from math import *<\/p>\n\n\n\n
alpha = 40 # angle of apha in degree unit
alpha = alpha*pi\/180
D = 4 # Beam diameter mm
R = D\/2 # radius of incident beam
n= 1.46 # refractive index of lens
L = 5 # distance from lens<\/p>\n\n\n\n
DOF1 = Rsqrt(1-n<\/em>nsin(alpha)<\/em>sin(alpha)) t1 = DOF1 dr1 = sin(alpha)(n<\/em>cos(alpha)-sqrt(1-nn<\/em>sin(alpha)sin(alpha))) dr2 = n<\/em>sin(alpha)sin(alpha) + cos(alpha)<\/em>sqrt(1-nn<\/em>sin(alpha)sin(alpha)) dr = 2<\/em>L*dr1\/dr2<\/p>\n\n\n\n print(f’Incident beam size ={2*R} (mm)’) <\/p>\n","protected":false},"excerpt":{"rendered":" from math import * #Axicon focus: https:\/\/www.edmundoptics.com\/knowledge-#center\/application-notes\/lasers\/an-in-depth-look-at-axicons\/ #constant ring size t, but totoal size dr increase with distance L alpha = 40 # angle of apha in degree unitalpha = alpha*pi\/180D = 4 # Beam diameter mmR = D\/2 # radius of incident beamn= 1.46 # refractive index of lensL = 5 # distance from […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[1],"tags":[],"_links":{"self":[{"href":"https:\/\/laserphotonics.uk\/index.php?rest_route=\/wp\/v2\/posts\/2010"}],"collection":[{"href":"https:\/\/laserphotonics.uk\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/laserphotonics.uk\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/laserphotonics.uk\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/laserphotonics.uk\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2010"}],"version-history":[{"count":2,"href":"https:\/\/laserphotonics.uk\/index.php?rest_route=\/wp\/v2\/posts\/2010\/revisions"}],"predecessor-version":[{"id":2012,"href":"https:\/\/laserphotonics.uk\/index.php?rest_route=\/wp\/v2\/posts\/2010\/revisions\/2012"}],"wp:attachment":[{"href":"https:\/\/laserphotonics.uk\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2010"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/laserphotonics.uk\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2010"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/laserphotonics.uk\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2010"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
DOF2 = sin(alpha)cos(alpha)<\/em>(ncos(alpha)-sqrt(1-n<\/em>nsin(alpha)<\/em>sin(alpha)))
DOF = DOF1\/DOF2<\/p>\n\n\n\n#t: ring thickness<\/h1>\n\n\n\n
t2 = cos(alpha)* (nsin(alpha)<\/em>sin(alpha)+cos(alpha)sqrt(1-n<\/em>nsin(alpha)<\/em>sin(alpha)))
t= t1\/t2<\/p>\n\n\n\n#dr: totoal spot size (outside of ring edge)<\/h1>\n\n\n\n
print(f’DOF={DOF} (mm)’)
print(f’Ring thickness={t} (mm)’)
print(f’Ring size in total={dr} (mm)’)<\/p>\n\n\n\nfrom math import *\r\n\r\n\r\n# Axicon focus: https:\/\/www.edmundoptics.com\/knowledge-center\/application-notes\/lasers\/an-in-depth-look-at-axicons\/\r\n# constant ring size t, but totoal size dr increase with distance L \r\n# \r\nalpha = 40 # angle of apha in degree unit\r\nalpha = alpha*pi\/180\r\nD = 4 # Beam diameter mm\r\nR = D\/2 # radius of incident beam\r\nn= 1.46 # refractive index of lens\r\nL = 5 # distance from lens\r\n\r\n# DOF\r\nDOF1 = R*sqrt(1-n*n*sin(alpha)*sin(alpha))\r\nDOF2 = sin(alpha)*cos(alpha)*(n*cos(alpha)-sqrt(1-n*n*sin(alpha)*sin(alpha)))\r\nDOF = DOF1\/DOF2\r\n\r\n#t: ring thickness\r\nt1 = DOF1\r\nt2 = cos(alpha)* (n*sin(alpha)*sin(alpha)+cos(alpha)*sqrt(1-n*n*sin(alpha)*sin(alpha)))\r\nt= t1\/t2\r\n\r\n#dr: totoal spot size (outside of ring edge)\r\ndr1 = sin(alpha)*(n*cos(alpha)-sqrt(1-n*n*sin(alpha)*sin(alpha)))\r\ndr2 = n*sin(alpha)*sin(alpha) + cos(alpha)*sqrt(1-n*n*sin(alpha)*sin(alpha))\r\ndr = 2*L*dr1\/dr2\r\n\r\nprint(f'Incident beam size ={2*R} (mm)')\r\nprint(f'DOF={DOF} (mm)')\r\nprint(f'Ring thickness={t} (mm)')\r\nprint(f'Ring size in total={dr} (mm)')<\/code><\/pre>\n\n\n\n