Lateral-shift variable aberration generators

Iwona A. Palusinski; José M. Sasián; John E. Greivenkamp

doi:10.1364/AO.38.000086

Applied Optics
Vol. 38,
Issue 1,
pp. 86-90
(1999)
•https://doi.org/10.1364/AO.38.000086

Lateral-shift variable aberration generators

Iwona A. Palusinski, José M. Sasián, and John E. Greivenkamp

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Iwona A. Palusinski, José M. Sasián, and John E. Greivenkamp, "Lateral-shift variable aberration generators," Appl. Opt. 38, 86-90 (1999)

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Previously assigned OCIS codes
- Lens system design (080.3620)
- Aberrations (global) (220.1010)
- Aspherics (220.1250)

About this Article
History
- Original Manuscript: May 8, 1998
- Revised Manuscript: September 15, 1998
- Published: January 1, 1999

Abstract

We describe and analyze an optical device capable of generating tilt, defocus, astigmatism, coma, and spherical aberration wave-front deformation. This optical device consists of a pair of aspheric plates that produce aberrations by laterally shifting one plate relative to the other. The surface descriptions of these optical plates are provided, and their aberration-inducing properties are verified with ray-tracing software. In addition, we examine the versatility and the limitations of using variable aberration generators and provide insight into how aberrations may be controlled by a simple lateral shift. The device may find application in aberration control in lens systems that are nonrotationally symmetric.

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Wave-front Deformation	Surface Description T(x, y)	Element Shift (direction, amount)	Result after Shifting Both Elements W(x, y)/(n - 1)
1. Tilt in y	kxy	x, a	k 2 ay
2. Tilt in y	$k \frac{y^{2}}{2}$	y, a	k 2 ay
3. Defocus	$k (\frac{x^{3}}{3} + y^{2} x)$	x, a	$k [2 a (x^{2} + y^{2}) + \frac{2 a^{3}}{3}]$
4. Astigmatism	kxy ²	x, a	k 2 ay ²
5. Astigmatism	$k \frac{y^{3}}{3}$	y, a	$k (2 {ay}^{2} + \frac{2 a^{3}}{3})$
6. Coma	$k (\frac{x^{3} y}{3} + y^{3} x)$	x, a	$k [2 ay (x^{2} + y^{2}) + \frac{y 2 a^{3}}{3}]$
7. Coma	$k (\frac{x^{2} y^{2}}{2} + \frac{y^{4}}{4})$	y, a	$k [2 ay (x^{2} + y^{2}) + y 2 a^{3}]$
8. Spherical	$k (\frac{x^{5}}{5} + \frac{2 x^{3} y^{2}}{3} + {xy}^{4})$	x, a	$k 2 a [{(x^{2} + y^{2})}^{2} + x^{2} 2 a^{2} + \frac{a^{4}}{5} + \frac{2 y^{2} a^{2}}{3}]$
9. Line coma y	kxy ³	x, a	k 2 ay ³
10. Line coma y	$k \frac{y^{4}}{4}$	y, a	k(2 ay ³ + y2a ³)

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