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Display properties: number-header: $R_n^{|l|}(\rho)$ or $Z_n^l(x,y)$+Numbers:+- params:+ n: '2'+ l: '0'+ form: radial+ number: 2*t^2 - 1+ comment: Radial part for Noll $j=4$, OSA/ANSI $j=4$, Fringe $j=4$, Wyant $j=3$;+ defocus.+- params:+ n: '2'+ l: '0'+ form: cartesian+ number: 2*x^2 + 2*y^2 - 1+ comment: Noll $j=4$, OSA/ANSI $j=4$, Fringe $j=4$, Wyant $j=3$; defocus.+- params:+ n: '2'+ l: '2'+ form: cartesian+ number: x^2 - y^2+ comment: Noll $j=6$, OSA/ANSI $j=5$, Fringe $j=5$, Wyant $j=4$; vertical astigmatism.+- params:+ n: '2'+ l: '-2'+ form: cartesian+ number: 2*x*y+ comment: Noll $j=5$, OSA/ANSI $j=3$, Fringe $j=6$, Wyant $j=5$; oblique astigmatism.+- params:+ n: '3'+ l: '1'+ form: radial+ number: 3*t^3 - 2*t+ comment: Radial part for $l=1$ (Noll $j=8$, OSA/ANSI $j=8$, Fringe $j=7$, Wyant+ $j=6$; horizontal coma) and $l=-1$ (Noll $j=7$, OSA/ANSI $j=7$, Fringe $j=8$,+ Wyant $j=7$; vertical coma).+- params:+ n: '3'+ l: '1'+ form: cartesian+ number: 3*x^3 + 3*x*y^2 - 2*x+ comment: Noll $j=8$, OSA/ANSI $j=8$, Fringe $j=7$, Wyant $j=6$; horizontal coma.+- params:+ n: '3'+ l: '-1'+ form: cartesian+ number: 3*x^2*y + 3*y^3 - 2*y+ comment: Noll $j=7$, OSA/ANSI $j=7$, Fringe $j=8$, Wyant $j=7$; vertical coma.+- params:+ n: '3'+ l: '3'+ form: cartesian+ number: x^3 - 3*x*y^2+ comment: Noll $j=10$, OSA/ANSI $j=9$, Fringe $j=10$, Wyant $j=9$; oblique trefoil.+- params:+ n: '3'+ l: '-3'+ form: cartesian+ number: 3*x^2*y - y^3+ comment: Noll $j=9$, OSA/ANSI $j=6$, Fringe $j=11$, Wyant $j=10$; vertical trefoil.+- params:+ n: '4'+ l: '0'+ form: radial+ number: 6*t^4 - 6*t^2 + 1+ comment: Radial part for Noll $j=11$, OSA/ANSI $j=12$, Fringe $j=9$, Wyant $j=8$;+ primary spherical aberration.+- params:+ n: '4'+ l: '0'+ form: cartesian+ number: 6*x^4 + 12*x^2*y^2 + 6*y^4 - 6*x^2 - 6*y^2 + 1+ comment: Noll $j=11$, OSA/ANSI $j=12$, Fringe $j=9$, Wyant $j=8$; primary spherical+ aberration.+- params:+ n: '4'+ l: '2'+ form: radial+ number: 4*t^4 - 3*t^2+ comment: Radial part for $l=2$ (Noll $j=12$, OSA/ANSI $j=13$, Fringe $j=12$, Wyant+ $j=11$; vertical secondary astigmatism) and $l=-2$ (Noll $j=13$, OSA/ANSI $j=11$,+ Fringe $j=13$, Wyant $j=12$; oblique secondary astigmatism).+- params:+ n: '4'+ l: '2'+ form: cartesian+ number: 4*x^4 - 4*y^4 - 3*x^2 + 3*y^2+ comment: Noll $j=12$, OSA/ANSI $j=13$, Fringe $j=12$, Wyant $j=11$; vertical secondary+ astigmatism.+- params:+ n: '4'+ l: '-2'+ form: cartesian+ number: 8*x^3*y + 8*x*y^3 - 6*x*y+ comment: Noll $j=13$, OSA/ANSI $j=11$, Fringe $j=13$, Wyant $j=12$; oblique secondary+ astigmatism.+- params:+ n: '4'+ l: '4'+ form: cartesian+ number: x^4 - 6*x^2*y^2 + y^4+ comment: Noll $j=14$, OSA/ANSI $j=14$, Fringe $j=17$, Wyant $j=16$; vertical quadrafoil.+- params:+ n: '4'+ l: '-4'+ form: cartesian+ number: 4*x^3*y - 4*x*y^3+ comment: Noll $j=15$, OSA/ANSI $j=10$, Fringe $j=18$, Wyant $j=17$; oblique quadrafoil.+- params:+ n: '5'+ l: '1'+ form: radial+ number: 10*t^5 - 12*t^3 + 3*t+ comment: Radial part for $l=1$ (Noll $j=16$, OSA/ANSI $j=18$, Fringe $j=14$, Wyant+ $j=13$) and $l=-1$ (Noll $j=17$, OSA/ANSI $j=17$, Fringe $j=15$, Wyant $j=14$).+- params:+ n: '5'+ l: '1'+ form: cartesian+ number: 10*x^5 + 20*x^3*y^2 + 10*x*y^4 - 12*x^3 - 12*x*y^2 + 3*x+ comment: Noll $j=16$, OSA/ANSI $j=18$, Fringe $j=14$, Wyant $j=13$.+- params:+ n: '5'+ l: '-1'+ form: cartesian+ number: 10*x^4*y + 20*x^2*y^3 + 10*y^5 - 12*x^2*y - 12*y^3 + 3*y+ comment: Noll $j=17$, OSA/ANSI $j=17$, Fringe $j=15$, Wyant $j=14$.+- params:+ n: '5'+ l: '3'+ form: radial+ number: 5*t^5 - 4*t^3+ comment: Radial part for $l=3$ (Noll $j=18$, OSA/ANSI $j=19$, Fringe $j=19$, Wyant+ $j=18$) and $l=-3$ (Noll $j=19$, OSA/ANSI $j=16$, Fringe $j=20$, Wyant $j=19$).+- params:+ n: '5'+ l: '3'+ form: cartesian+ number: 5*x^5 - 10*x^3*y^2 - 15*x*y^4 - 4*x^3 + 12*x*y^2+ comment: Noll $j=18$, OSA/ANSI $j=19$, Fringe $j=19$, Wyant $j=18$.+- params:+ n: '5'+ l: '-3'+ form: cartesian+ number: 15*x^4*y + 10*x^2*y^3 - 5*y^5 - 12*x^2*y + 4*y^3+ comment: Noll $j=19$, OSA/ANSI $j=16$, Fringe $j=20$, Wyant $j=19$.+- params:+ n: '5'+ l: '5'+ form: cartesian+ number: x^5 - 10*x^3*y^2 + 5*x*y^4+ comment: Noll $j=20$, OSA/ANSI $j=20$, Fringe $j=26$, Wyant $j=25$.+- params:+ n: '5'+ l: '-5'+ form: cartesian+ number: 5*x^4*y - 10*x^2*y^3 + y^5+ comment: Noll $j=21$, OSA/ANSI $j=15$, Fringe $j=27$, Wyant $j=26$.+- params:+ n: '6'+ l: '0'+ form: radial+ number: 20*t^6 - 30*t^4 + 12*t^2 - 1+ comment: Radial part for Noll $j=22$, OSA/ANSI $j=24$, Fringe $j=16$, Wyant $j=15$.+- params:+ n: '6'+ l: '0'+ form: cartesian+ number: 20*x^6 + 60*x^4*y^2 + 60*x^2*y^4 + 20*y^6 - 30*x^4 - 60*x^2*y^2 - 30*y^4+ + 12*x^2 + 12*y^2 - 1+ comment: Noll $j=22$, OSA/ANSI $j=24$, Fringe $j=16$, Wyant $j=15$.+- params:+ n: '6'+ l: '2'+ form: radial+ number: 15*t^6 - 20*t^4 + 6*t^2+ comment: Radial part for $l=2$ (Noll $j=24$, OSA/ANSI $j=25$, Fringe $j=21$, Wyant+ $j=20$) and $l=-2$ (Noll $j=23$, OSA/ANSI $j=23$, Fringe $j=22$, Wyant $j=21$).+- params:+ n: '6'+ l: '2'+ form: cartesian+ number: 15*x^6 + 15*x^4*y^2 - 15*x^2*y^4 - 15*y^6 - 20*x^4 + 20*y^4 + 6*x^2 - 6*y^2+ comment: Noll $j=24$, OSA/ANSI $j=25$, Fringe $j=21$, Wyant $j=20$.+- params:+ n: '6'+ l: '-2'+ form: cartesian+ number: 30*x^5*y + 60*x^3*y^3 + 30*x*y^5 - 40*x^3*y - 40*x*y^3 + 12*x*y+ comment: Noll $j=23$, OSA/ANSI $j=23$, Fringe $j=22$, Wyant $j=21$.+- params:+ n: '6'+ l: '4'+ form: radial+ number: 6*t^6 - 5*t^4+ comment: Radial part for $l=4$ (Noll $j=26$, OSA/ANSI $j=26$, Fringe $j=28$, Wyant+ $j=27$) and $l=-4$ (Noll $j=25$, OSA/ANSI $j=22$, Fringe $j=29$, Wyant $j=28$).+- params:+ n: '6'+ l: '4'+ form: cartesian+ number: 6*x^6 - 30*x^4*y^2 - 30*x^2*y^4 + 6*y^6 - 5*x^4 + 30*x^2*y^2 - 5*y^4+ comment: Noll $j=26$, OSA/ANSI $j=26$, Fringe $j=28$, Wyant $j=27$.+- params:+ n: '6'+ l: '-4'+ form: cartesian+ number: 24*x^5*y - 24*x*y^5 - 20*x^3*y + 20*x*y^3+ comment: Noll $j=25$, OSA/ANSI $j=22$, Fringe $j=29$, Wyant $j=28$.+- params:+ n: '6'+ l: '6'+ form: cartesian+ number: x^6 - 15*x^4*y^2 + 15*x^2*y^4 - y^6+ comment: Noll $j=28$, OSA/ANSI $j=27$, Fringe $j=37$, Wyant $j=36$.+- params:+ n: '6'+ l: '-6'+ form: cartesian+ number: 6*x^5*y - 20*x^3*y^3 + 6*x*y^5+ comment: Noll $j=27$, OSA/ANSI $j=21$, Fringe $j=38$, Wyant $j=37$.+- params:+ n: '7'+ l: '1'+ form: radial+ number: 35*t^7 - 60*t^5 + 30*t^3 - 4*t+ comment: Radial part for $l=1$ (Noll $j=30$, OSA/ANSI $j=32$, Fringe $j=23$, Wyant+ $j=22$) and $l=-1$ (Noll $j=29$, OSA/ANSI $j=31$, Fringe $j=24$, Wyant $j=23$).+- params:+ n: '7'+ l: '1'+ form: cartesian+ number: 35*x^7 + 105*x^5*y^2 + 105*x^3*y^4 + 35*x*y^6 - 60*x^5 - 120*x^3*y^2 - 60*x*y^4+ + 30*x^3 + 30*x*y^2 - 4*x+ comment: Noll $j=30$, OSA/ANSI $j=32$, Fringe $j=23$, Wyant $j=22$.+- params:+ n: '7'+ l: '-1'+ form: cartesian+ number: 35*x^6*y + 105*x^4*y^3 + 105*x^2*y^5 + 35*y^7 - 60*x^4*y - 120*x^2*y^3 -+ 60*y^5 + 30*x^2*y + 30*y^3 - 4*y+ comment: Noll $j=29$, OSA/ANSI $j=31$, Fringe $j=24$, Wyant $j=23$.+- params:+ n: '7'+ l: '3'+ form: radial+ number: 21*t^7 - 30*t^5 + 10*t^3+ comment: Radial part for $l=3$ (Noll $j=32$, OSA/ANSI $j=33$, Fringe $j=30$, Wyant+ $j=29$) and $l=-3$ (Noll $j=31$, OSA/ANSI $j=30$, Fringe $j=31$, Wyant $j=30$).+- params:+ n: '7'+ l: '3'+ form: cartesian+ number: 21*x^7 - 21*x^5*y^2 - 105*x^3*y^4 - 63*x*y^6 - 30*x^5 + 60*x^3*y^2 + 90*x*y^4+ + 10*x^3 - 30*x*y^2+ comment: Noll $j=32$, OSA/ANSI $j=33$, Fringe $j=30$, Wyant $j=29$.+- params:+ n: '7'+ l: '-3'+ form: cartesian+ number: 63*x^6*y + 105*x^4*y^3 + 21*x^2*y^5 - 21*y^7 - 90*x^4*y - 60*x^2*y^3 + 30*y^5+ + 30*x^2*y - 10*y^3+ comment: Noll $j=31$, OSA/ANSI $j=30$, Fringe $j=31$, Wyant $j=30$.+- params:+ n: '7'+ l: '5'+ form: radial+ number: 7*t^7 - 6*t^5+ comment: Radial part for $l=5$ (Noll $j=34$, OSA/ANSI $j=34$, Fringe $j=39$, Wyant+ $j=38$) and $l=-5$ (Noll $j=33$, OSA/ANSI $j=29$, Fringe $j=40$, Wyant $j=39$).+- params:+ n: '7'+ l: '5'+ form: cartesian+ number: 7*x^7 - 63*x^5*y^2 - 35*x^3*y^4 + 35*x*y^6 - 6*x^5 + 60*x^3*y^2 - 30*x*y^4+ comment: Noll $j=34$, OSA/ANSI $j=34$, Fringe $j=39$, Wyant $j=38$.+- params:+ n: '7'+ l: '-5'+ form: cartesian+ number: 35*x^6*y - 35*x^4*y^3 - 63*x^2*y^5 + 7*y^7 - 30*x^4*y + 60*x^2*y^3 - 6*y^5+ comment: Noll $j=33$, OSA/ANSI $j=29$, Fringe $j=40$, Wyant $j=39$.+- params:+ n: '7'+ l: '7'+ form: cartesian+ number: x^7 - 21*x^5*y^2 + 35*x^3*y^4 - 7*x*y^6+ comment: Noll $j=36$, OSA/ANSI $j=35$, Fringe $j=50$, Wyant $j=49$.+- params:+ n: '7'+ l: '-7'+ form: cartesian+ number: 7*x^6*y - 35*x^4*y^3 + 21*x^2*y^5 - y^7+ comment: Noll $j=35$, OSA/ANSI $j=28$, Fringe $j=51$, Wyant $j=50$.+- params:+ n: '8'+ l: '0'+ form: radial+ number: 70*t^8 - 140*t^6 + 90*t^4 - 20*t^2 + 1+ comment: Radial part for Noll $j=37$, OSA/ANSI $j=40$, Fringe $j=25$, Wyant $j=24$.+- params:+ n: '8'+ l: '0'+ form: cartesian+ number: 70*x^8 + 280*x^6*y^2 + 420*x^4*y^4 + 280*x^2*y^6 + 70*y^8 - 140*x^6 - 420*x^4*y^2+ - 420*x^2*y^4 - 140*y^6 + 90*x^4 + 180*x^2*y^2 + 90*y^4 - 20*x^2 - 20*y^2 + 1+ comment: Noll $j=37$, OSA/ANSI $j=40$, Fringe $j=25$, Wyant $j=24$.+- params:+ n: '8'+ l: '2'+ form: radial+ number: 56*t^8 - 105*t^6 + 60*t^4 - 10*t^2+ comment: Radial part for $l=2$ (Noll $j=38$, OSA/ANSI $j=41$, Fringe $j=32$, Wyant+ $j=31$) and $l=-2$ (Noll $j=39$, OSA/ANSI $j=39$, Fringe $j=33$, Wyant $j=32$).+- params:+ n: '8'+ l: '2'+ form: cartesian+ number: 56*x^8 + 112*x^6*y^2 - 112*x^2*y^6 - 56*y^8 - 105*x^6 - 105*x^4*y^2 + 105*x^2*y^4+ + 105*y^6 + 60*x^4 - 60*y^4 - 10*x^2 + 10*y^2+ comment: Noll $j=38$, OSA/ANSI $j=41$, Fringe $j=32$, Wyant $j=31$.+- params:+ n: '8'+ l: '-2'+ form: cartesian+ number: 112*x^7*y + 336*x^5*y^3 + 336*x^3*y^5 + 112*x*y^7 - 210*x^5*y - 420*x^3*y^3+ - 210*x*y^5 + 120*x^3*y + 120*x*y^3 - 20*x*y+ comment: Noll $j=39$, OSA/ANSI $j=39$, Fringe $j=33$, Wyant $j=32$.+- params:+ n: '8'+ l: '4'+ form: radial+ number: 28*t^8 - 42*t^6 + 15*t^4+ comment: Radial part for $l=4$ (Noll $j=40$, OSA/ANSI $j=42$, Fringe $j=41$, Wyant+ $j=40$) and $l=-4$ (Noll $j=41$, OSA/ANSI $j=38$, Fringe $j=42$, Wyant $j=41$).+- params:+ n: '8'+ l: '4'+ form: cartesian+ number: 28*x^8 - 112*x^6*y^2 - 280*x^4*y^4 - 112*x^2*y^6 + 28*y^8 - 42*x^6 + 210*x^4*y^2+ + 210*x^2*y^4 - 42*y^6 + 15*x^4 - 90*x^2*y^2 + 15*y^4+ comment: Noll $j=40$, OSA/ANSI $j=42$, Fringe $j=41$, Wyant $j=40$.+- params:+ n: '8'+ l: '-4'+ form: cartesian+ number: 112*x^7*y + 112*x^5*y^3 - 112*x^3*y^5 - 112*x*y^7 - 168*x^5*y + 168*x*y^5+ + 60*x^3*y - 60*x*y^3+ comment: Noll $j=41$, OSA/ANSI $j=38$, Fringe $j=42$, Wyant $j=41$.+- params:+ n: '8'+ l: '6'+ form: radial+ number: 8*t^8 - 7*t^6+ comment: Radial part for $l=6$ (Noll $j=42$, OSA/ANSI $j=43$, Fringe $j=52$, Wyant+ $j=51$) and $l=-6$ (Noll $j=43$, OSA/ANSI $j=37$, Fringe $j=53$, Wyant $j=52$).+- params:+ n: '8'+ l: '6'+ form: cartesian+ number: 8*x^8 - 112*x^6*y^2 + 112*x^2*y^6 - 8*y^8 - 7*x^6 + 105*x^4*y^2 - 105*x^2*y^4+ + 7*y^6+ comment: Noll $j=42$, OSA/ANSI $j=43$, Fringe $j=52$, Wyant $j=51$.+- params:+ n: '8'+ l: '-6'+ form: cartesian+ number: 48*x^7*y - 112*x^5*y^3 - 112*x^3*y^5 + 48*x*y^7 - 42*x^5*y + 140*x^3*y^3+ - 42*x*y^5+ comment: Noll $j=43$, OSA/ANSI $j=37$, Fringe $j=53$, Wyant $j=52$.+- params:+ n: '8'+ l: '8'+ form: cartesian+ number: x^8 - 28*x^6*y^2 + 70*x^4*y^4 - 28*x^2*y^6 + y^8+ comment: Noll $j=44$, OSA/ANSI $j=44$, Fringe $j=65$, Wyant $j=64$.+- params:+ n: '8'+ l: '-8'+ form: cartesian+ number: 8*x^7*y - 56*x^5*y^3 + 56*x^3*y^5 - 8*x*y^7+ comment: Noll $j=45$, OSA/ANSI $j=36$, Fringe $j=66$, Wyant $j=65$.+- params:+ n: '9'+ l: '1'+ form: radial+ number: 126*t^9 - 280*t^7 + 210*t^5 - 60*t^3 + 5*t+ comment: Radial part for $l=1$ (Noll $j=46$, OSA/ANSI $j=50$, Fringe $j=34$, Wyant+ $j=33$) and $l=-1$ (Noll $j=47$, OSA/ANSI $j=49$, Fringe $j=35$, Wyant $j=34$).+- params:+ n: '9'+ l: '1'+ form: cartesian+ number: 126*x^9 + 504*x^7*y^2 + 756*x^5*y^4 + 504*x^3*y^6 + 126*x*y^8 - 280*x^7+ - 840*x^5*y^2 - 840*x^3*y^4 - 280*x*y^6 + 210*x^5 + 420*x^3*y^2 + 210*x*y^4 -+ 60*x^3 - 60*x*y^2 + 5*x+ comment: Noll $j=46$, OSA/ANSI $j=50$, Fringe $j=34$, Wyant $j=33$.+- params:+ n: '9'+ l: '-1'+ form: cartesian+ number: 126*x^8*y + 504*x^6*y^3 + 756*x^4*y^5 + 504*x^2*y^7 + 126*y^9 - 280*x^6*y+ - 840*x^4*y^3 - 840*x^2*y^5 - 280*y^7 + 210*x^4*y + 420*x^2*y^3 + 210*y^5 - 60*x^2*y+ - 60*y^3 + 5*y+ comment: Noll $j=47$, OSA/ANSI $j=49$, Fringe $j=35$, Wyant $j=34$.+- params:+ n: '9'+ l: '3'+ form: radial+ number: 84*t^9 - 168*t^7 + 105*t^5 - 20*t^3+ comment: Radial part for $l=3$ (Noll $j=48$, OSA/ANSI $j=51$, Fringe $j=43$, Wyant+ $j=42$) and $l=-3$ (Noll $j=49$, OSA/ANSI $j=48$, Fringe $j=44$, Wyant $j=43$).+- params:+ n: '9'+ l: '3'+ form: cartesian+ number: 84*x^9 - 504*x^5*y^4 - 672*x^3*y^6 - 252*x*y^8 - 168*x^7 + 168*x^5*y^2 ++ 840*x^3*y^4 + 504*x*y^6 + 105*x^5 - 210*x^3*y^2 - 315*x*y^4 - 20*x^3 + 60*x*y^2+ comment: Noll $j=48$, OSA/ANSI $j=51$, Fringe $j=43$, Wyant $j=42$.+- params:+ n: '9'+ l: '-3'+ form: cartesian+ number: 252*x^8*y + 672*x^6*y^3 + 504*x^4*y^5 - 84*y^9 - 504*x^6*y - 840*x^4*y^3+ - 168*x^2*y^5 + 168*y^7 + 315*x^4*y + 210*x^2*y^3 - 105*y^5 - 60*x^2*y + 20*y^3+ comment: Noll $j=49$, OSA/ANSI $j=48$, Fringe $j=44$, Wyant $j=43$.+- params:+ n: '9'+ l: '5'+ form: radial+ number: 36*t^9 - 56*t^7 + 21*t^5+ comment: Radial part for $l=5$ (Noll $j=50$, OSA/ANSI $j=52$, Fringe $j=54$, Wyant+ $j=53$) and $l=-5$ (Noll $j=51$, OSA/ANSI $j=47$, Fringe $j=55$, Wyant $j=54$).+- params:+ n: '9'+ l: '5'+ form: cartesian+ number: 36*x^9 - 288*x^7*y^2 - 504*x^5*y^4 + 180*x*y^8 - 56*x^7 + 504*x^5*y^2 ++ 280*x^3*y^4 - 280*x*y^6 + 21*x^5 - 210*x^3*y^2 + 105*x*y^4+ comment: Noll $j=50$, OSA/ANSI $j=52$, Fringe $j=54$, Wyant $j=53$.+- params:+ n: '9'+ l: '-5'+ form: cartesian+ number: 180*x^8*y - 504*x^4*y^5 - 288*x^2*y^7 + 36*y^9 - 280*x^6*y + 280*x^4*y^3+ + 504*x^2*y^5 - 56*y^7 + 105*x^4*y - 210*x^2*y^3 + 21*y^5+ comment: Noll $j=51$, OSA/ANSI $j=47$, Fringe $j=55$, Wyant $j=54$.+- params:+ n: '9'+ l: '7'+ form: radial+ number: 9*t^9 - 8*t^7+ comment: Radial part for $l=7$ (Noll $j=52$, OSA/ANSI $j=53$, Fringe $j=67$, Wyant+ $j=66$) and $l=-7$ (Noll $j=53$, OSA/ANSI $j=46$, Fringe $j=68$, Wyant $j=67$).+- params:+ n: '9'+ l: '7'+ form: cartesian+ number: 9*x^9 - 180*x^7*y^2 + 126*x^5*y^4 + 252*x^3*y^6 - 63*x*y^8 - 8*x^7 + 168*x^5*y^2+ - 280*x^3*y^4 + 56*x*y^6+ comment: Noll $j=52$, OSA/ANSI $j=53$, Fringe $j=67$, Wyant $j=66$.+- params:+ n: '9'+ l: '-7'+ form: cartesian+ number: 63*x^8*y - 252*x^6*y^3 - 126*x^4*y^5 + 180*x^2*y^7 - 9*y^9 - 56*x^6*y ++ 280*x^4*y^3 - 168*x^2*y^5 + 8*y^7+ comment: Noll $j=53$, OSA/ANSI $j=46$, Fringe $j=68$, Wyant $j=67$.+- params:+ n: '9'+ l: '9'+ form: cartesian+ number: x^9 - 36*x^7*y^2 + 126*x^5*y^4 - 84*x^3*y^6 + 9*x*y^8+ comment: Noll $j=54$, OSA/ANSI $j=54$, Fringe $j=82$, Wyant $j=81$.+- params:+ n: '9'+ l: '-9'+ form: cartesian+ number: 9*x^8*y - 84*x^6*y^3 + 126*x^4*y^5 - 36*x^2*y^7 + y^9+ comment: Noll $j=55$, OSA/ANSI $j=45$, Fringe $j=83$, Wyant $j=82$.+- params:+ n: '10'+ l: '0'+ form: radial+ number: 252*t^10 - 630*t^8 + 560*t^6 - 210*t^4 + 30*t^2 - 1+ comment: Radial part for Noll $j=56$, OSA/ANSI $j=60$, Fringe $j=36$, Wyant $j=35$.+- params:+ n: '10'+ l: '0'+ form: cartesian+ number: 252*x^10 + 1260*x^8*y^2 + 2520*x^6*y^4 + 2520*x^4*y^6 + 1260*x^2*y^8 + 252*y^10+ - 630*x^8 - 2520*x^6*y^2 - 3780*x^4*y^4 - 2520*x^2*y^6 - 630*y^8 + 560*x^6 + 1680*x^4*y^2+ + 1680*x^2*y^4 + 560*y^6 - 210*x^4 - 420*x^2*y^2 - 210*y^4 + 30*x^2 + 30*y^2 -+ 1+ comment: Noll $j=56$, OSA/ANSI $j=60$, Fringe $j=36$, Wyant $j=35$.+- params:+ n: '10'+ l: '2'+ form: radial+ number: 210*t^10 - 504*t^8 + 420*t^6 - 140*t^4 + 15*t^2+ comment: Radial part for $l=2$ (Noll $j=58$, OSA/ANSI $j=61$, Fringe $j=45$, Wyant+ $j=44$) and $l=-2$ (Noll $j=57$, OSA/ANSI $j=59$, Fringe $j=46$, Wyant $j=45$).+- params:+ n: '10'+ l: '2'+ form: cartesian+ number: 210*x^10 + 630*x^8*y^2 + 420*x^6*y^4 - 420*x^4*y^6 - 630*x^2*y^8 - 210*y^10+ - 504*x^8 - 1008*x^6*y^2 + 1008*x^2*y^6 + 504*y^8 + 420*x^6 + 420*x^4*y^2 - 420*x^2*y^4+ - 420*y^6 - 140*x^4 + 140*y^4 + 15*x^2 - 15*y^2+ comment: Noll $j=58$, OSA/ANSI $j=61$, Fringe $j=45$, Wyant $j=44$.+- params:+ n: '10'+ l: '-2'+ form: cartesian+ number: 420*x^9*y + 1680*x^7*y^3 + 2520*x^5*y^5 + 1680*x^3*y^7 + 420*x*y^9 - 1008*x^7*y+ - 3024*x^5*y^3 - 3024*x^3*y^5 - 1008*x*y^7 + 840*x^5*y + 1680*x^3*y^3 + 840*x*y^5+ - 280*x^3*y - 280*x*y^3 + 30*x*y+ comment: Noll $j=57$, OSA/ANSI $j=59$, Fringe $j=46$, Wyant $j=45$.+- params:+ n: '10'+ l: '4'+ form: radial+ number: 120*t^10 - 252*t^8 + 168*t^6 - 35*t^4+ comment: Radial part for $l=4$ (Noll $j=60$, OSA/ANSI $j=62$, Fringe $j=56$, Wyant+ $j=55$) and $l=-4$ (Noll $j=59$, OSA/ANSI $j=58$, Fringe $j=57$, Wyant $j=56$).+- params:+ n: '10'+ l: '4'+ form: cartesian+ number: 120*x^10 - 360*x^8*y^2 - 1680*x^6*y^4 - 1680*x^4*y^6 - 360*x^2*y^8 + 120*y^10+ - 252*x^8 + 1008*x^6*y^2 + 2520*x^4*y^4 + 1008*x^2*y^6 - 252*y^8 + 168*x^6 - 840*x^4*y^2+ - 840*x^2*y^4 + 168*y^6 - 35*x^4 + 210*x^2*y^2 - 35*y^4+ comment: Noll $j=60$, OSA/ANSI $j=62$, Fringe $j=56$, Wyant $j=55$.+- params:+ n: '10'+ l: '-4'+ form: cartesian+ number: 480*x^9*y + 960*x^7*y^3 - 960*x^3*y^7 - 480*x*y^9 - 1008*x^7*y - 1008*x^5*y^3+ + 1008*x^3*y^5 + 1008*x*y^7 + 672*x^5*y - 672*x*y^5 - 140*x^3*y + 140*x*y^3+ comment: Noll $j=59$, OSA/ANSI $j=58$, Fringe $j=57$, Wyant $j=56$.+- params:+ n: '10'+ l: '6'+ form: radial+ number: 45*t^10 - 72*t^8 + 28*t^6+ comment: Radial part for $l=6$ (Noll $j=62$, OSA/ANSI $j=63$, Fringe $j=69$, Wyant+ $j=68$) and $l=-6$ (Noll $j=61$, OSA/ANSI $j=57$, Fringe $j=70$, Wyant $j=69$).+- params:+ n: '10'+ l: '6'+ form: cartesian+ number: 45*x^10 - 585*x^8*y^2 - 630*x^6*y^4 + 630*x^4*y^6 + 585*x^2*y^8 - 45*y^10+ - 72*x^8 + 1008*x^6*y^2 - 1008*x^2*y^6 + 72*y^8 + 28*x^6 - 420*x^4*y^2 + 420*x^2*y^4+ - 28*y^6+ comment: Noll $j=62$, OSA/ANSI $j=63$, Fringe $j=69$, Wyant $j=68$.+- params:+ n: '10'+ l: '-6'+ form: cartesian+ number: 270*x^9*y - 360*x^7*y^3 - 1260*x^5*y^5 - 360*x^3*y^7 + 270*x*y^9 - 432*x^7*y+ + 1008*x^5*y^3 + 1008*x^3*y^5 - 432*x*y^7 + 168*x^5*y - 560*x^3*y^3 + 168*x*y^5+ comment: Noll $j=61$, OSA/ANSI $j=57$, Fringe $j=70$, Wyant $j=69$.+- params:+ n: '10'+ l: '8'+ form: radial+ number: 10*t^10 - 9*t^8+ comment: Radial part for $l=8$ (Noll $j=64$, OSA/ANSI $j=64$, Fringe $j=84$, Wyant+ $j=83$) and $l=-8$ (Noll $j=63$, OSA/ANSI $j=56$, Fringe $j=85$, Wyant $j=84$).+- params:+ n: '10'+ l: '8'+ form: cartesian+ number: 10*x^10 - 270*x^8*y^2 + 420*x^6*y^4 + 420*x^4*y^6 - 270*x^2*y^8 + 10*y^10+ - 9*x^8 + 252*x^6*y^2 - 630*x^4*y^4 + 252*x^2*y^6 - 9*y^8+ comment: Noll $j=64$, OSA/ANSI $j=64$, Fringe $j=84$, Wyant $j=83$.+- params:+ n: '10'+ l: '-8'+ form: cartesian+ number: 80*x^9*y - 480*x^7*y^3 + 480*x^3*y^7 - 80*x*y^9 - 72*x^7*y + 504*x^5*y^3+ - 504*x^3*y^5 + 72*x*y^7+ comment: Noll $j=63$, OSA/ANSI $j=56$, Fringe $j=85$, Wyant $j=84$.+- params:+ n: '10'+ l: '10'+ form: cartesian+ number: x^10 - 45*x^8*y^2 + 210*x^6*y^4 - 210*x^4*y^6 + 45*x^2*y^8 - y^10+ comment: Noll $j=66$, OSA/ANSI $j=65$, Fringe $j=101$, Wyant $j=100$.+- params:+ n: '10'+ l: '-10'+ form: cartesian+ number: 10*x^9*y - 120*x^7*y^3 + 252*x^5*y^5 - 120*x^3*y^7 + 10*x*y^9+ comment: Noll $j=65$, OSA/ANSI $j=55$, Fringe $j=102$, Wyant $j=101$.+- params:+ n: '11'+ l: '1'+ form: radial+ number: 462*t^11 - 1260*t^9 + 1260*t^7 - 560*t^5 + 105*t^3 - 6*t+ comment: Radial part for $l=1$ (Noll $j=68$, OSA/ANSI $j=72$, Fringe $j=47$, Wyant+ $j=46$) and $l=-1$ (Noll $j=67$, OSA/ANSI $j=71$, Fringe $j=48$, Wyant $j=47$).+- params:+ n: '11'+ l: '1'+ form: cartesian+ number: 462*x^11 + 2310*x^9*y^2 + 4620*x^7*y^4 + 4620*x^5*y^6 + 2310*x^3*y^8 + 462*x*y^10+ - 1260*x^9 - 5040*x^7*y^2 - 7560*x^5*y^4 - 5040*x^3*y^6 - 1260*x*y^8 + 1260*x^7+ + 3780*x^5*y^2 + 3780*x^3*y^4 + 1260*x*y^6 - 560*x^5 - 1120*x^3*y^2 - 560*x*y^4+ + 105*x^3 + 105*x*y^2 - 6*x+ comment: Noll $j=68$, OSA/ANSI $j=72$, Fringe $j=47$, Wyant $j=46$.+- params:+ n: '11'+ l: '-1'+ form: cartesian+ number: 462*x^10*y + 2310*x^8*y^3 + 4620*x^6*y^5 + 4620*x^4*y^7 + 2310*x^2*y^9 ++ 462*y^11 - 1260*x^8*y - 5040*x^6*y^3 - 7560*x^4*y^5 - 5040*x^2*y^7 - 1260*y^9+ + 1260*x^6*y + 3780*x^4*y^3 + 3780*x^2*y^5 + 1260*y^7 - 560*x^4*y - 1120*x^2*y^3+ - 560*y^5 + 105*x^2*y + 105*y^3 - 6*y+ comment: Noll $j=67$, OSA/ANSI $j=71$, Fringe $j=48$, Wyant $j=47$.+- params:+ n: '11'+ l: '3'+ form: radial+ number: 330*t^11 - 840*t^9 + 756*t^7 - 280*t^5 + 35*t^3+ comment: Radial part for $l=3$ (Noll $j=70$, OSA/ANSI $j=73$, Fringe $j=58$, Wyant+ $j=57$) and $l=-3$ (Noll $j=69$, OSA/ANSI $j=70$, Fringe $j=59$, Wyant $j=58$).+- params:+ n: '11'+ l: '3'+ form: cartesian+ number: 330*x^11 + 330*x^9*y^2 - 1980*x^7*y^4 - 4620*x^5*y^6 - 3630*x^3*y^8 - 990*x*y^10+ - 840*x^9 + 5040*x^5*y^4 + 6720*x^3*y^6 + 2520*x*y^8 + 756*x^7 - 756*x^5*y^2 -+ 3780*x^3*y^4 - 2268*x*y^6 - 280*x^5 + 560*x^3*y^2 + 840*x*y^4 + 35*x^3 - 105*x*y^2+ comment: Noll $j=70$, OSA/ANSI $j=73$, Fringe $j=58$, Wyant $j=57$.+- params:+ n: '11'+ l: '-3'+ form: cartesian+ number: 990*x^10*y + 3630*x^8*y^3 + 4620*x^6*y^5 + 1980*x^4*y^7 - 330*x^2*y^9 -+ 330*y^11 - 2520*x^8*y - 6720*x^6*y^3 - 5040*x^4*y^5 + 840*y^9 + 2268*x^6*y + 3780*x^4*y^3+ + 756*x^2*y^5 - 756*y^7 - 840*x^4*y - 560*x^2*y^3 + 280*y^5 + 105*x^2*y - 35*y^3+ comment: Noll $j=69$, OSA/ANSI $j=70$, Fringe $j=59$, Wyant $j=58$.+- params:+ n: '11'+ l: '5'+ form: radial+ number: 165*t^11 - 360*t^9 + 252*t^7 - 56*t^5+ comment: Radial part for $l=5$ (Noll $j=72$, OSA/ANSI $j=74$, Fringe $j=71$, Wyant+ $j=70$) and $l=-5$ (Noll $j=71$, OSA/ANSI $j=69$, Fringe $j=72$, Wyant $j=71$).+- params:+ n: '11'+ l: '5'+ form: cartesian+ number: 165*x^11 - 1155*x^9*y^2 - 3630*x^7*y^4 - 2310*x^5*y^6 + 825*x^3*y^8 + 825*x*y^10+ - 360*x^9 + 2880*x^7*y^2 + 5040*x^5*y^4 - 1800*x*y^8 + 252*x^7 - 2268*x^5*y^2+ - 1260*x^3*y^4 + 1260*x*y^6 - 56*x^5 + 560*x^3*y^2 - 280*x*y^4+ comment: Noll $j=72$, OSA/ANSI $j=74$, Fringe $j=71$, Wyant $j=70$.+- params:+ n: '11'+ l: '-5'+ form: cartesian+ number: 825*x^10*y + 825*x^8*y^3 - 2310*x^6*y^5 - 3630*x^4*y^7 - 1155*x^2*y^9 ++ 165*y^11 - 1800*x^8*y + 5040*x^4*y^5 + 2880*x^2*y^7 - 360*y^9 + 1260*x^6*y - 1260*x^4*y^3+ - 2268*x^2*y^5 + 252*y^7 - 280*x^4*y + 560*x^2*y^3 - 56*y^5+ comment: Noll $j=71$, OSA/ANSI $j=69$, Fringe $j=72$, Wyant $j=71$.+- params:+ n: '11'+ l: '7'+ form: radial+ number: 55*t^11 - 90*t^9 + 36*t^7+ comment: Radial part for $l=7$ (Noll $j=74$, OSA/ANSI $j=75$, Fringe $j=86$, Wyant+ $j=85$) and $l=-7$ (Noll $j=73$, OSA/ANSI $j=68$, Fringe $j=87$, Wyant $j=86$).+- params:+ n: '11'+ l: '7'+ form: cartesian+ number: 55*x^11 - 1045*x^9*y^2 - 330*x^7*y^4 + 2310*x^5*y^6 + 1155*x^3*y^8 - 385*x*y^10+ - 90*x^9 + 1800*x^7*y^2 - 1260*x^5*y^4 - 2520*x^3*y^6 + 630*x*y^8 + 36*x^7 - 756*x^5*y^2+ + 1260*x^3*y^4 - 252*x*y^6+ comment: Noll $j=74$, OSA/ANSI $j=75$, Fringe $j=86$, Wyant $j=85$.+- params:+ n: '11'+ l: '-7'+ form: cartesian+ number: 385*x^10*y - 1155*x^8*y^3 - 2310*x^6*y^5 + 330*x^4*y^7 + 1045*x^2*y^9 -+ 55*y^11 - 630*x^8*y + 2520*x^6*y^3 + 1260*x^4*y^5 - 1800*x^2*y^7 + 90*y^9 + 252*x^6*y+ - 1260*x^4*y^3 + 756*x^2*y^5 - 36*y^7+ comment: Noll $j=73$, OSA/ANSI $j=68$, Fringe $j=87$, Wyant $j=86$.+- params:+ n: '11'+ l: '9'+ form: radial+ number: 11*t^11 - 10*t^9+ comment: Radial part for $l=9$ (Noll $j=76$, OSA/ANSI $j=76$, Fringe $j=103$, Wyant+ $j=102$) and $l=-9$ (Noll $j=75$, OSA/ANSI $j=67$, Fringe $j=104$, Wyant $j=103$).+- params:+ n: '11'+ l: '9'+ form: cartesian+ number: 11*x^11 - 385*x^9*y^2 + 990*x^7*y^4 + 462*x^5*y^6 - 825*x^3*y^8 + 99*x*y^10+ - 10*x^9 + 360*x^7*y^2 - 1260*x^5*y^4 + 840*x^3*y^6 - 90*x*y^8+ comment: Noll $j=76$, OSA/ANSI $j=76$, Fringe $j=103$, Wyant $j=102$.+- params:+ n: '11'+ l: '-9'+ form: cartesian+ number: 99*x^10*y - 825*x^8*y^3 + 462*x^6*y^5 + 990*x^4*y^7 - 385*x^2*y^9 + 11*y^11+ - 90*x^8*y + 840*x^6*y^3 - 1260*x^4*y^5 + 360*x^2*y^7 - 10*y^9+ comment: Noll $j=75$, OSA/ANSI $j=67$, Fringe $j=104$, Wyant $j=103$.+- params:+ n: '11'+ l: '11'+ form: cartesian+ number: x^11 - 55*x^9*y^2 + 330*x^7*y^4 - 462*x^5*y^6 + 165*x^3*y^8 - 11*x*y^10+ comment: Noll $j=78$, OSA/ANSI $j=77$, Fringe $j=122$, Wyant $j=121$.+- params:+ n: '11'+ l: '-11'+ form: cartesian+ number: 11*x^10*y - 165*x^8*y^3 + 462*x^6*y^5 - 330*x^4*y^7 + 55*x^2*y^9 - y^11+ comment: Noll $j=77$, OSA/ANSI $j=66$, Fringe $j=123$, Wyant $j=122$.+- params:+ n: '12'+ l: '0'+ form: radial+ number: 924*t^12 - 2772*t^10 + 3150*t^8 - 1680*t^6 + 420*t^4 - 42*t^2 + 1+ comment: Radial part for Noll $j=79$, OSA/ANSI $j=84$, Fringe $j=49$, Wyant $j=48$.+- params:+ n: '12'+ l: '0'+ form: cartesian+ number: 924*x^12 + 5544*x^10*y^2 + 13860*x^8*y^4 + 18480*x^6*y^6 + 13860*x^4*y^8+ + 5544*x^2*y^10 + 924*y^12 - 2772*x^10 - 13860*x^8*y^2 - 27720*x^6*y^4 - 27720*x^4*y^6+ - 13860*x^2*y^8 - 2772*y^10 + 3150*x^8 + 12600*x^6*y^2 + 18900*x^4*y^4 + 12600*x^2*y^6+ + 3150*y^8 - 1680*x^6 - 5040*x^4*y^2 - 5040*x^2*y^4 - 1680*y^6 + 420*x^4 + 840*x^2*y^2+ + 420*y^4 - 42*x^2 - 42*y^2 + 1+ comment: Noll $j=79$, OSA/ANSI $j=84$, Fringe $j=49$, Wyant $j=48$.+- params:+ n: '12'+ l: '2'+ form: radial+ number: 792*t^12 - 2310*t^10 + 2520*t^8 - 1260*t^6 + 280*t^4 - 21*t^2+ comment: Radial part for $l=2$ (Noll $j=80$, OSA/ANSI $j=85$, Fringe $j=60$, Wyant+ $j=59$) and $l=-2$ (Noll $j=81$, OSA/ANSI $j=83$, Fringe $j=61$, Wyant $j=60$).+- params:+ n: '12'+ l: '2'+ form: cartesian+ number: 792*x^12 + 3168*x^10*y^2 + 3960*x^8*y^4 - 3960*x^4*y^8 - 3168*x^2*y^10 -+ 792*y^12 - 2310*x^10 - 6930*x^8*y^2 - 4620*x^6*y^4 + 4620*x^4*y^6 + 6930*x^2*y^8+ + 2310*y^10 + 2520*x^8 + 5040*x^6*y^2 - 5040*x^2*y^6 - 2520*y^8 - 1260*x^6 - 1260*x^4*y^2+ + 1260*x^2*y^4 + 1260*y^6 + 280*x^4 - 280*y^4 - 21*x^2 + 21*y^2+ comment: Noll $j=80$, OSA/ANSI $j=85$, Fringe $j=60$, Wyant $j=59$.+- params:+ n: '12'+ l: '-2'+ form: cartesian+ number: 1584*x^11*y + 7920*x^9*y^3 + 15840*x^7*y^5 + 15840*x^5*y^7 + 7920*x^3*y^9+ + 1584*x*y^11 - 4620*x^9*y - 18480*x^7*y^3 - 27720*x^5*y^5 - 18480*x^3*y^7 - 4620*x*y^9+ + 5040*x^7*y + 15120*x^5*y^3 + 15120*x^3*y^5 + 5040*x*y^7 - 2520*x^5*y - 5040*x^3*y^3+ - 2520*x*y^5 + 560*x^3*y + 560*x*y^3 - 42*x*y+ comment: Noll $j=81$, OSA/ANSI $j=83$, Fringe $j=61$, Wyant $j=60$.+- params:+ n: '12'+ l: '4'+ form: radial+ number: 495*t^12 - 1320*t^10 + 1260*t^8 - 504*t^6 + 70*t^4+ comment: Radial part for $l=4$ (Noll $j=82$, OSA/ANSI $j=86$, Fringe $j=73$, Wyant+ $j=72$) and $l=-4$ (Noll $j=83$, OSA/ANSI $j=82$, Fringe $j=74$, Wyant $j=73$).+- params:+ n: '12'+ l: '4'+ form: cartesian+ number: 495*x^12 - 990*x^10*y^2 - 8415*x^8*y^4 - 13860*x^6*y^6 - 8415*x^4*y^8 -+ 990*x^2*y^10 + 495*y^12 - 1320*x^10 + 3960*x^8*y^2 + 18480*x^6*y^4 + 18480*x^4*y^6+ + 3960*x^2*y^8 - 1320*y^10 + 1260*x^8 - 5040*x^6*y^2 - 12600*x^4*y^4 - 5040*x^2*y^6+ + 1260*y^8 - 504*x^6 + 2520*x^4*y^2 + 2520*x^2*y^4 - 504*y^6 + 70*x^4 - 420*x^2*y^2+ + 70*y^4+ comment: Noll $j=82$, OSA/ANSI $j=86$, Fringe $j=73$, Wyant $j=72$.+- params:+ n: '12'+ l: '-4'+ form: cartesian+ number: 1980*x^11*y + 5940*x^9*y^3 + 3960*x^7*y^5 - 3960*x^5*y^7 - 5940*x^3*y^9+ - 1980*x*y^11 - 5280*x^9*y - 10560*x^7*y^3 + 10560*x^3*y^7 + 5280*x*y^9 + 5040*x^7*y+ + 5040*x^5*y^3 - 5040*x^3*y^5 - 5040*x*y^7 - 2016*x^5*y + 2016*x*y^5 + 280*x^3*y+ - 280*x*y^3+ comment: Noll $j=83$, OSA/ANSI $j=82$, Fringe $j=74$, Wyant $j=73$.+- params:+ n: '12'+ l: '6'+ form: radial+ number: 220*t^12 - 495*t^10 + 360*t^8 - 84*t^6+ comment: Radial part for $l=6$ (Noll $j=84$, OSA/ANSI $j=87$, Fringe $j=88$, Wyant+ $j=87$) and $l=-6$ (Noll $j=85$, OSA/ANSI $j=81$, Fringe $j=89$, Wyant $j=88$).+- params:+ n: '12'+ l: '6'+ form: cartesian+ number: 220*x^12 - 2640*x^10*y^2 - 5940*x^8*y^4 + 5940*x^4*y^8 + 2640*x^2*y^10 -+ 220*y^12 - 495*x^10 + 6435*x^8*y^2 + 6930*x^6*y^4 - 6930*x^4*y^6 - 6435*x^2*y^8+ + 495*y^10 + 360*x^8 - 5040*x^6*y^2 + 5040*x^2*y^6 - 360*y^8 - 84*x^6 + 1260*x^4*y^2+ - 1260*x^2*y^4 + 84*y^6+ comment: Noll $j=84$, OSA/ANSI $j=87$, Fringe $j=88$, Wyant $j=87$.+- params:+ n: '12'+ l: '-6'+ form: cartesian+ number: 1320*x^11*y - 440*x^9*y^3 - 7920*x^7*y^5 - 7920*x^5*y^7 - 440*x^3*y^9 ++ 1320*x*y^11 - 2970*x^9*y + 3960*x^7*y^3 + 13860*x^5*y^5 + 3960*x^3*y^7 - 2970*x*y^9+ + 2160*x^7*y - 5040*x^5*y^3 - 5040*x^3*y^5 + 2160*x*y^7 - 504*x^5*y + 1680*x^3*y^3+ - 504*x*y^5+ comment: Noll $j=85$, OSA/ANSI $j=81$, Fringe $j=89$, Wyant $j=88$.+- params:+ n: '12'+ l: '8'+ form: radial+ number: 66*t^12 - 110*t^10 + 45*t^8+ comment: Radial part for $l=8$ (Noll $j=86$, OSA/ANSI $j=88$, Fringe $j=105$, Wyant+ $j=104$) and $l=-8$ (Noll $j=87$, OSA/ANSI $j=80$, Fringe $j=106$, Wyant $j=105$).+- params:+ n: '12'+ l: '8'+ form: cartesian+ number: 66*x^12 - 1716*x^10*y^2 + 990*x^8*y^4 + 5544*x^6*y^6 + 990*x^4*y^8 - 1716*x^2*y^10+ + 66*y^12 - 110*x^10 + 2970*x^8*y^2 - 4620*x^6*y^4 - 4620*x^4*y^6 + 2970*x^2*y^8+ - 110*y^10 + 45*x^8 - 1260*x^6*y^2 + 3150*x^4*y^4 - 1260*x^2*y^6 + 45*y^8+ comment: Noll $j=86$, OSA/ANSI $j=88$, Fringe $j=105$, Wyant $j=104$.+- params:+ n: '12'+ l: '-8'+ form: cartesian+ number: 528*x^11*y - 2640*x^9*y^3 - 3168*x^7*y^5 + 3168*x^5*y^7 + 2640*x^3*y^9 -+ 528*x*y^11 - 880*x^9*y + 5280*x^7*y^3 - 5280*x^3*y^7 + 880*x*y^9 + 360*x^7*y -+ 2520*x^5*y^3 + 2520*x^3*y^5 - 360*x*y^7+ comment: Noll $j=87$, OSA/ANSI $j=80$, Fringe $j=106$, Wyant $j=105$.+- params:+ n: '12'+ l: '10'+ form: radial+ number: 12*t^12 - 11*t^10+ comment: Radial part for $l=10$ (Noll $j=88$, OSA/ANSI $j=89$, Fringe $j=124$, Wyant+ $j=123$) and $l=-10$ (Noll $j=89$, OSA/ANSI $j=79$, Fringe $j=125$, Wyant $j=124$).+- params:+ n: '12'+ l: '10'+ form: cartesian+ number: 12*x^12 - 528*x^10*y^2 + 1980*x^8*y^4 - 1980*x^4*y^8 + 528*x^2*y^10 - 12*y^12+ - 11*x^10 + 495*x^8*y^2 - 2310*x^6*y^4 + 2310*x^4*y^6 - 495*x^2*y^8 + 11*y^10+ comment: Noll $j=88$, OSA/ANSI $j=89$, Fringe $j=124$, Wyant $j=123$.+- params:+ n: '12'+ l: '-10'+ form: cartesian+ number: 120*x^11*y - 1320*x^9*y^3 + 1584*x^7*y^5 + 1584*x^5*y^7 - 1320*x^3*y^9 ++ 120*x*y^11 - 110*x^9*y + 1320*x^7*y^3 - 2772*x^5*y^5 + 1320*x^3*y^7 - 110*x*y^9+ comment: Noll $j=89$, OSA/ANSI $j=79$, Fringe $j=125$, Wyant $j=124$.+- params:+ n: '12'+ l: '12'+ form: cartesian+ number: x^12 - 66*x^10*y^2 + 495*x^8*y^4 - 924*x^6*y^6 + 495*x^4*y^8 - 66*x^2*y^10+ + y^12+ comment: Noll $j=90$, OSA/ANSI $j=90$, Fringe $j=145$, Wyant $j=144$.+- params:+ n: '12'+ l: '-12'+ form: cartesian+ number: 12*x^11*y - 220*x^9*y^3 + 792*x^7*y^5 - 792*x^5*y^7 + 220*x^3*y^9 - 12*x*y^11+ comment: Noll $j=91$, OSA/ANSI $j=78$, Fringe $j=146$, Wyant $j=145$.+- params:+ n: '13'+ l: '1'+ form: radial+ number: 1716*t^13 - 5544*t^11 + 6930*t^9 - 4200*t^7 + 1260*t^5 - 168*t^3 + 7*t+ comment: Radial part for $l=1$ (Noll $j=92$, OSA/ANSI $j=98$, Fringe $j=62$, Wyant+ $j=61$) and $l=-1$ (Noll $j=93$, OSA/ANSI $j=97$, Fringe $j=63$, Wyant $j=62$).+- params:+ n: '13'+ l: '3'+ form: radial+ number: 1287*t^13 - 3960*t^11 + 4620*t^9 - 2520*t^7 + 630*t^5 - 56*t^3+ comment: Radial part for $l=3$ (Noll $j=94$, OSA/ANSI $j=99$, Fringe $j=75$, Wyant+ $j=74$) and $l=-3$ (Noll $j=95$, OSA/ANSI $j=96$, Fringe $j=76$, Wyant $j=75$).+- params:+ n: '13'+ l: '5'+ form: radial+ number: 715*t^13 - 1980*t^11 + 1980*t^9 - 840*t^7 + 126*t^5+ comment: Radial part for $l=5$ (Noll $j=96$, OSA/ANSI $j=100$, Fringe $j=90$, Wyant+ $j=89$) and $l=-5$ (Noll $j=97$, OSA/ANSI $j=95$, Fringe $j=91$, Wyant $j=90$).+- params:+ n: '13'+ l: '7'+ form: radial+ number: 286*t^13 - 660*t^11 + 495*t^9 - 120*t^7+ comment: Radial part for $l=7$ (Noll $j=98$, OSA/ANSI $j=101$, Fringe $j=107$, Wyant+ $j=106$) and $l=-7$ (Noll $j=99$, OSA/ANSI $j=94$, Fringe $j=108$, Wyant $j=107$).+- params:+ n: '13'+ l: '9'+ form: radial+ number: 78*t^13 - 132*t^11 + 55*t^9+ comment: Radial part for $l=9$ (Noll $j=100$, OSA/ANSI $j=102$, Fringe $j=126$,+ Wyant $j=125$) and $l=-9$ (Noll $j=101$, OSA/ANSI $j=93$, Fringe $j=127$, Wyant+ $j=126$).+- params:+ n: '13'+ l: '11'+ form: radial+ number: 13*t^13 - 12*t^11+ comment: Radial part for $l=11$ (Noll $j=102$, OSA/ANSI $j=103$, Fringe $j=147$,+ Wyant $j=146$) and $l=-11$ (Noll $j=103$, OSA/ANSI $j=92$, Fringe $j=148$, Wyant+ $j=147$).+- params:+ n: '14'+ l: '0'+ form: radial+ number: 3432*t^14 - 12012*t^12 + 16632*t^10 - 11550*t^8 + 4200*t^6 - 756*t^4 + 56*t^2+ - 1+ comment: Radial part for Noll $j=106$, OSA/ANSI $j=112$, Fringe $j=64$, Wyant $j=63$.+- params:+ n: '14'+ l: '2'+ form: radial+ number: 3003*t^14 - 10296*t^12 + 13860*t^10 - 9240*t^8 + 3150*t^6 - 504*t^4 + 28*t^2+ comment: Radial part for $l=2$ (Noll $j=108$, OSA/ANSI $j=113$, Fringe $j=77$, Wyant+ $j=76$) and $l=-2$ (Noll $j=107$, OSA/ANSI $j=111$, Fringe $j=78$, Wyant $j=77$).+- params:+ n: '14'+ l: '4'+ form: radial+ number: 2002*t^14 - 6435*t^12 + 7920*t^10 - 4620*t^8 + 1260*t^6 - 126*t^4+ comment: Radial part for $l=4$ (Noll $j=110$, OSA/ANSI $j=114$, Fringe $j=92$, Wyant+ $j=91$) and $l=-4$ (Noll $j=109$, OSA/ANSI $j=110$, Fringe $j=93$, Wyant $j=92$).+- params:+ n: '14'+ l: '6'+ form: radial+ number: 1001*t^14 - 2860*t^12 + 2970*t^10 - 1320*t^8 + 210*t^6+ comment: Radial part for $l=6$ (Noll $j=112$, OSA/ANSI $j=115$, Fringe $j=109$,+ Wyant $j=108$) and $l=-6$ (Noll $j=111$, OSA/ANSI $j=109$, Fringe $j=110$, Wyant+ $j=109$).+- params:+ n: '14'+ l: '8'+ form: radial+ number: 364*t^14 - 858*t^12 + 660*t^10 - 165*t^8+ comment: Radial part for $l=8$ (Noll $j=114$, OSA/ANSI $j=116$, Fringe $j=128$,+ Wyant $j=127$) and $l=-8$ (Noll $j=113$, OSA/ANSI $j=108$, Fringe $j=129$, Wyant+ $j=128$).+- params:+ n: '14'+ l: '10'+ form: radial+ number: 91*t^14 - 156*t^12 + 66*t^10+ comment: Radial part for $l=10$ (Noll $j=116$, OSA/ANSI $j=117$, Fringe $j=149$,+ Wyant $j=148$) and $l=-10$ (Noll $j=115$, OSA/ANSI $j=107$, Fringe $j=150$, Wyant+ $j=149$).+- params:+ n: '14'+ l: '12'+ form: radial+ number: 14*t^14 - 13*t^12+ comment: Radial part for $l=12$ (Noll $j=118$, OSA/ANSI $j=118$, Fringe $j=172$,+ Wyant $j=171$) and $l=-12$ (Noll $j=117$, OSA/ANSI $j=106$, Fringe $j=173$, Wyant+ $j=172$).+- params:+ n: '15'+ l: '1'+ form: radial+ number: 6435*t^15 - 24024*t^13 + 36036*t^11 - 27720*t^9 + 11550*t^7 - 2520*t^5 ++ 252*t^3 - 8*t+ comment: Radial part for $l=1$ (Noll $j=122$, OSA/ANSI $j=128$, Fringe $j=79$, Wyant+ $j=78$) and $l=-1$ (Noll $j=121$, OSA/ANSI $j=127$, Fringe $j=80$, Wyant $j=79$).+- params:+ n: '15'+ l: '3'+ form: radial+ number: 5005*t^15 - 18018*t^13 + 25740*t^11 - 18480*t^9 + 6930*t^7 - 1260*t^5 ++ 84*t^3+ comment: Radial part for $l=3$ (Noll $j=124$, OSA/ANSI $j=129$, Fringe $j=94$, Wyant+ $j=93$) and $l=-3$ (Noll $j=123$, OSA/ANSI $j=126$, Fringe $j=95$, Wyant $j=94$).+- params:+ n: '15'+ l: '5'+ form: radial+ number: 3003*t^15 - 10010*t^13 + 12870*t^11 - 7920*t^9 + 2310*t^7 - 252*t^5+ comment: Radial part for $l=5$ (Noll $j=126$, OSA/ANSI $j=130$, Fringe $j=111$,+ Wyant $j=110$) and $l=-5$ (Noll $j=125$, OSA/ANSI $j=125$, Fringe $j=112$, Wyant+ $j=111$).+- params:+ n: '15'+ l: '7'+ form: radial+ number: 1365*t^15 - 4004*t^13 + 4290*t^11 - 1980*t^9 + 330*t^7+ comment: Radial part for $l=7$ (Noll $j=128$, OSA/ANSI $j=131$, Fringe $j=130$,+ Wyant $j=129$) and $l=-7$ (Noll $j=127$, OSA/ANSI $j=124$, Fringe $j=131$, Wyant+ $j=130$).+- params:+ n: '15'+ l: '9'+ form: radial+ number: 455*t^15 - 1092*t^13 + 858*t^11 - 220*t^9+ comment: Radial part for $l=9$ (Noll $j=130$, OSA/ANSI $j=132$, Fringe $j=151$,+ Wyant $j=150$) and $l=-9$ (Noll $j=129$, OSA/ANSI $j=123$, Fringe $j=152$, Wyant+ $j=151$).+- params:+ n: '15'+ l: '11'+ form: radial+ number: 105*t^15 - 182*t^13 + 78*t^11+ comment: Radial part for $l=11$ (Noll $j=132$, OSA/ANSI $j=133$, Fringe $j=174$,+ Wyant $j=173$) and $l=-11$ (Noll $j=131$, OSA/ANSI $j=122$, Fringe $j=175$, Wyant+ $j=174$).+- params:+ n: '15'+ l: '13'+ form: radial+ number: 15*t^15 - 14*t^13+ comment: Radial part for $l=13$ (Noll $j=134$, OSA/ANSI $j=134$, Fringe $j=199$,+ Wyant $j=198$) and $l=-13$ (Noll $j=133$, OSA/ANSI $j=121$, Fringe $j=200$, Wyant+ $j=199$).+- params:+ n: '16'+ l: '0'+ form: radial+ number: 12870*t^16 - 51480*t^14 + 84084*t^12 - 72072*t^10 + 34650*t^8 - 9240*t^6+ + 1260*t^4 - 72*t^2 + 1+ comment: Radial part for Noll $j=137$, OSA/ANSI $j=144$, Fringe $j=81$, Wyant $j=80$.+- params:+ n: '16'+ l: '2'+ form: radial+ number: 11440*t^16 - 45045*t^14 + 72072*t^12 - 60060*t^10 + 27720*t^8 - 6930*t^6+ + 840*t^4 - 36*t^2+ comment: Radial part for $l=2$ (Noll $j=138$, OSA/ANSI $j=145$, Fringe $j=96$, Wyant+ $j=95$) and $l=-2$ (Noll $j=139$, OSA/ANSI $j=143$, Fringe $j=97$, Wyant $j=96$).+- params:+ n: '16'+ l: '4'+ form: radial+ number: 8008*t^16 - 30030*t^14 + 45045*t^12 - 34320*t^10 + 13860*t^8 - 2772*t^6+ + 210*t^4+ comment: Radial part for $l=4$ (Noll $j=140$, OSA/ANSI $j=146$, Fringe $j=113$,+ Wyant $j=112$) and $l=-4$ (Noll $j=141$, OSA/ANSI $j=142$, Fringe $j=114$, Wyant+ $j=113$).+- params:+ n: '16'+ l: '6'+ form: radial+ number: 4368*t^16 - 15015*t^14 + 20020*t^12 - 12870*t^10 + 3960*t^8 - 462*t^6+ comment: Radial part for $l=6$ (Noll $j=142$, OSA/ANSI $j=147$, Fringe $j=132$,+ Wyant $j=131$) and $l=-6$ (Noll $j=143$, OSA/ANSI $j=141$, Fringe $j=133$, Wyant+ $j=132$).+- params:+ n: '16'+ l: '8'+ form: radial+ number: 1820*t^16 - 5460*t^14 + 6006*t^12 - 2860*t^10 + 495*t^8+ comment: Radial part for $l=8$ (Noll $j=144$, OSA/ANSI $j=148$, Fringe $j=153$,+ Wyant $j=152$) and $l=-8$ (Noll $j=145$, OSA/ANSI $j=140$, Fringe $j=154$, Wyant+ $j=153$).+- params:+ n: '16'+ l: '10'+ form: radial+ number: 560*t^16 - 1365*t^14 + 1092*t^12 - 286*t^10+ comment: Radial part for $l=10$ (Noll $j=146$, OSA/ANSI $j=149$, Fringe $j=176$,+ Wyant $j=175$) and $l=-10$ (Noll $j=147$, OSA/ANSI $j=139$, Fringe $j=177$, Wyant+ $j=176$).+- params:+ n: '16'+ l: '12'+ form: radial+ number: 120*t^16 - 210*t^14 + 91*t^12+ comment: Radial part for $l=12$ (Noll $j=148$, OSA/ANSI $j=150$, Fringe $j=201$,+ Wyant $j=200$) and $l=-12$ (Noll $j=149$, OSA/ANSI $j=138$, Fringe $j=202$, Wyant+ $j=201$).+- params:+ n: '16'+ l: '14'+ form: radial+ number: 16*t^16 - 15*t^14+ comment: Radial part for $l=14$ (Noll $j=150$, OSA/ANSI $j=151$, Fringe $j=228$,+ Wyant $j=227$) and $l=-14$ (Noll $j=151$, OSA/ANSI $j=137$, Fringe $j=229$, Wyant+ $j=228$).+- params:+ n: '17'+ l: '1'+ form: radial+ number: 24310*t^17 - 102960*t^15 + 180180*t^13 - 168168*t^11 + 90090*t^9 - 27720*t^7+ + 4620*t^5 - 360*t^3 + 9*t+ comment: Radial part for $l=1$ (Noll $j=154$, OSA/ANSI $j=162$, Fringe $j=98$, Wyant+ $j=97$) and $l=-1$ (Noll $j=155$, OSA/ANSI $j=161$, Fringe $j=99$, Wyant $j=98$).+- params:+ n: '17'+ l: '3'+ form: radial+ number: 19448*t^17 - 80080*t^15 + 135135*t^13 - 120120*t^11 + 60060*t^9 - 16632*t^7+ + 2310*t^5 - 120*t^3+ comment: Radial part for $l=3$ (Noll $j=156$, OSA/ANSI $j=163$, Fringe $j=115$,+ Wyant $j=114$) and $l=-3$ (Noll $j=157$, OSA/ANSI $j=160$, Fringe $j=116$, Wyant+ $j=115$).+- params:+ n: '17'+ l: '5'+ form: radial+ number: 12376*t^17 - 48048*t^15 + 75075*t^13 - 60060*t^11 + 25740*t^9 - 5544*t^7+ + 462*t^5+ comment: Radial part for $l=5$ (Noll $j=158$, OSA/ANSI $j=164$, Fringe $j=134$,+ Wyant $j=133$) and $l=-5$ (Noll $j=159$, OSA/ANSI $j=159$, Fringe $j=135$, Wyant+ $j=134$).+- params:+ n: '17'+ l: '7'+ form: radial+ number: 6188*t^17 - 21840*t^15 + 30030*t^13 - 20020*t^11 + 6435*t^9 - 792*t^7+ comment: Radial part for $l=7$ (Noll $j=160$, OSA/ANSI $j=165$, Fringe $j=155$,+ Wyant $j=154$) and $l=-7$ (Noll $j=161$, OSA/ANSI $j=158$, Fringe $j=156$, Wyant+ $j=155$).+- params:+ n: '17'+ l: '9'+ form: radial+ number: 2380*t^17 - 7280*t^15 + 8190*t^13 - 4004*t^11 + 715*t^9+ comment: Radial part for $l=9$ (Noll $j=162$, OSA/ANSI $j=166$, Fringe $j=178$,+ Wyant $j=177$) and $l=-9$ (Noll $j=163$, OSA/ANSI $j=157$, Fringe $j=179$, Wyant+ $j=178$).+- params:+ n: '17'+ l: '11'+ form: radial+ number: 680*t^17 - 1680*t^15 + 1365*t^13 - 364*t^11+ comment: Radial part for $l=11$ (Noll $j=164$, OSA/ANSI $j=167$, Fringe $j=203$,+ Wyant $j=202$) and $l=-11$ (Noll $j=165$, OSA/ANSI $j=156$, Fringe $j=204$, Wyant+ $j=203$).+- params:+ n: '17'+ l: '13'+ form: radial+ number: 136*t^17 - 240*t^15 + 105*t^13+ comment: Radial part for $l=13$ (Noll $j=166$, OSA/ANSI $j=168$, Fringe $j=230$,+ Wyant $j=229$) and $l=-13$ (Noll $j=167$, OSA/ANSI $j=155$, Fringe $j=231$, Wyant+ $j=230$).+- params:+ n: '17'+ l: '15'+ form: radial+ number: 17*t^17 - 16*t^15+ comment: Radial part for $l=15$ (Noll $j=168$, OSA/ANSI $j=169$, Fringe $j=259$,+ Wyant $j=258$) and $l=-15$ (Noll $j=169$, OSA/ANSI $j=154$, Fringe $j=260$, Wyant+ $j=259$).+- params:+ n: '18'+ l: '0'+ form: radial+ number: 48620*t^18 - 218790*t^16 + 411840*t^14 - 420420*t^12 + 252252*t^10 - 90090*t^8+ + 18480*t^6 - 1980*t^4 + 90*t^2 - 1+ comment: Radial part for Noll $j=172$, OSA/ANSI $j=180$, Fringe $j=100$, Wyant $j=99$.+- params:+ n: '18'+ l: '2'+ form: radial+ number: 43758*t^18 - 194480*t^16 + 360360*t^14 - 360360*t^12 + 210210*t^10 - 72072*t^8+ + 13860*t^6 - 1320*t^4 + 45*t^2+ comment: Radial part for $l=2$ (Noll $j=174$, OSA/ANSI $j=181$, Fringe $j=117$,+ Wyant $j=116$) and $l=-2$ (Noll $j=173$, OSA/ANSI $j=179$, Fringe $j=118$, Wyant+ $j=117$).+- params:+ n: '18'+ l: '4'+ form: radial+ number: 31824*t^18 - 136136*t^16 + 240240*t^14 - 225225*t^12 + 120120*t^10 - 36036*t^8+ + 5544*t^6 - 330*t^4+ comment: Radial part for $l=4$ (Noll $j=176$, OSA/ANSI $j=182$, Fringe $j=136$,+ Wyant $j=135$) and $l=-4$ (Noll $j=175$, OSA/ANSI $j=178$, Fringe $j=137$, Wyant+ $j=136$).+- params:+ n: '18'+ l: '6'+ form: radial+ number: 18564*t^18 - 74256*t^16 + 120120*t^14 - 100100*t^12 + 45045*t^10 - 10296*t^8+ + 924*t^6+ comment: Radial part for $l=6$ (Noll $j=178$, OSA/ANSI $j=183$, Fringe $j=157$,+ Wyant $j=156$) and $l=-6$ (Noll $j=177$, OSA/ANSI $j=177$, Fringe $j=158$, Wyant+ $j=157$).+- params:+ n: '18'+ l: '8'+ form: radial+ number: 8568*t^18 - 30940*t^16 + 43680*t^14 - 30030*t^12 + 10010*t^10 - 1287*t^8+ comment: Radial part for $l=8$ (Noll $j=180$, OSA/ANSI $j=184$, Fringe $j=180$,+ Wyant $j=179$) and $l=-8$ (Noll $j=179$, OSA/ANSI $j=176$, Fringe $j=181$, Wyant+ $j=180$).+- params:+ n: '18'+ l: '10'+ form: radial+ number: 3060*t^18 - 9520*t^16 + 10920*t^14 - 5460*t^12 + 1001*t^10+ comment: Radial part for $l=10$ (Noll $j=182$, OSA/ANSI $j=185$, Fringe $j=205$,+ Wyant $j=204$) and $l=-10$ (Noll $j=181$, OSA/ANSI $j=175$, Fringe $j=206$, Wyant+ $j=205$).+- params:+ n: '18'+ l: '12'+ form: radial+ number: 816*t^18 - 2040*t^16 + 1680*t^14 - 455*t^12+ comment: Radial part for $l=12$ (Noll $j=184$, OSA/ANSI $j=186$, Fringe $j=232$,+ Wyant $j=231$) and $l=-12$ (Noll $j=183$, OSA/ANSI $j=174$, Fringe $j=233$, Wyant+ $j=232$).+- params:+ n: '18'+ l: '14'+ form: radial+ number: 153*t^18 - 272*t^16 + 120*t^14+ comment: Radial part for $l=14$ (Noll $j=186$, OSA/ANSI $j=187$, Fringe $j=261$,+ Wyant $j=260$) and $l=-14$ (Noll $j=185$, OSA/ANSI $j=173$, Fringe $j=262$, Wyant+ $j=261$).+- params:+ n: '18'+ l: '16'+ form: radial+ number: 18*t^18 - 17*t^16+ comment: Radial part for $l=16$ (Noll $j=188$, OSA/ANSI $j=188$, Fringe $j=292$,+ Wyant $j=291$) and $l=-16$ (Noll $j=187$, OSA/ANSI $j=172$, Fringe $j=293$, Wyant+ $j=292$).+- params:+ n: '19'+ l: '1'+ form: radial+ number: 92378*t^19 - 437580*t^17 + 875160*t^15 - 960960*t^13 + 630630*t^11 - 252252*t^9+ + 60060*t^7 - 7920*t^5 + 495*t^3 - 10*t+ comment: Radial part for $l=1$ (Noll $j=192$, OSA/ANSI $j=200$, Fringe $j=119$,+ Wyant $j=118$) and $l=-1$ (Noll $j=191$, OSA/ANSI $j=199$, Fringe $j=120$, Wyant+ $j=119$).+- params:+ n: '19'+ l: '3'+ form: radial+ number: 75582*t^19 - 350064*t^17 + 680680*t^15 - 720720*t^13 + 450450*t^11 - 168168*t^9+ + 36036*t^7 - 3960*t^5 + 165*t^3+ comment: Radial part for $l=3$ (Noll $j=194$, OSA/ANSI $j=201$, Fringe $j=138$,+ Wyant $j=137$) and $l=-3$ (Noll $j=193$, OSA/ANSI $j=198$, Fringe $j=139$, Wyant+ $j=138$).+- params:+ n: '19'+ l: '5'+ form: radial+ number: 50388*t^19 - 222768*t^17 + 408408*t^15 - 400400*t^13 + 225225*t^11 - 72072*t^9+ + 12012*t^7 - 792*t^5+ comment: Radial part for $l=5$ (Noll $j=196$, OSA/ANSI $j=202$, Fringe $j=159$,+ Wyant $j=158$) and $l=-5$ (Noll $j=195$, OSA/ANSI $j=197$, Fringe $j=160$, Wyant+ $j=159$).+- params:+ n: '19'+ l: '7'+ form: radial+ number: 27132*t^19 - 111384*t^17 + 185640*t^15 - 160160*t^13 + 75075*t^11 - 18018*t^9+ + 1716*t^7+ comment: Radial part for $l=7$ (Noll $j=198$, OSA/ANSI $j=203$, Fringe $j=182$,+ Wyant $j=181$) and $l=-7$ (Noll $j=197$, OSA/ANSI $j=196$, Fringe $j=183$, Wyant+ $j=182$).+- params:+ n: '19'+ l: '9'+ form: radial+ number: 11628*t^19 - 42840*t^17 + 61880*t^15 - 43680*t^13 + 15015*t^11 - 2002*t^9+ comment: Radial part for $l=9$ (Noll $j=200$, OSA/ANSI $j=204$, Fringe $j=207$,+ Wyant $j=206$) and $l=-9$ (Noll $j=199$, OSA/ANSI $j=195$, Fringe $j=208$, Wyant+ $j=207$).+- params:+ n: '19'+ l: '11'+ form: radial+ number: 3876*t^19 - 12240*t^17 + 14280*t^15 - 7280*t^13 + 1365*t^11+ comment: Radial part for $l=11$ (Noll $j=202$, OSA/ANSI $j=205$, Fringe $j=234$,+ Wyant $j=233$) and $l=-11$ (Noll $j=201$, OSA/ANSI $j=194$, Fringe $j=235$, Wyant+ $j=234$).+- params:+ n: '19'+ l: '13'+ form: radial+ number: 969*t^19 - 2448*t^17 + 2040*t^15 - 560*t^13+ comment: Radial part for $l=13$ (Noll $j=204$, OSA/ANSI $j=206$, Fringe $j=263$,+ Wyant $j=262$) and $l=-13$ (Noll $j=203$, OSA/ANSI $j=193$, Fringe $j=264$, Wyant+ $j=263$).+- params:+ n: '19'+ l: '15'+ form: radial+ number: 171*t^19 - 306*t^17 + 136*t^15+ comment: Radial part for $l=15$ (Noll $j=206$, OSA/ANSI $j=207$, Fringe $j=294$,+ Wyant $j=293$) and $l=-15$ (Noll $j=205$, OSA/ANSI $j=192$, Fringe $j=295$, Wyant+ $j=294$).+- params:+ n: '19'+ l: '17'+ form: radial+ number: 19*t^19 - 18*t^17+ comment: Radial part for $l=17$ (Noll $j=208$, OSA/ANSI $j=208$, Fringe $j=327$,+ Wyant $j=326$) and $l=-17$ (Noll $j=207$, OSA/ANSI $j=191$, Fringe $j=328$, Wyant+ $j=327$).+- params:+ n: '20'+ l: '0'+ form: radial+ number: 184756*t^20 - 923780*t^18 + 1969110*t^16 - 2333760*t^14 + 1681680*t^12 -+ 756756*t^10 + 210210*t^8 - 34320*t^6 + 2970*t^4 - 110*t^2 + 1+ comment: Radial part for Noll $j=211$, OSA/ANSI $j=220$, Fringe $j=121$, Wyant $j=120$.+- params:+ n: '20'+ l: '2'+ form: radial+ number: 167960*t^20 - 831402*t^18 + 1750320*t^16 - 2042040*t^14 + 1441440*t^12 -+ 630630*t^10 + 168168*t^8 - 25740*t^6 + 1980*t^4 - 55*t^2+ comment: Radial part for $l=2$ (Noll $j=212$, OSA/ANSI $j=221$, Fringe $j=140$,+ Wyant $j=139$) and $l=-2$ (Noll $j=213$, OSA/ANSI $j=219$, Fringe $j=141$, Wyant+ $j=140$).+- params:+ n: '20'+ l: '4'+ form: radial+ number: 125970*t^20 - 604656*t^18 + 1225224*t^16 - 1361360*t^14 + 900900*t^12 -+ 360360*t^10 + 84084*t^8 - 10296*t^6 + 495*t^4+ comment: Radial part for $l=4$ (Noll $j=214$, OSA/ANSI $j=222$, Fringe $j=161$,+ Wyant $j=160$) and $l=-4$ (Noll $j=215$, OSA/ANSI $j=218$, Fringe $j=162$, Wyant+ $j=161$).+- params:+ n: '20'+ l: '6'+ form: radial+ number: 77520*t^20 - 352716*t^18 + 668304*t^16 - 680680*t^14 + 400400*t^12 - 135135*t^10+ + 24024*t^8 - 1716*t^6+ comment: Radial part for $l=6$ (Noll $j=216$, OSA/ANSI $j=223$, Fringe $j=184$,+ Wyant $j=183$) and $l=-6$ (Noll $j=217$, OSA/ANSI $j=217$, Fringe $j=185$, Wyant+ $j=184$).+- params:+ n: '20'+ l: '8'+ form: radial+ number: 38760*t^20 - 162792*t^18 + 278460*t^16 - 247520*t^14 + 120120*t^12 - 30030*t^10+ + 3003*t^8+ comment: Radial part for $l=8$ (Noll $j=218$, OSA/ANSI $j=224$, Fringe $j=209$,+ Wyant $j=208$) and $l=-8$ (Noll $j=219$, OSA/ANSI $j=216$, Fringe $j=210$, Wyant+ $j=209$).+- params:+ n: '20'+ l: '10'+ form: radial+ number: 15504*t^20 - 58140*t^18 + 85680*t^16 - 61880*t^14 + 21840*t^12 - 3003*t^10+ comment: Radial part for $l=10$ (Noll $j=220$, OSA/ANSI $j=225$, Fringe $j=236$,+ Wyant $j=235$) and $l=-10$ (Noll $j=221$, OSA/ANSI $j=215$, Fringe $j=237$, Wyant+ $j=236$).+- params:+ n: '20'+ l: '12'+ form: radial+ number: 4845*t^20 - 15504*t^18 + 18360*t^16 - 9520*t^14 + 1820*t^12+ comment: Radial part for $l=12$ (Noll $j=222$, OSA/ANSI $j=226$, Fringe $j=265$,+ Wyant $j=264$) and $l=-12$ (Noll $j=223$, OSA/ANSI $j=214$, Fringe $j=266$, Wyant+ $j=265$).+- params:+ n: '20'+ l: '14'+ form: radial+ number: 1140*t^20 - 2907*t^18 + 2448*t^16 - 680*t^14+ comment: Radial part for $l=14$ (Noll $j=224$, OSA/ANSI $j=227$, Fringe $j=296$,+ Wyant $j=295$) and $l=-14$ (Noll $j=225$, OSA/ANSI $j=213$, Fringe $j=297$, Wyant+ $j=296$).+- params:+ n: '20'+ l: '16'+ form: radial+ number: 190*t^20 - 342*t^18 + 153*t^16+ comment: Radial part for $l=16$ (Noll $j=226$, OSA/ANSI $j=228$, Fringe $j=329$,+ Wyant $j=328$) and $l=-16$ (Noll $j=227$, OSA/ANSI $j=212$, Fringe $j=330$, Wyant+ $j=329$).+- params:+ n: '20'+ l: '18'+ form: radial+ number: 20*t^20 - 19*t^18+ comment: Radial part for $l=18$ (Noll $j=228$, OSA/ANSI $j=229$, Fringe $j=364$,+ Wyant $j=363$) and $l=-18$ (Noll $j=229$, OSA/ANSI $j=211$, Fringe $j=365$, Wyant+ $j=364$).
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