Aberrations for grazing incidence telescopes

Timo T. Saha

doi:10.1364/AO.27.001492

Applied Optics
Vol. 27,
Issue 8,
pp. 1492-1498
(1988)
•https://doi.org/10.1364/AO.27.001492

Aberrations for grazing incidence telescopes

Timo T. Saha

Not Accessible

Your library or personal account may give you access

Get PDF
Email
Share
Get Citation
Copy Citation Text
Timo T. Saha, "Aberrations for grazing incidence telescopes," Appl. Opt. 27, 1492-1498 (1988)

Export Citation
- BibTex
- Endnote (RIS)
- HTML
- Plain Text
Citation alert
Save article

Abstract

The wavefront aberration polynomial and transverse ray aberration expansions will be derived for grazing incidence two-mirror Wolter telescopes including all paraboloid–hyperboloid and paraboloid–ellipsoid combinations. The reference sphere is determined with the help of the principal surface of the telescope, and the aberration polynomials will be given as functions of the coordinates of the ray intersection with the reference sphere. Third, and some of the fifth- and seventh-order aberration terms will be analyzed. Also, the well-known relationship between wavefront aberration polynomial and transverse ray aberration polynomials will be verified.

Full Article | PDF Article

More Like This

Transverse ray aberrations for paraboloid–hyperboloid telescopes

Timo T. Saha
Appl. Opt. 24(12) 1856-1863 (1985)

Primary aberrations for grazing incidence

Carl E. Winkler and Dietrich Korsch
Appl. Opt. 16(9) 2464-2469 (1977)

Equal-curvature grazing-incidence x-ray telescopes

Timo T. Saha and William Zhang
Appl. Opt. 42(22) 4599-4605 (2003)

Previous Article Next Article

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Figures (4)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Tables (3)

You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Equations (62)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

W₁₃₁	$- \frac{1}{{4 z}_{p}^{3}}$	Third-order coma
W₂₂₀	$\frac{1}{{2 z}_{p}^{2}} (\frac{1}{2 z_{p}} + \frac{1}{R_{1}} + \frac{1}{R_{2}})$	Third-order astigmatism
W₂₂₂	$\frac{1}{{2 z}_{p}^{3}}$	And Petzval
W₁₅₁	$- \frac{1}{{8 z}_{p}^{5}}$	Fifth-order linear coma
W₂₄₀	$\frac{1}{{4 z}_{p}^{4}} (\frac{5}{8 z_{p}} + \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{f}{2 R_{1} R_{2}})$	Fifth order
W₂₄₂	$\frac{3}{{4 z}_{p}^{5}}$	Oblique spherical
W₃₃₁	$- \frac{1}{{2 z}_{p}^{3}} (\frac{f}{z_{p} R_{1} R_{2}} - \frac{1}{R_{1}^{2}} + \frac{1}{R_{2}^{2}} - \frac{1}{R_{1} R_{2}})$	Fifth-order elliptical coma
W₂₆₀	$\frac{f}{8 R_{1} R_{2} z_{p}^{6}}$	Seventh-order term
W₃₅₁	$\frac{f}{{8 z}_{p}^{5} R_{1} R_{2}} (\frac{1}{R_{1}} - \frac{1}{R_{2}})$	Seventh-order term

	Type 1	Type 2	Type 4
f	190.5000	99.9243	99.9243
L	202.4273	85.0025	85.0025
R1max	12.3650	5.5012	5.5012
R1min	12.1725	4.5512	4.5512
R2max	12.1725	4.5512	−3.4406
R2min	11.6224	3.5753	−2.9643
R₁	−0.194844	−1.050719	−1.05071
R₂	−0.194151	0.74783	−0.74793
e	1.001023	1.010571	0.989540

Type	Half-field angle (rad)	rms spot radius		rms OPD
Type	Half-field angle (rad)	Ray tracing (μm)	TRA Eq. (μm)	Ray tracing (μm)	OPD Eqs. (μm)
	0	0	0	0	0
I	0.001	5.556	5.544	3.8055	3.8055
	0.003	47.831	46.963	34.2380	34.2409
	0	0	0	0	0
II	0.001	1.350	1.350	0.0481	0.0480
	0.003	10.718	10.700	0.3801	0.3793
	0.006	42.309	42.231	0.4982	0.4970
	0	0	0	0	0
IV	0.001	12.482	12.626	0.3115	0.3152
	0.003	111.970	113.487	2.9049	2.8289

W₁₃₁	$- \frac{1}{{4 z}_{p}^{3}}$	Third-order coma
W₂₂₀	$\frac{1}{{2 z}_{p}^{2}} (\frac{1}{2 z_{p}} + \frac{1}{R_{1}} + \frac{1}{R_{2}})$	Third-order astigmatism
W₂₂₂	$\frac{1}{{2 z}_{p}^{3}}$	And Petzval
W₁₅₁	$- \frac{1}{{8 z}_{p}^{5}}$	Fifth-order linear coma
W₂₄₀	$\frac{1}{{4 z}_{p}^{4}} (\frac{5}{8 z_{p}} + \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{f}{2 R_{1} R_{2}})$	Fifth order
W₂₄₂	$\frac{3}{{4 z}_{p}^{5}}$	Oblique spherical
W₃₃₁	$- \frac{1}{{2 z}_{p}^{3}} (\frac{f}{z_{p} R_{1} R_{2}} - \frac{1}{R_{1}^{2}} + \frac{1}{R_{2}^{2}} - \frac{1}{R_{1} R_{2}})$	Fifth-order elliptical coma
W₂₆₀	$\frac{f}{8 R_{1} R_{2} z_{p}^{6}}$	Seventh-order term
W₃₅₁	$\frac{f}{{8 z}_{p}^{5} R_{1} R_{2}} (\frac{1}{R_{1}} - \frac{1}{R_{2}})$	Seventh-order term

	Type 1	Type 2	Type 4
f	190.5000	99.9243	99.9243
L	202.4273	85.0025	85.0025
R1max	12.3650	5.5012	5.5012
R1min	12.1725	4.5512	4.5512
R2max	12.1725	4.5512	−3.4406
R2min	11.6224	3.5753	−2.9643
R₁	−0.194844	−1.050719	−1.05071
R₂	−0.194151	0.74783	−0.74793
e	1.001023	1.010571	0.989540

Abstract

Cited By

Figures (4)

Tables (3)

Equations (62)

Applied Optics