Abstract

We describe a design methodology for synthesizing cubic-phase optical elements using two-dimensional subwavelength microstructures. We combined a numerical and experimental approach to demonstrate that by spatially varying the geometric properties of binary subwavelength gratings it is possible to produce a diffractive element with a cubic-phase profile. A test element was designed and fabricated for operation in the LWIR, ~λ=10.6 µm. Experimental results verify the cubic-phase nature of the element.

© 2008 Optical Society of America

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References

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2004 (1)

1998 (1)

1996 (1)

1995 (2)

1994 (1)

Cathey, W.T.

Deaver, D. M.

Dowski, E. R.

Dowski, E.R.

Fainman, Y.

Ford, J.

Hugonin, J.

Lalanne, P.

Mait, J. N.

Mirotznik, M. S.

Noponen, E.

Prather, D. W.

Pustai, D. M.

Taylor, M. G.

Turunen, J.

van der Gracht, J.

Xu, F.

Appl. Opt. (3)

J. Opt. Soc. Am. A (2)

Opt. Lett. (1)

Other (4)

M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, "Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: enhanced transmittance matrix approach," J. Opt. Soc. Am. A 12, 1077- (1995).
[CrossRef]

J. van der Gracht and G. Euliss, "Information optimized extended depth-of-field imaging systems," Proc. SPIE Aerosense Conf., Orlando, FL, (2001).
[CrossRef]

J. van der Gracht, P. Pauca, H. Setty, R. Narayanswamy, R. Plemmons, S. Prasad and T. Torgersen, "Iris Recognition with Enhanced Depth-of-Field Image Acquisition," Proc. SPIE Conference on Defense and Homeland Security, Orlando, FL, (2004).

J. van der Gracht, E. R. Dowski, W. T. Cathey, and J. Bowen, "Aspheric Optical Elements for Extended Depth of Field", SPIE Proceedings on Novel Optical System Design and Optimization, 2537, San Diego, (1995).

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Figures (9)

Fig. 1.
Fig. 1.

Illustration of subwavelength cell-encoded element. At each cell of the DE a binary subwavelength grating is used to provide an effective property.

Fig. 2.
Fig. 2.

Phase distribution of a cubic phase plate.

Fig. 3.
Fig. 3.

Illustration of the subwavelength cell-encoding algorithm applied to a cubic phase element. The cubic phase distribution (shown in Figure 2) is decomposed into a finite number of cells. Each cell is formed by a suitable subwavelength grating.

Fig. 4.
Fig. 4.

Fabricated subwavelength cubic phase element. The insert shows a SEM image of the binary subwavelength gratings that make up the entire element.

Fig. 5.
Fig. 5.

MTF slices corresponding to the ideal cubic element (solid blue line), the phase quantized design (dotted red line) and the designed element with an added etch depth error (dashed green line). (a) Shows the MTF for the in-focus condition. (b) Shows the MTF for strong misfocus error of one wavelength.

Fig. 6.
Fig. 6.

Simulated images of two targets at different object distances. (a) The imaging system has a clear pupil aperture, (b) The imaging system model includes the designed cubic phase element modified by the measured fabrication etch depth error. (c) The image of (b) has been deblurred using a single Wiener restoration filter matched to the in-focus imaging condition.

Fig. 7.
Fig. 7.

Simulated PSF of a cubic phase element. The figure on the left predicts the PSF in the focal plane while the figure on the right predicts the PSF for 1 wave of misfocus.

Fig. 8.
Fig. 8.

Experimental setup used to characterize the subwavelength cubic element shown in Figure 4.

Fig. 9.
Fig. 9.

Experimental results for the subwavelength cubic phase element reveal a PSF that exhibits the general behavior of a continuous phase cubic element and is reasonably invariant to misfocus.

Equations (2)

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P ( x , y ) = exp ( j α [ x 3 + y 3 ] λ ) , x < L 2 , y < L 2 ,
ϕ ( x , y ) = mod [ α L 3 ( x 3 + y 3 ) , 2 π ] , x < L 2 , y < L 2 ,

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