Conditions under which two-element variable power lenses can be created. Part 2.
Application to specific designs

Charles E. Campbell

doi:10.1364/JOSAA.28.002153

Journal of the Optical Society of America A
Vol. 28,
Issue 10,
pp. 2153-2159
(2011)
•https://doi.org/10.1364/JOSAA.28.002153

Conditions under which two-element variable power lenses can be created. Part 2. Application to specific designs

Charles E. Campbell

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Charles E. Campbell, "Conditions under which two-element variable power lenses can be created. Part 2. Application to specific designs," J. Opt. Soc. Am. A 28, 2153-2159 (2011)

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Abstract

It was found in Part 1 of this paper [J. Opt. Soc. Am. A 28, 2148 (2011)] that only variable power optical effects that can be described by quadratic functions can be formed by laterally translating two-element variable power lenses. In the case of rotationally translating two-element variable power lenses, possible designs are found by mapping possible laterally translating designs from a Cartesian space to the polar coordinate space of the rotationally translating lens. Several designs that have been manufactured or suggested theoretically are examined in Part 2 to see which ones are true variable power lenses.

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Unnormalized Zernike Coefficients	Spectra	El
$c_{1}^{- 1}$	0	0
$c_{1}^{1}$	$- 1.5035$	$- 1.7277$
$c_{2}^{- 2}$	0.1879	0.3387
$c_{2}^{0}$	0	0
$c_{2}^{2}$	0	0
$c_{3}^{- 3}$	0	0
$c_{3}^{- 1}$	0	0
$c_{3}^{1}$	$- 0.7518$	$- 0.8668$
$c_{3}^{3}$	0.7518	0.8929
$c_{4}^{- 4}$	$- 0.2506$	$- 0.2207$
$c_{4}^{- 2}$	0.0626	0.1141

Zernike Coefficients	Spectra	El
$c_{1}^{- 1}$	0.817	$- 0.4902$
$c_{1}^{1}$	0.1452	0
$c_{2}^{- 2}$	$- 0.03$	0
$c_{2}^{0}$	4.427	4.4472
$c_{2}^{2}$	$- 0.264$	0.101
$c_{3}^{- 3}$	$- 0.8867$	$- 0.4697$
$c_{3}^{- 1}$	0.0711	$- 0.1795$
$c_{3}^{1}$	0.0013	0
$c_{3}^{3}$	0.0043	0
$c_{4}^{- 4}$	$- 0.0018$	0
$c_{4}^{- 2}$	0.0002	0
$c_{4}^{0}$	0	0.0176
$c_{4}^{2}$	0.0343	$- 0.0297$
$c_{4}^{4}$	$- 0.1373$	$- 0.172$

	Spectra Full	Spectra Half	El Full	El Half
$c_{1}^{- 1}$	0.1845	0.1015	$- 0.1102$	$- 0.1102$
$c_{1}^{1}$	0.0328	0.0337	0.0000	0.0000
$c_{2}^{- 2}$	$- 0.0068$	$- 0.0024$	0.0000	0.0000
$c_{2}^{0}$	1.0000	1.0000	1.0000	1.0000
$c_{2}^{2}$	$- 0.0596$	$- 0.0357$	0.0227	0.0227
$c_{3}^{- 3}$	$- 0.2003$	$- 0.0684$	$- 0.1056$	$- 0.1056$
$c_{3}^{- 1}$	0.0161	0.0043	$- 0.0404$	$- 0.0403$
$c_{3}^{1}$	0.0003	0.0004	0.0000	0.0000
$c_{3}^{3}$	0.0010	$- 0.0019$	0.0000	0.0000
$c_{4}^{- 4}$	$- 0.0004$	$- 0.0009$	0.0000	0.0000
$c_{4}^{- 2}$	0.0000	0.0000	0.0000	0.0000
$c_{4}^{0}$	0.0000	0.0000	0.0040	0.0040
$c_{4}^{2}$	0.0077	0.0095	$- 0.0067$	$- 0.0067$
$c_{4}^{4}$	$- 0.0310$	$- 0.0662$	$- 0.0387$	$- 0.0387$

Unnormalized Zernike Coefficients	Spectra	El
$c_{1}^{- 1}$	0	0
$c_{1}^{1}$	$- 1.5035$	$- 1.7277$
$c_{2}^{- 2}$	0.1879	0.3387
$c_{2}^{0}$	0	0
$c_{2}^{2}$	0	0
$c_{3}^{- 3}$	0	0
$c_{3}^{- 1}$	0	0
$c_{3}^{1}$	$- 0.7518$	$- 0.8668$
$c_{3}^{3}$	0.7518	0.8929
$c_{4}^{- 4}$	$- 0.2506$	$- 0.2207$
$c_{4}^{- 2}$	0.0626	0.1141

Zernike Coefficients	Spectra	El
$c_{1}^{- 1}$	0.817	$- 0.4902$
$c_{1}^{1}$	0.1452	0
$c_{2}^{- 2}$	$- 0.03$	0
$c_{2}^{0}$	4.427	4.4472
$c_{2}^{2}$	$- 0.264$	0.101
$c_{3}^{- 3}$	$- 0.8867$	$- 0.4697$
$c_{3}^{- 1}$	0.0711	$- 0.1795$
$c_{3}^{1}$	0.0013	0
$c_{3}^{3}$	0.0043	0
$c_{4}^{- 4}$	$- 0.0018$	0
$c_{4}^{- 2}$	0.0002	0
$c_{4}^{0}$	0	0.0176
$c_{4}^{2}$	0.0343	$- 0.0297$
$c_{4}^{4}$	$- 0.1373$	$- 0.172$

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Tables (3)

Equations (65)

Journal of the Optical Society of America A