Problem 1000. Image Processing 004: Zernike Coefficients

Created by Richard Zapor

Solve Later

{"parts":[{"partUri":"/matlab/document.xml","contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?><w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Fit Zernike Terms to a wavefront.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>The class notes of</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://www.visualopticslab.com/OPTI535/Lectures/Class06_08.pdf\"><w:r><w:t>Schwiegerling UofA</w:t></w:r></w:hyperlink><w:r><w:t> on ANSI Standard Zernike terms is the basis for this challenge. Pages 13 and 14 give the term definitions implemented in the zern_data_v01.m routine provided in the function template.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"center\"/></w:pPr><w:customXml w:element=\"image\"><w:customXmlPr><w:attr w:name=\"height\" w:val=\"-1\"/><w:attr w:name=\"width\" w:val=\"-1\"/><w:attr w:name=\"verticalAlign\" w:val=\"baseline\"/><w:attr w:name=\"altText\" w:val=\"\"/><w:attr w:name=\"relationshipId\" w:val=\"rId1\"/></w:customXmlPr></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>ANSI Standard Zernike Chart:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Algorithm Description:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[M=surface array to be fit by Zernike terms; \n-valid data is circle of normalized radius<=1\nUse the R and T arrays to create the A array\nR=radial normalized distance from center of array\nT=angular radian value from center of array\nA=fitting array [valid_data_pts,terms]\n\nCreate A * z_fit = M(valid_data_pts)\n[valid_pts,terms] * [terms,1] = [valid_pts,1]\n\nLoop term=0:terms-1\n- Create the 2-D array of z-terms uisng z=zern_data_v01(term,R,T)\n- A(:,term+1) = z(valid_data_pts)\nEnd Loop\n\nSolve for z_fit: pinv(A)*M(valid_pts)  or A\\M(valid_pts)]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Inputs:</w:t></w:r><w:r><w:t> [M N R T] where N is number of Zernike terms for fit</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Outputs:</w:t></w:r><w:r><w:t> [v] Zernike fit vector of length N</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Creation of the M surface and expected v fit vector can be seen in the Test Suite.</w:t></w:r></w:p></w:body></w:document>","relationship":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/image","target":"/media/image1.JPEG","relationshipId":"rId1"}]},{"partUri":"/media/image1.JPEG","contentType":"image/JPEG","content":"data:image/JPEG;base64,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","relationship":null}],"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","target":"/matlab/document.xml","relationshipId":"rId1"}]}

<div style = "text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; "><div style="block-size: 888.85px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 444.433px; transform-origin: 407px 444.433px; vertical-align: baseline; "><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 109.15px 7.91667px; transform-origin: 109.15px 7.91667px; unicode-bidi: normal; "><span style="font-weight: 700; ">Fit Zernike Terms to a wavefront.</span></span></div><div style="block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 56.7833px 7.91667px; transform-origin: 56.7833px 7.91667px; unicode-bidi: normal; "><span style="">The class notes of</span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; "><span style=""> </span></span><a target='_blank' href = "http://www.visualopticslab.com/OPTI535/Lectures/Class06_08.pdf"><span style=""><span style="">Schwiegerling UofA</span></span></a><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 253.6px 7.91667px; transform-origin: 253.6px 7.91667px; unicode-bidi: normal; "><span style=""> on ANSI Standard Zernike terms is the basis for this challenge. Pages 13 and 14 give the term definitions implemented in the zern_data_v01.m routine provided in the function template.</span></span></div><div style="block-size: 319.917px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 159.967px; text-align: center; transform-origin: 384px 159.967px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><img class="imageNode" style="vertical-align: baseline" 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" data-image-state="image-loaded"></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 92.9667px 7.91667px; transform-origin: 92.9667px 7.91667px; unicode-bidi: normal; "><span style="">ANSI Standard Zernike Chart:</span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 75.8333px 7.91667px; transform-origin: 75.8333px 7.91667px; unicode-bidi: normal; "><span style="font-weight: 700; ">Algorithm Description:</span></span></div><div style="background-color: rgb(247, 247, 247); block-size: 326.933px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 163.467px; transform-origin: 404px 163.467px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; "><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 169.4px 7.91667px; transform-origin: 169.4px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; perspective-origin: 61.6px 7.91667px; transform-origin: 61.6px 7.91667px; ">M=surface array </span><span style="border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 100.1px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 100.1px 7.91667px; ">to be fit by Zernike terms</span><span style="margin-inline-end: 0px; margin-right: 0px; perspective-origin: 7.7px 7.91667px; transform-origin: 7.7px 7.91667px; ">; </span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 173.25px 7.91667px; transform-origin: 173.25px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; perspective-origin: 46.2px 7.91667px; transform-origin: 46.2px 7.91667px; ">-valid data </span><span style="border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 127.05px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 127.05px 7.91667px; ">is circle of normalized radius&lt;=1</span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 169.4px 7.91667px; transform-origin: 169.4px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; perspective-origin: 15.4px 7.91667px; transform-origin: 15.4px 7.91667px; ">Use </span><span style="border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 154px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 154px 7.91667px; ">the R and T arrays to create the A array</span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 188.65px 7.91667px; transform-origin: 188.65px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; perspective-origin: 77px 7.91667px; transform-origin: 77px 7.91667px; ">R=radial normalized </span><span style="border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 111.65px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 111.65px 7.91667px; ">distance from center of array</span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 165.55px 7.91667px; transform-origin: 165.55px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; perspective-origin: 65.45px 7.91667px; transform-origin: 65.45px 7.91667px; ">T=angular radian </span><span style="border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 100.1px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 100.1px 7.91667px; ">value from center of array</span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 146.3px 7.91667px; transform-origin: 146.3px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; perspective-origin: 61.6px 7.91667px; transform-origin: 61.6px 7.91667px; ">A=fitting array </span><span style="border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 84.7px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 84.7px 7.91667px; ">[valid_data_pts,terms]</span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 7.91667px; transform-origin: 0px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; "></span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 138.6px 7.91667px; transform-origin: 138.6px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; perspective-origin: 26.95px 7.91667px; transform-origin: 26.95px 7.91667px; ">Create </span><span style="border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 111.65px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 111.65px 7.91667px; ">A * z_fit = M(valid_data_pts)</span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 173.25px 7.91667px; transform-origin: 173.25px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; ">[valid_pts,terms] * [terms,1] = [valid_pts,1]</span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 7.91667px; transform-origin: 0px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; "></span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 73.15px 7.91667px; transform-origin: 73.15px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; perspective-origin: 19.25px 7.91667px; transform-origin: 19.25px 7.91667px; ">Loop </span><span style="border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 53.9px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 53.9px 7.91667px; ">term=0:terms-1</span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 250.25px 7.91667px; transform-origin: 250.25px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; perspective-origin: 50.05px 7.91667px; transform-origin: 50.05px 7.91667px; ">- Create the </span><span style="border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 200.2px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 200.2px 7.91667px; ">2-D array of z-terms uisng z=zern_data_v01(term,R,T)</span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 127.05px 7.91667px; transform-origin: 127.05px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; ">- A(:,term+1) = z(valid_data_pts)</span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 30.8px 7.91667px; transform-origin: 30.8px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; perspective-origin: 15.4px 7.91667px; transform-origin: 15.4px 7.91667px; ">End </span><span style="border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 15.4px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 15.4px 7.91667px; ">Loop</span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 7.91667px; transform-origin: 0px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; "></span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 215.6px 7.91667px; transform-origin: 215.6px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; perspective-origin: 23.1px 7.91667px; transform-origin: 23.1px 7.91667px; ">Solve </span><span style="border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 119.35px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 119.35px 7.91667px; ">for z_fit: pinv(A)*M(valid_pts)</span><span style="margin-inline-end: 0px; margin-right: 0px; perspective-origin: 7.7px 7.91667px; transform-origin: 7.7px 7.91667px; ">  </span><span style="border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 65.45px 7.91667px; text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 65.45px 7.91667px; ">or A\M(valid_pts)</span></span></div></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.3333px 7.91667px; transform-origin: 23.3333px 7.91667px; unicode-bidi: normal; "><span style="font-weight: 700; ">Inputs:</span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 162.55px 7.91667px; transform-origin: 162.55px 7.91667px; unicode-bidi: normal; "><span style=""> [M N R T] where N is number of Zernike terms for fit</span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 29.1667px 7.91667px; transform-origin: 29.1667px 7.91667px; unicode-bidi: normal; "><span style="font-weight: 700; ">Outputs:</span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 98.7833px 7.91667px; transform-origin: 98.7833px 7.91667px; unicode-bidi: normal; "><span style=""> [v] Zernike fit vector of length N</span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 250.083px 7.91667px; transform-origin: 250.083px 7.91667px; unicode-bidi: normal; "><span style="">Creation of the M surface and expected v fit vector can be seen in the Test Suite.</span></span></div></div></div>

*Fit Zernike Terms to a wavefront.*

The class notes of <http://www.visualopticslab.com/OPTI535/Lectures/Class06_08.pdf Schwiegerling UofA> on ANSI Standard Zernike terms is the basis for this challenge.  Pages 13 and 14 give the term definitions implemented in the zern_data_v01.m routine provided in the function template.

<<https://sites.google.com/site/razapor/_/rsrc/1350774824076/matlab_cody/Zernike_UA_480.jpg>>

ANSI Standard Zernike Chart:

*Algorithm Description:*

M=surface array to be fit by Zernike terms; 
  -valid data is circle of normalized radius<=1
  Use the R and T arrays to create the A array
  R=radial normalized distance from center of array
  T=angular radian value from center of array
  A=fitting array [valid_data_pts,terms]

Create A * z_fit = M(valid_data_pts)
  [valid_pts,terms] * [terms,1] = [valid_pts,1]

Loop term=0:terms-1
  - Create the 2-D array of z-terms uisng z=zern_data_v01(term,R,T)
  - A(:,term+1) = z(valid_data_pts)
  End Loop
  
  Solve for z_fit: pinv(A)*M(valid_pts)  or A\M(valid_pts)

*Inputs:* [M N R T] where N is number of Zernike terms for fit

*Outputs:* [v] Zernike fit vector of length N

Creation of the M surface and expected v fit vector can be seen in the Test Suite.

Solve

Solution Stats

20 Solutions
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Last Solution submitted on Oct 01, 2020

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3 Comments

Rafael S.T. Vieira on 12 Sep 2020

Could you please fix the function urlwrite? Or remove it...adding the code for the function zern_data_v01(j,r,t) at the end of the live script. Good problem.

Richard Zapor on 29 Sep 2020

Link fixed 9/29/20202.
All submissions being re-evaluated

Rafael S.T. Vieira on 1 Oct 2020

Thanks, Richard.

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