{"id":1243,"date":"2024-09-07T12:44:13","date_gmt":"2024-09-07T12:44:13","guid":{"rendered":"http:\/\/robinluo.top\/?p=1243"},"modified":"2024-09-07T13:36:19","modified_gmt":"2024-09-07T13:36:19","slug":"zernike-noll-%e5%ba%8f%e5%88%97","status":"publish","type":"post","link":"https:\/\/robinluo.top\/?p=1243","title":{"rendered":"Zernike Noll \u5e8f\u5217"},"content":{"rendered":"\n

zernike \u8f93\u5165\u5404\u5bf9\u5e94\u70b9 \u5bf9\u5e94\u7684\u5dee\u503c \u5c31\u53ef\u4ee5\u8ba1\u7b97\u51fa\u50cf\u5dee<\/p>\n\n\n\n

<\/p>\n\n\n\n

\u6cfd\u5c3c\u514b\u591a\u9879\u5f0f\u662f\u4e00\u4e2a\u6b63\u4ea4\u591a\u9879\u5f0f\uff0c\u5206\u4e3a\u5947\u5076\u4e24\u7c7b\u3002<\/p>\n\n\n\n

\u5947\u591a\u9879\u5f0f\uff1a<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

\u5076\u591a\u9879\u5f0f\uff1a<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

\u5176\u4e2d\uff1a<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

\u8fd9\u91ccfai\u4e3a\u65b9\u4f4d\u89d2\uff0c\u8303\u56f4[0-2pi]\uff1bp\u4e3a\u5f84\u5411\u8ddd\u79bb\uff0c\u8303\u56f4[0,1]\uff1bn-m\u5927\u4e8e\u7b49\u4e8e0\uff1b<\/p>\n\n\n\n

\u5982\u679cn-m=0\uff0c\u5219R=0\u3002<\/p>\n\n\n\n

\u6839\u636e\u4e0d\u540c\u7684m\u548cn\u503c\uff0c\u53ef\u4ee5\u5f97\u5230\u4e0d\u540c\u7684\u591a\u9879\u5f0f\uff0c\u7528j\u8868\u793a\u4e0d\u540c\u7684\u591a\u9879\u5f0f\uff0c\u901a\u5e38\u79f0\u4e3aNoll\u5e8f\u5217\uff1a<\/p>\n\n\n\n

n,m<\/th>0,0<\/td>1,1<\/td>1,\u22121<\/td>2,0<\/td>2,\u22122<\/td><\/tr>
j<\/th>1<\/td>2<\/td>3<\/td>4<\/td>5<\/td><\/tr>
n,m<\/th>2,2<\/td>3,\u22121<\/td>3,1<\/td>3,\u22123<\/td>3,3<\/td><\/tr>
j<\/th>6<\/td>7<\/td>8<\/td>9<\/td>10<\/td><\/tr>
n,m<\/th>4,0<\/td>4,2<\/td>4,\u22122<\/td>4,4<\/td>4,\u22124<\/td><\/tr>
j<\/th>11<\/td>12<\/td>13<\/td>14<\/td>15<\/td><\/tr>
n,m<\/th>5,1<\/td>5,\u22121<\/td>5,3<\/td>5,\u22123<\/td>5,5<\/td><\/tr>
j<\/th>16<\/td>17<\/td>18<\/td>19<\/td>20<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

jtonmtable \u5bf9\u5e94\u7684\u5c31\u662f\u8fd9\u4e2a\u5e8f\u5217<\/p>\n\n\n\n

n m<\/p>\n\n\n\n

1 0 0
2 1 1
3 1 -1
4 2 0
5 2 -2
6 2 2
7 3 -1
8 3 1
9 3 -3
10 3 3
11 4 0
12 4 2
13 4 -2
14 4 4
15 4 -4<\/p>\n\n\n\n

<\/p>\n\n\n\n

azimtable \u5bf9\u5e94\u7684\u5c31\u662f cos sin \u89d2\u5ea6\u7684\u7cfb\u6570<\/p>\n\n\n\n

cos sin <\/p>\n\n\n\n

1 0 0
2 1 0
3 0 1
4 0 0
5 0 2
6 2 0
7 0 1
8 1 0
9 0 3
10 3 0
11 0 0
12 2 0
13 0 2
14 4 0
15 0 4<\/p>\n\n\n\n

<\/p>\n\n\n\n

radialtable \u5bf9\u5e94\u7684\u5305\u62ec \u6839\u53f7\u7cfb\u6570\u4e86<\/p>\n\n\n\n

<\/p>\n\n\n\n

Noll\u5e8f\u5217\u524d15\u9879\u6cfd\u5c3c\u514b\u591a\u9879\u5f0f\u4e3a\uff1a<\/p>\n\n\n\n

1<\/td>1<\/td><\/tr>
2<\/td>2\u03c1cos\u03b8<\/td><\/tr>
3<\/td>2\u03c1sin\u03b8<\/td><\/tr>
4<\/td>\u221a3(2\u03c12\u22121)<\/td><\/tr>
5<\/td>\u221a6\u03c12sin2\u03b8<\/td><\/tr>
6<\/td>\u221a6\u03c12cos2\u03b8<\/td><\/tr>
7<\/td>\u221a3(3\u03c13\u22122\u03c1)sin\u03b8<\/td><\/tr>
8<\/td>\u221a3(3\u03c13\u22122\u03c1)cos\u03b8<\/td><\/tr>
9<\/td>\u221a8\u03c13sin3\u03b8<\/td><\/tr>
10<\/td>\u221a8\u03c13cos3\u03b8<\/td><\/tr>
11<\/td>\u221a5(6\u03c14\u22126\u03c12+1)<\/td><\/tr>
12<\/td>\u221a10(4\u03c14\u22123\u03c12)cos2\u03b8<\/td><\/tr>
13<\/td>\u221a10(4\u03c14\u22123\u03c12)sin2\u03b8<\/td><\/tr>
14<\/td>\u221a10\u03c14cos4\u03b8<\/td><\/tr>
15<\/td>\u221a10\u03c14sin4\u03b8<\/td><\/tr><\/tbody><\/table><\/figure>\n","protected":false},"excerpt":{"rendered":"

zernike \u8f93\u5165\u5404\u5bf9\u5e94\u70b9 \u5bf9\u5e94\u7684\u5dee\u503c \u5c31\u53ef\u4ee5\u8ba1\u7b97\u51fa\u50cf\u5dee \u6cfd\u5c3c\u514b\u591a\u9879\u5f0f\u662f\u4e00\u4e2a\u6b63\u4ea4\u591a\u9879\u5f0f\uff0c\u5206\u4e3a\u5947\u5076\u4e24\u7c7b\u3002 \u5947\u591a\u9879\u5f0f\uff1a \u5076\u591a\u9879\u5f0f\uff1a \u5176\u4e2d\uff1a \u8fd9\u91ccfai\u4e3a\u65b9\u4f4d\u89d2\uff0c\u8303\u56f4[0-2pi]\uff1bp\u4e3a\u5f84\u5411\u8ddd\u79bb\uff0c\u8303\u56f4[0,1]\uff1bn-m\u5927\u4e8e\u7b49\u4e8e0\uff1b \u5982\u679cn-m=0\uff0c\u5219R=0\u3002 \u6839\u636e\u4e0d\u540c\u7684m\u548cn\u503c\uff0c\u53ef\u4ee5\u5f97\u5230\u4e0d\u540c\u7684\u591a\u9879\u5f0f\uff0c\u7528j\u8868\u793a\u4e0d\u540c\u7684\u591a\u9879\u5f0f\uff0c\u901a\u5e38\u79f0\u4e3aNoll\u5e8f\u5217\uff1a n,m 0,0 1,1 1,\u22121 2,0 2,\u22122 j 1 2 3 4 5 n,m 2,2 3,\u22121 3,1 3,\u22123 3,3 j 6 7 8 9 10 n,m 4,0 4,2 4,\u22122 4,4 4,\u22124 j 11 12 13 14 15 n,m 5,1 5,\u22121 5,3 5,\u22123 5,5 j 16 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[117],"tags":[183,182],"_links":{"self":[{"href":"https:\/\/robinluo.top\/index.php?rest_route=\/wp\/v2\/posts\/1243"}],"collection":[{"href":"https:\/\/robinluo.top\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/robinluo.top\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/robinluo.top\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/robinluo.top\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1243"}],"version-history":[{"count":6,"href":"https:\/\/robinluo.top\/index.php?rest_route=\/wp\/v2\/posts\/1243\/revisions"}],"predecessor-version":[{"id":1252,"href":"https:\/\/robinluo.top\/index.php?rest_route=\/wp\/v2\/posts\/1243\/revisions\/1252"}],"wp:attachment":[{"href":"https:\/\/robinluo.top\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1243"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/robinluo.top\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1243"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/robinluo.top\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1243"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}