Abstract

Equations are presented for the third-order Seidel aberrations of the Gabor superlens (GSL) as a function of microtelescope channel position within the aperture array. To reveal the origin and form of increasing aberration with channel height, Seidel coefficients are derived as a function of the accumulating pitch difference between the lens arrays and the aberrations present in the centered channel. Two- and three-element Gabor lenses are investigated and their aberrations are expressed as a function of first-order design parameters. The derived theory is then compared to a real ray trace simulation to demonstrate the accuracy of third-order aberration theory to predict GSL image quality.

© 2014 Optical Society of America

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References

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  1. C. Hembd-Sölner, R. F. Stephens, and M. C. Huntley, “Imaging properties of the Gabor superlens,” J. Opt. A 1, 94–102 (1999).
    [CrossRef]
  2. K. Stollberg, A. Brückner, J. Duparré, P. Dannberg, A. Braüer, and A. Tünnermann, “The Gabor superlens as an alternative wafer-level camera approach inspired by superposition compound eyes of nocturnal insects,” Opt. Express 17, 15747–15759 (2009).
    [CrossRef]
  3. D. Gabor, “Optical system composed of lenticules,” U.K. Patent541,753 (December10, 1941).
  4. D. Gabor, “Optical system composed of lenticules,” U.S. Patent2,351,034 (July13, 1944).
  5. J. Duparré, “Microoptical telescope compound eye,” Opt. Express 13, 889–903 (2005).
    [CrossRef]
  6. N. Lindlein, “Simulation of micro-optical systems including microlens arrays,” J. Opt. A 4, S1–S9 (2002).
    [CrossRef]
  7. R. Leitel, “A wafer-level camera approach based on the Gabor superlens,” Proc. SPIE 7716, 77160L (2010).
    [CrossRef]
  8. H. R. Fallah, “Design and simulation of a high-resolution superposition compound eye,” J. Mod. Opt. 54, 67–76 (2007).
    [CrossRef]
  9. A. Garza-Rivera, “Design of an ultra-thin objective lens based on superposition compound eye,” Proc. SPIE 7930, 79300D (2011).
    [CrossRef]
  10. J. Duparré, “Chirped arrays of refractive ellipsoidal microlenses for aberration correction under oblique incidence,” Opt. Express 13, 10539–10551 (2005).
    [CrossRef]
  11. A. E. Conrady, Applied Optics and Optical Design (Oxford University, 1929).
  12. H. H. Hopkins, Wave Theory of Aberrations (Oxford University, 1950).
  13. W. T. Welford, Aberrations of Optical Systems (Adam Hilger, 1986).
  14. R. V. Shack, “The use of normalization in the application of simple optical systems,” Proc. SPIE 0054, 155–162 (1974).
    [CrossRef]
  15. P. L. Ruben, “Aberrations arising from decentrations and tilts,” J. Opt. Soc. Am. A 54, 45–52 (1964).
    [CrossRef]
  16. R. S. Longhurst, “Proc. Phys. Soc. B,” Ph.D. thesis (University of London, 1950).
  17. C. G. Wynne, “Primary aberrations and conjugate change,” Proc. Phys. Soc. B 65, 429–437 (1952).
    [CrossRef]
  18. Radient Zemax, Zemax 12 R2 SP1, Version September 28, (2012).

2011

A. Garza-Rivera, “Design of an ultra-thin objective lens based on superposition compound eye,” Proc. SPIE 7930, 79300D (2011).
[CrossRef]

2010

R. Leitel, “A wafer-level camera approach based on the Gabor superlens,” Proc. SPIE 7716, 77160L (2010).
[CrossRef]

2009

2007

H. R. Fallah, “Design and simulation of a high-resolution superposition compound eye,” J. Mod. Opt. 54, 67–76 (2007).
[CrossRef]

2005

2002

N. Lindlein, “Simulation of micro-optical systems including microlens arrays,” J. Opt. A 4, S1–S9 (2002).
[CrossRef]

1999

C. Hembd-Sölner, R. F. Stephens, and M. C. Huntley, “Imaging properties of the Gabor superlens,” J. Opt. A 1, 94–102 (1999).
[CrossRef]

1974

R. V. Shack, “The use of normalization in the application of simple optical systems,” Proc. SPIE 0054, 155–162 (1974).
[CrossRef]

1964

P. L. Ruben, “Aberrations arising from decentrations and tilts,” J. Opt. Soc. Am. A 54, 45–52 (1964).
[CrossRef]

1952

C. G. Wynne, “Primary aberrations and conjugate change,” Proc. Phys. Soc. B 65, 429–437 (1952).
[CrossRef]

Braüer, A.

Brückner, A.

Conrady, A. E.

A. E. Conrady, Applied Optics and Optical Design (Oxford University, 1929).

Dannberg, P.

Duparré, J.

Fallah, H. R.

H. R. Fallah, “Design and simulation of a high-resolution superposition compound eye,” J. Mod. Opt. 54, 67–76 (2007).
[CrossRef]

Gabor, D.

D. Gabor, “Optical system composed of lenticules,” U.S. Patent2,351,034 (July13, 1944).

D. Gabor, “Optical system composed of lenticules,” U.K. Patent541,753 (December10, 1941).

Garza-Rivera, A.

A. Garza-Rivera, “Design of an ultra-thin objective lens based on superposition compound eye,” Proc. SPIE 7930, 79300D (2011).
[CrossRef]

Hembd-Sölner, C.

C. Hembd-Sölner, R. F. Stephens, and M. C. Huntley, “Imaging properties of the Gabor superlens,” J. Opt. A 1, 94–102 (1999).
[CrossRef]

Hopkins, H. H.

H. H. Hopkins, Wave Theory of Aberrations (Oxford University, 1950).

Huntley, M. C.

C. Hembd-Sölner, R. F. Stephens, and M. C. Huntley, “Imaging properties of the Gabor superlens,” J. Opt. A 1, 94–102 (1999).
[CrossRef]

Leitel, R.

R. Leitel, “A wafer-level camera approach based on the Gabor superlens,” Proc. SPIE 7716, 77160L (2010).
[CrossRef]

Lindlein, N.

N. Lindlein, “Simulation of micro-optical systems including microlens arrays,” J. Opt. A 4, S1–S9 (2002).
[CrossRef]

Longhurst, R. S.

R. S. Longhurst, “Proc. Phys. Soc. B,” Ph.D. thesis (University of London, 1950).

Ruben, P. L.

P. L. Ruben, “Aberrations arising from decentrations and tilts,” J. Opt. Soc. Am. A 54, 45–52 (1964).
[CrossRef]

Shack, R. V.

R. V. Shack, “The use of normalization in the application of simple optical systems,” Proc. SPIE 0054, 155–162 (1974).
[CrossRef]

Stephens, R. F.

C. Hembd-Sölner, R. F. Stephens, and M. C. Huntley, “Imaging properties of the Gabor superlens,” J. Opt. A 1, 94–102 (1999).
[CrossRef]

Stollberg, K.

Tünnermann, A.

Welford, W. T.

W. T. Welford, Aberrations of Optical Systems (Adam Hilger, 1986).

Wynne, C. G.

C. G. Wynne, “Primary aberrations and conjugate change,” Proc. Phys. Soc. B 65, 429–437 (1952).
[CrossRef]

J. Mod. Opt.

H. R. Fallah, “Design and simulation of a high-resolution superposition compound eye,” J. Mod. Opt. 54, 67–76 (2007).
[CrossRef]

J. Opt. A

C. Hembd-Sölner, R. F. Stephens, and M. C. Huntley, “Imaging properties of the Gabor superlens,” J. Opt. A 1, 94–102 (1999).
[CrossRef]

N. Lindlein, “Simulation of micro-optical systems including microlens arrays,” J. Opt. A 4, S1–S9 (2002).
[CrossRef]

J. Opt. Soc. Am. A

P. L. Ruben, “Aberrations arising from decentrations and tilts,” J. Opt. Soc. Am. A 54, 45–52 (1964).
[CrossRef]

Opt. Express

Proc. Phys. Soc. B

C. G. Wynne, “Primary aberrations and conjugate change,” Proc. Phys. Soc. B 65, 429–437 (1952).
[CrossRef]

Proc. SPIE

R. V. Shack, “The use of normalization in the application of simple optical systems,” Proc. SPIE 0054, 155–162 (1974).
[CrossRef]

R. Leitel, “A wafer-level camera approach based on the Gabor superlens,” Proc. SPIE 7716, 77160L (2010).
[CrossRef]

A. Garza-Rivera, “Design of an ultra-thin objective lens based on superposition compound eye,” Proc. SPIE 7930, 79300D (2011).
[CrossRef]

Other

A. E. Conrady, Applied Optics and Optical Design (Oxford University, 1929).

H. H. Hopkins, Wave Theory of Aberrations (Oxford University, 1950).

W. T. Welford, Aberrations of Optical Systems (Adam Hilger, 1986).

D. Gabor, “Optical system composed of lenticules,” U.K. Patent541,753 (December10, 1941).

D. Gabor, “Optical system composed of lenticules,” U.S. Patent2,351,034 (July13, 1944).

Radient Zemax, Zemax 12 R2 SP1, Version September 28, (2012).

R. S. Longhurst, “Proc. Phys. Soc. B,” Ph.D. thesis (University of London, 1950).

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Figures (5)

Fig. 1.
Fig. 1.

Three-element GSL. The center channel (blue) forms a tightly focused image and aberrations increase as channels move outward in the array.

Fig. 2.
Fig. 2.

(a) Layout of a two-element GSL and (b) layout of a three-element GSL. As shown elements are plano-convex. Length parameters are air-equivalent values.

Fig. 3.
Fig. 3.

Marginal and chief rays passing through two channels of the Gabor superlens.

Fig. 4.
Fig. 4.

Top: Optical layout of channels C0,0 through C0,3 of a two-element GSL. Bottom: Transverse ray aberrations computed from third-order aberration theory and the real ray-tracing model.

Fig. 5.
Fig. 5.

Top: Optical layout of channels C0,0 through C0,3 of a three-element GSL. Bottom: Transverse ray aberrations computed from third-order aberration theory and the real ray-tracing model.

Tables (2)

Tables Icon

Table 1. Two-Element GSL Design Parameters

Tables Icon

Table 2. Three-Element GSL Design Parameters

Equations (17)

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Mi=(Mi11Mi12δiMi21Mi22γi001).
Msys=MnM2M1=(M11M12M13M21M22M23001),
(hα1)=Msys(hα1),
F=popoprfr[Gabor condition,two element]F=fodfo+frdfr[focusing condition]F/#=fepo[systemF/#]fe=Ffodfo[EFL].
F=dpodpffopo+fopfpoffdpodpffopo+fopffrpo+frpfpoff+prfffr[Gabor condition,three element](popf)fo=(popr)d[common axis]1ff=1fo+1dfo[field lens conjugates].
SI=14y4φ3σI[spherical aberration]SII=12Hy2φ2σII[coma]SIII=H2φσIII[astigmatism]SIV=H2φσIV[field curvature]SV=2H3y2σV[distortion].
σI=(n+2)n(n1)2X24(n+1)n(n1)XY+(3n+2)nY2+n2(n1)2σII=(n+1)n(n1)X(2n+1)nYσIII=1σIV=1nσV=0.
ΔσI=0ΔσII=TσIΔσIII=2TσII+T2σIΔσIV=0ΔσV=T(σIV+3σIII)+3T2σII+T3σI,
SI*=SISII*=(hδh0)SII+TSISIII*=(hδh0)2SIII+2T(hδh0)SII+T2SISIV*=(hδh0)2SIVSV*=(hδh0)3SV+T[(hδh0)2SIV+3(hδh0)2SIII]+3T2(hδh0)SII+T3SI,
T=δudp.
δi,j=i2+j2(PrPo).
Ti,j=2i2+j2(PrPo)po.
(hδi,jh0)=(hi2+j2(PrPo)foαmax).
ΔSIVi,j=SrIVi,jSrIV0,0.
(hδi,jh0)r=(hi2+j2(PrPo)foαmax)Tri,j=0.
(hδi,jh0)f=(hi2+j2(PfPo)foαmax)Tfi,j=2i2+j2(PfPo)po.
εx=SI*2uρ3+(SIII*+SIV*)2uρ2εy=SI*2uρ3+3SII*2uρ2+SIII*uρ2+(SIII*+SIV*)2uρ2,

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