03bcm, and at the same time to ensure high reflectivity in the visible and infrared bands, the selected medium must have low light absorption from the visible to infrared bands. Based on this requirement, ThF<sup>4<\/sup>, YbF<sup>2<\/sup>, PbF<sup>2<\/sup>, BaF<sup>2<\/sup>, etc. can be used as low-refractive index materials, and ZnSe, ZnS can be used as high-refractive index materials. In the comprehensive analysis, we choose YbF3 and ZnS as the enhanced high and low refractive index film pair for the Ag layer.<\/p>\n<p>As far as the light-weight primary mirror is concerned, in order to ensure high reflectivity in the visible region, we choose a pair of dielectric films. The whole membrane system is designed as: Sub\/Ag (YbF<sup>3<\/sup>\/ZnS) Air.<\/p>\n<p>The relative measurement was carried out with a Hitachi 340 spectrophotometer.<br \/>\nThe standard reflector was an all-dielectric band total reflection film developed by Optoelectronics, and the reflectivity was greater than 99.99%. 5%.<br \/>\nThe reflectance measurement results are as follows: 0.50\u03bcm ~ 0.85\u03bcm reflectivity greater than 98.5%;<br \/>\nThe reflectivity of 30\u03bcm is greater than 99.5%; 8.00\u03bcm ~ 12.00\u03bcm reflectivity greater than 97.0%.<\/p>\n<p>The light-duty fused silica mirror film has been tested in humidity, high and low temperature and salt water, and all conditions of the test meet the requirements of GB1320-77.<\/p>\n<\/div><div style=\"text-align:right;\"><a class=\"fusion-button button-flat fusion-button-default-size button-default fusion-button-default button-1 fusion-button-default-span fusion-button-default-type\" target=\"_self\" href=\"https:\/\/www.szlaser.com\/index.php\/measurement-of-off-axis-paraboloids\/\"><span class=\"fusion-button-text awb-button__text awb-button__text--default\">Contrastive measurement of off-axis paraboloids &gt;<\/span><\/a><\/div><\/div><\/div><\/div><\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":7,"featured_media":0,"parent":8230,"menu_order":158,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"footnotes":""},"class_list":["post-11153","page","type-page","status-publish","hentry"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v18.7 (Yoast SEO v25.8) - 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