Abstract

We address and correct errors that we found in the polynomials and figures in our paper [V. N. Mahajan and G.-m. Dai, J. Opt. Soc. Am. A 24, 2994 (2007) [CrossRef]  ].

© 2012 Optical Society of America

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References

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  1. V. N. Mahajan and G.-m. Dai, “Orthonormal polynomials in wavefront analysis: analytical solution,” J. Opt. Soc. Am. A 24, 2994–3016 (2007).
    [CrossRef]
  2. V. N. Mahajan, “Orthonormal polynomials in wavefront analysis,” Handbook of Optics, 3rd ed., V. N. Mahajan, ed., Vol. II (McGraw Hill, 2009), pp. 11.3–11.41.

2007

J. Opt. Soc. Am. A

Other

V. N. Mahajan, “Orthonormal polynomials in wavefront analysis,” Handbook of Optics, 3rd ed., V. N. Mahajan, ed., Vol. II (McGraw Hill, 2009), pp. 11.3–11.41.

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Figures (1)

Fig. 1.
Fig. 1.

Interferogram and PSF for polynomials E6 (astigmatism), E11 (spherical), R6 (astigmatism), and R11 (spherical) for a sigma value of one wavelength.

Equations (24)

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H29(ρ,θ)=(15.56917599ρ+130.07864353ρ3291.15952742ρ5+190.97455178ρ7)sinθ+1.41366362ρ5sin5θ,
H30(ρ,θ)=(15.56917599ρ+130.07864353ρ3291.15952742ρ5+190.97455178ρ7)cosθ1.41366362ρ5cos5θ,
H33(ρ,θ)=(3.87525156ρ+41.84243767ρ3117.56342978ρ5+94.71450820ρ7)sinθ+(38.04631430ρ5+54.80141514ρ7)sin5θ,
H34(ρ,θ)=(3.87525156ρ41.84243767ρ3+117.56342978ρ594.71450820ρ7)cosθ+(38.04631430ρ5+54.80141514ρ7)cos5θ,
H35(ρ,θ)=(3.10311187ρ34.93479698ρ3+102.08124605ρ585.32630533ρ7)sinθ+(6.01202622ρ510.14399046ρ7)sin5θ+8.97812952ρ7sin7θ,
H36(ρ,θ)=(3.10311187ρ34.93479698ρ3+102.08124605ρ585.32630533ρ7)cosθ+(6.01202622ρ5+10.14399046ρ7)cos5θ+8.97812952ρ7cos7θ,
H38(ρ,θ)=(42.96232789+287.78381063ρ2565.13651608ρ4+339.98298180ρ6)ρ2cos2θ+(8.4978641413.58537785ρ2)ρ4cos4θ,
H39(ρ,θ)=(42.96232789+287.78381063ρ2565.13651608ρ4+339.98298180ρ6)ρ2sin2θ(8.4978641413.58537785ρ2)ρ4sin4θ,
H20(x,y)=(2.17600247+13.23551876ρ2+13.64110699ρ4)x119.18577680ρ2x3+95.34862128x5,
H21(x,y)=(2.1760024713.23551876ρ2+45.95178131ρ4)y119.18577680ρ2y3+95.34862128y5,
H29(x,y)=(15.56917599+130.07864353ρ2284.09120931ρ4+190.97455178ρ6)y28.2732724ρ2y3+22.61861792y5,
H30(x,y)=(15.56917599+130.07864353ρ2298.22784553ρ4+190.97455178ρ6)x+28.27327243ρ2x322.61861792x5,
H21(30°)=0.71499593Z30.72488884Z70.46636441Z17+1.72029850Z21,
E6(x,y)=[6/b232b2+3b4][b2(1b2)+b2(3b21)x2(3b2)y2],
E11(ρ,θ)=(5/α)[3+2b2+3b424(1+b2)ρ2+48ρ412(1b2)ρ2cos2θ],
E12=5/8b2(195475b2+558b4422b6+159b815b10)β1Z115/8b2(105205b2+194b4114b6+5b8+15b10)β1Z4+(1/2)15b2(75155b2+174b4134b6+55b815b10)β1Z6102b2(32b2+2b63b8)β1Z11+b2αγ1Z12,
β=αγ,
E14=(5/2/4)(1b2)2b4(3510b2b4)γ1Z1+(515/2/8)(1b2)2b4(7+2b2b4)γ1Z415/8b4(3570b2+56b426b6+5b8)γ1Z6+(5/82)(1b2)2b4(7+10b2+7b4)γ1Z11(5/8)b4(76b2+6b67b8)γ1Z12+(γ/8)b4Z14,
E15=(15/4)b3(58b2+3b4)δ1Z5(5/4)(1b4)b3δ1Z13+b3(δ/2)Z15,
R12=(3μ/16a2νη){(105550a2+1559a42836a6+2695a81078a10)Z1+53(1474a2+205a4360a6+335a8134a10)Z4+(5/2)3/2(35156a2+421a4530a6+265a8)Z6+215(14a2+6a44a6)Z11+[(7/2)5/2η/(1a2)]Z12},
η=945a2+139a4237a6+201a867a10=(1a2)μ2,
S37(x,y)=2.3447555855.32128002ρ2+283.78448194ρ4532.71123567ρ6+332.94452229ρ8+8(12.75329096ρ220.75498320ρ4)x2+8(12.75329096+20.75498320ρ2)x4.
cj,k=14a1a2aadx1a21a2ZjRkdy
14a1a2aadx1a21a2RjRjdy=δjj.

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