Abstract

In this erratum, two errors in our recently published paper [Appl. Opt. 56, 8570 (2017) [CrossRef]  ] are corrected.

© 2018 Optical Society of America

  • 1. The term of wij0(1) in Table 1 of Ref. [1] should be written as A1iB1jwij0(1); thus we should define a new parameter w^ij0(1) to represent it,
    w^ij0(1)=A1iB1jwij0(1)
    In addition, the expression of w240(E) in Table 1 is incorrect and needs to be revised. Consequently, Table 1 should be revised as follows:
    w400(E)=9ϕ1w^300(1)w300(2)w220(E)=3ϕ1(w^120(1)w300(2)+w^300(1)w120(2))+4ϕ2w^120(1)w120(2)w040(E)=ϕ1w^120(1)w120(2)w500(E)=12ϕ1(w^300(1)w400(2)+w^400(1)w300(2))w140(E)=2ϕ1(w^120(1)w220(2)+w^220(1)w120(2))+8ϕ2(w^120(1)w040(2)+w^040(1)w120(2))w320(E)=2ϕ1[2(w^120(1)w400(2)+w^400(1)w120(2))+3(w^300(1)w220(2)+w^220(1)w300(2))]+4ϕ2(w^120(1)w220(2)+w^220(1)w120(2))w600(E)=ϕ1[15(w^300(1)w500(2)+w^500(1)w300(2))+16w^400(1)w400(2)]w240(E)=ϕ1[3(w^120(1)w320(2)+w^320(1)w120(2)+w^140(1)w300(2)+w^300(1)w140(2))+4w^220(1)w220(2)]+8ϕ2(w^040(1)w220(2)+w^220(1)w040(2)+w^120(1)w140(2)+w^140(1)w120(2))w420(E)=ϕ1[8(w^220(1)w400(2)+w^400(1)w220(2))+9(w^320(1)w300(2)+w^300(1)w320(2))+5(w^500(1)w120(2)+w^120(1)w500(2))]+4ϕ2(w^320(1)w120(2)+w^120(1)w320(2)+w^220(1)w220(2))w060(E)=ϕ1(w^120(1)w140(2)+w^140(1)w120(2))+16ϕ2w^040(1)w040(2).
    Accordingly, in the paragraph below Eq. (57), wij0(1)w˜ij0 should be revised to be w^ij0(1)w˜ij0.
  • 2. The expression c3,2* is missing in Appendix A, and thus should have appeared as
    c3,2*=(c0,2c3,0+c1,2c2,0)sinαtanαrmc3,2.

    The above two errors do not affect the numerical calculations in Section 5 in Ref. [1], since the calculations were based on the correct equations.

REFERENCE

1. L. Lu and Y. Cao, “Sixth-order wave aberration theory of ultrawide-angle optical systems,” Appl. Opt. 56, 8570–8583 (2017). [CrossRef]  

References

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  1. L. Lu and Y. Cao, “Sixth-order wave aberration theory of ultrawide-angle optical systems,” Appl. Opt. 56, 8570–8583 (2017).
    [Crossref]

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Equations (3)

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w ^ i j 0 ( 1 ) = A 1 i B 1 j w i j 0 ( 1 )
w 400 ( E ) = 9 ϕ 1 w ^ 300 ( 1 ) w 300 ( 2 ) w 220 ( E ) = 3 ϕ 1 ( w ^ 120 ( 1 ) w 300 ( 2 ) + w ^ 300 ( 1 ) w 120 ( 2 ) ) + 4 ϕ 2 w ^ 120 ( 1 ) w 120 ( 2 ) w 040 ( E ) = ϕ 1 w ^ 120 ( 1 ) w 120 ( 2 ) w 500 ( E ) = 12 ϕ 1 ( w ^ 300 ( 1 ) w 400 ( 2 ) + w ^ 400 ( 1 ) w 300 ( 2 ) ) w 140 ( E ) = 2 ϕ 1 ( w ^ 120 ( 1 ) w 220 ( 2 ) + w ^ 220 ( 1 ) w 120 ( 2 ) ) + 8 ϕ 2 ( w ^ 120 ( 1 ) w 040 ( 2 ) + w ^ 040 ( 1 ) w 120 ( 2 ) ) w 320 ( E ) = 2 ϕ 1 [ 2 ( w ^ 120 ( 1 ) w 400 ( 2 ) + w ^ 400 ( 1 ) w 120 ( 2 ) ) + 3 ( w ^ 300 ( 1 ) w 220 ( 2 ) + w ^ 220 ( 1 ) w 300 ( 2 ) ) ] + 4 ϕ 2 ( w ^ 120 ( 1 ) w 220 ( 2 ) + w ^ 220 ( 1 ) w 120 ( 2 ) ) w 600 ( E ) = ϕ 1 [ 15 ( w ^ 300 ( 1 ) w 500 ( 2 ) + w ^ 500 ( 1 ) w 300 ( 2 ) ) + 16 w ^ 400 ( 1 ) w 400 ( 2 ) ] w 240 ( E ) = ϕ 1 [ 3 ( w ^ 120 ( 1 ) w 320 ( 2 ) + w ^ 320 ( 1 ) w 120 ( 2 ) + w ^ 140 ( 1 ) w 300 ( 2 ) + w ^ 300 ( 1 ) w 140 ( 2 ) ) + 4 w ^ 220 ( 1 ) w 220 ( 2 ) ] + 8 ϕ 2 ( w ^ 040 ( 1 ) w 220 ( 2 ) + w ^ 220 ( 1 ) w 040 ( 2 ) + w ^ 120 ( 1 ) w 140 ( 2 ) + w ^ 140 ( 1 ) w 120 ( 2 ) ) w 420 ( E ) = ϕ 1 [ 8 ( w ^ 220 ( 1 ) w 400 ( 2 ) + w ^ 400 ( 1 ) w 220 ( 2 ) ) + 9 ( w ^ 320 ( 1 ) w 300 ( 2 ) + w ^ 300 ( 1 ) w 320 ( 2 ) ) + 5 ( w ^ 500 ( 1 ) w 120 ( 2 ) + w ^ 120 ( 1 ) w 500 ( 2 ) ) ] + 4 ϕ 2 ( w ^ 320 ( 1 ) w 120 ( 2 ) + w ^ 120 ( 1 ) w 320 ( 2 ) + w ^ 220 ( 1 ) w 220 ( 2 ) ) w 060 ( E ) = ϕ 1 ( w ^ 120 ( 1 ) w 140 ( 2 ) + w ^ 140 ( 1 ) w 120 ( 2 ) ) + 16 ϕ 2 w ^ 040 ( 1 ) w 040 ( 2 ) .
c 3 , 2 * = ( c 0 , 2 c 3 , 0 + c 1 , 2 c 2 , 0 ) sin α tan α r m c 3 , 2 .

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