It is a sufficient condition only, not a necessary and sufficient condition, for decomposing wavefront aberrations

Psang Lin

doi:10.1051/jeos/2022004

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Journal of the European Optical Society-Rapid Publications
Vol. 18, Issue 1, 2022004 (2022)

It is a sufficient condition only, not a necessary and sufficient condition, for decomposing wavefront aberrations

Psang Lin^*

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Department of Mechanical Engineering, Taiwan Cheng Kung University, Tainan 70101, China

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DOI: 10.1051/jeos/2022004 Cite this Article

Psang Lin. It is a sufficient condition only, not a necessary and sufficient condition, for decomposing wavefront aberrations[J]. Journal of the European Optical Society-Rapid Publications, 2022, 18(1): 2022004 Copy Citation Text

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The variation of W133 = C133h0ρ3/λ (where h0 = 17 mm, ρ = 21 mm, and λ = 550 µm) versus the separation of image plane Vimage for the optical system of [12]. The Gaussian image plane of this system is located at Vimage = 92.088474 mm when the object is placed at P0z = −200 mm. This figure shows that C133h0ρ3(cosϕ)3 has non-zero value when the image plane is not the Gaussian image plane. It also shows that C133 = 0 when Vimage = 92.088474 mm, indicating C133h0ρ3(cosϕ)3 is the defocus component of primary aberrations.

Fig. 1. The variation of W₁₃₃ = C₁₃₃h₀ρ³/λ (where h₀ = 17 mm, ρ = 21 mm, and λ = 550 µm) versus the separation of image plane V_image for the optical system of [12]. The Gaussian image plane of this system is located at V_image = 92.088474 mm when the object is placed at P_0z = −200 mm. This figure shows that C₁₃₃h₀ρ³(cosϕ)³ has non-zero value when the image plane is not the Gaussian image plane. It also shows that C₁₃₃ = 0 when V_image = 92.088474 mm, indicating C₁₃₃h₀ρ³(cosϕ)³ is the defocus component of primary aberrations.

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q = 4
m	p	(2q – 2p – m, 2p + m, m)	Aberration component
0	0	(8, 0, 0)	C800 $h_{0}^{8}$
	1	(6, 2, 0)	C620 $h_{0}^{6}$ ρ2
	2	(4, 4, 0)	C440 $h_{0}^{4}$ ρ4
	3	(2, 6, 0)	C260 $h_{0}^{2}$ ρ6
	4	(0, 8, 0)	C080ρ8
1	0	(7, 1, 1)	C711 $h_{0}^{7}$ ρcosϕ
	1	(5, 3, 1)	C531 $h_{0}^{5}$ ρ3cosϕ
	2	(3, 5, 1)	C351 $h_{0}^{3}$ ρ5cosϕ
	3	(1, 7, 1)	C171h0ρ7cosϕ
2	0	(6, 2, 2)	C622 $h_{0}^{6}$ ρ2(cosϕ)2
	1	(4, 4, 2)	C442 $h_{0}^{4}$ ρ4(cosϕ)2
	2	(2, 6, 2)	C262 $h_{0}^{2}$ ρ6(cosϕ)2
	3	(0, 8, 2)	No
3	0	(5, 3, 3)	C533 $h_{0}^{5}$ ρ3(cosϕ)3
	1	(3, 5, 3)	C353 $h_{0}^{3}$ ρ5(cosϕ)3
	2	(1, 7, 3)	C173h0ρ7(cosϕ)3
4	0	(4, 4, 4)	C444 $h_{0}^{4}$ ρ4(cosϕ)4
	1	(2, 6, 4)	C264 $h_{0}^{2}$ ρ6(cosϕ)4
	2	(0, 8, 4)	No
5	0	(3, 5, 5)	C355 $h_{0}^{3}$ ρ5(cosϕ)5
5	1	(1, 7, 5)	C175h0ρ7(cosϕ)5
6	0	(2, 6, 6)	C266 $h_{0}^{2}$ ρ6(cosϕ)6
6	1	(0, 8, 6)	No
7	0	(1, 7, 7)	C177h0ρ7(cosϕ)7
8	0	(0, 8, 8)	No

Table 0. Components of tertiary aberrations with q = 4 in axis-symmetrical system.

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q = 3
m	p	(2q – 2p – m, 2p + m, m)	Aberration component
0	0	(6, 0, 0)	C600 $h_{0}^{6}$
	1	(4, 2, 0)	C420 $h_{0}^{4}$ ρ2
	2	(2, 4, 0)	C240 $h_{0}^{2}$ ρ4
	3	(0, 6, 0)	C060ρ6
1	0	(5, 1, 1)	C511 $h_{0}^{5}$ ρcosϕ
	1	(3, 3, 1)	C331 $h_{0}^{3}$ ρ3cosϕ
	2	(1, 5, 1)	C151h0ρ5cosϕ
2	0	(4, 2, 2)	C422 $h_{0}^{4}$ ρ2(cosϕ)2
	1	(2, 4, 2)	C242 $h_{0}^{2}$ ρ4(cosϕ)2
	2	(0, 6, 2)	No
3	0	(3, 3, 3)	C333 $h_{0}^{3}$ ρ3(cosϕ)3
3	1	(1, 5, 3)	C153h0ρ5(cosϕ)3
4	0	(2, 4, 4)	C244 $h_{0}^{2}$ ρ4(cosϕ)4
4	1	(0, 6, 4)	No
5	0	(1, 5, 5)	C155h0ρ5(cosϕ)5
6	0	(0, 6, 6)	No