Abstract

Kinoforms (diffractive optical elements) were designed to produce different fan-out (i.e., spot) patterns when illuminated with green (543-nm wavelength) and red (633-nm) light. Three design examples are presented, each using one of three different techniques for this wavelength discrimination. If the fan-out pattern is to be produced in the near field (Fresnel region) of the kinoform, focusing–defocusing distinguishes between the two colors. For a far-field pattern the color distinction can be obtained either by active suppression of unwanted spots, which also decreases the diffraction efficiency, or, preferably, by an increase in the maximum phase modulation of the kinoform (to more than 2π rad). All three examples were designed with a method based on the full scalar wave equation and optimal-rotation-angle optimization. The designed kinoforms were manufactured and performed, at least qualitatively, as predicted by the design.

© 1998 Optical Society of America

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References

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1997 (1)

1996 (2)

1995 (2)

1994 (1)

1993 (1)

1991 (1)

1978 (1)

Bengtsson, J.

Bernhardt, M.

Bryngdahl, O.

Chen, M.-L.

Chen, Y.-S.

Cui, X.-M.

Dammann, H.

Dong, B.-Z.

Faklis, D.

Farn, M. W.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

Gu, B.-Y.

Li, D.-H.

Liu, H.-D.

Medeiros, S. S.

Morris, G. M.

Sommargren, G. E.

Stern, M. B.

Sweeney, D. W.

Veldkamp, W. B.

Wyrowski, F.

Zhang, G.-Q.

Zheng, S.-H.

Appl. Opt. (8)

Opt. Lett. (1)

Other (1)

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

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Figures (12)

Fig. 1
Fig. 1

Two color-discriminating mechanisms: (a) Propagation through the kinoform. (b) Free-space propagation. Wave fronts are shown as dashed lines.

Fig. 2
Fig. 2

Geometry for the calculation of U km , the field at spot m from pixel k.

Fig. 3
Fig. 3

Complex-number plane representation of the total field at spot m, assumed to be a green spot. Changing the phase modulation of pixel k by δφ kG leads to the field amplitude’s changing at spot m by Δl.

Fig. 4
Fig. 4

Flowchart of the complete algorithm.

Fig. 5
Fig. 5

Gray-scale representation of the designed relief height of the near-field kinoform. White and black represent the highest and lowest parts, respectively, of the relief.

Fig. 6
Fig. 6

Measured diffraction patterns for the near-field kinoform: (a) Illuminated by green light. (b) Illuminated by red light.

Fig. 7
Fig. 7

Performance of the algorithm as a function of the number of iterations for the design of a kinoform with active suppression: (a) The sum of intensity values in the spots for the different patterns. (b) The uniformity error in the desired spot patterns.

Fig. 8
Fig. 8

Designed relief height of the kinoform with active suppression of ghost spots.

Fig. 9
Fig. 9

Measured diffraction patterns for the kinoform with active suppression: (a) Illuminated by green light. (b) Illuminated by red light.

Fig. 10
Fig. 10

Designed relief height of the kinoform with increased phase modulation.

Fig. 11
Fig. 11

Calculated diffraction patterns (tenfold overexposed) for the kinoform with increased phase modulation: (a) Illuminated by green light. (b) Illuminated by red light.

Fig. 12
Fig. 12

Measured diffraction patterns for the kinoform with increased phase modulation: (a) Illuminated by green light. (b) Illuminated by red light.

Equations (17)

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Δ φ kX = 2 π   Δ T T X = 2 π   h c / n - h c λ X c = 2 π   n - 1 h λ X ,
U km = A km exp j φ km exp j φ inc + Δ φ k ,
Δ φ kR = λ G λ R   Δ φ kG = 0.86 Δ φ kG .
A km exp j φ km = 1 4 π - jk z - L r c jk - 1 r c × 4 A k r c exp jkr c sin k ˜ x a 2 k ˜ x sin k ˜ y b 2 k ˜ y ,
r c = x c - u 2 + y c - v 2 + L 2 1 / 2 ,
k ˜ x = k x + k x c - u r c , k ˜ y = k y + k y c - v r c .
Δ l = A km cos ϕ km - δ φ kG - A km cos   ϕ km ,
ϕ km = φ m - φ km + φ inc + Δ φ kG ,
m   Δ l = m   for   green   spots A km cos ϕ km - δ φ kG - A km cos   ϕ km + m   for   red   spots A km cos ϕ km - 0.86 δ φ kG - A km cos   ϕ km
= S G cos δ φ kG - α kG + S R cos 0.86 δ φ kG - α kR + const . ,
S X = sign S 1 X S 1 X 2 + S 2 X 2 1 / 2 , S 1 X = m   for   color   X   A km cos   ϕ km , S 2 X = m   for   color   X   A km sin   ϕ km , α kX = arctan S 2 X S 1 X ,
S 1 X = m   for   color   X   w m A km cos   ϕ km , S 2 X = m   for   color   X   w m A km sin   ϕ km .
f δ φ kG = W G S G cos δ φ kG - α kG + W R S R cos 0.86 δ φ kG - α kR + const ,
U m A m exp j φ m = k   U km = k   A km exp j φ km exp j φ inc + Δ φ k .
w m = w m old I m desired I m actual p ,
W X = W X old m   for   color   X   I m desired m   for   color   X   I m actual q .
unif .   err . X = max color   X I m actual I m desired - min color   X I m actual I m desired max color   X I m actual I m desired + min color   X I m actual I m desired .

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