Abstract

Wave aberrations of refractive photoresist microlenses and silicon microlenses were measured with a lateral shearing interferometer. Because of the silicon elements, a near-infrared working wavelength (λ = 1.32 μm) was used. The wave front was evaluated by a phase step technique with four steps. Integration of the phase distributions was performed with a computationally efficient Fourier transformation algorithm. The influence of the detector vidicon nonlinearity on the measured wave front was calculated. The defocusing behavior of the interferometer was investigated by fitting the measured wave fronts with the help of Zernike circle polynomials. It is shown that the reproducibility can be kept below λ/100 rms. Examples for the measured wave fronts of plano–convex silicon microlenses are discussed in detail.

© 1998 Optical Society of America

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References

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  1. Z. D. Popovic, R. A. Sprague, G. A. N. Connell, “Technique for monolithic fabrication of microlens arrays,” Appl. Opt. 27, 1281–1284 (1988).
    [CrossRef] [PubMed]
  2. D. Daly, R. F. Stevens, M. C. Hutley, N. Davies, “The manufacture of microlenses by melting photoresist,” Meas. Sci. Technol. 1, 759–766 (1990).
    [CrossRef]
  3. G. W. R. Leibbrandt, G. Harbers, P. J. Kunst, “Wave-front analysis with high accuracy by use of a double-grating lateral shearing interferometer,” Appl. Opt. 31, 6151–6161 (1996).
    [CrossRef]
  4. L. Erdmann, D. Efferenn, “Technique for monolithic fabrication of silicon microlenses with selectable rim angles,” Opt. Eng. 36, 1094–1098 (1997).
    [CrossRef]
  5. H. Sickinger, O. Falkenstörfer, N. Lindlein, J. Schwider, “Characterization of microlenses using a phase shifting shearing interferometer,” Opt. Eng. 33, 2680–2686 (1994).
    [CrossRef]
  6. K. R. Freischlad, C. L. Koliopoulos, “Modal estimation of a wave front from difference measurements using the discrete Fourier transform,” J. Opt. Soc. Am. A 3, 1852–1861 (1986).
    [CrossRef]
  7. M. V. R. K. Murty, “Lateral shearing interferometers,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1978), pp. 105–148.
  8. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1986), pp. 464–466.

1997

L. Erdmann, D. Efferenn, “Technique for monolithic fabrication of silicon microlenses with selectable rim angles,” Opt. Eng. 36, 1094–1098 (1997).
[CrossRef]

1996

G. W. R. Leibbrandt, G. Harbers, P. J. Kunst, “Wave-front analysis with high accuracy by use of a double-grating lateral shearing interferometer,” Appl. Opt. 31, 6151–6161 (1996).
[CrossRef]

1994

H. Sickinger, O. Falkenstörfer, N. Lindlein, J. Schwider, “Characterization of microlenses using a phase shifting shearing interferometer,” Opt. Eng. 33, 2680–2686 (1994).
[CrossRef]

1990

D. Daly, R. F. Stevens, M. C. Hutley, N. Davies, “The manufacture of microlenses by melting photoresist,” Meas. Sci. Technol. 1, 759–766 (1990).
[CrossRef]

1988

1986

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1986), pp. 464–466.

Connell, G. A. N.

Daly, D.

D. Daly, R. F. Stevens, M. C. Hutley, N. Davies, “The manufacture of microlenses by melting photoresist,” Meas. Sci. Technol. 1, 759–766 (1990).
[CrossRef]

Davies, N.

D. Daly, R. F. Stevens, M. C. Hutley, N. Davies, “The manufacture of microlenses by melting photoresist,” Meas. Sci. Technol. 1, 759–766 (1990).
[CrossRef]

Efferenn, D.

L. Erdmann, D. Efferenn, “Technique for monolithic fabrication of silicon microlenses with selectable rim angles,” Opt. Eng. 36, 1094–1098 (1997).
[CrossRef]

Erdmann, L.

L. Erdmann, D. Efferenn, “Technique for monolithic fabrication of silicon microlenses with selectable rim angles,” Opt. Eng. 36, 1094–1098 (1997).
[CrossRef]

Falkenstörfer, O.

H. Sickinger, O. Falkenstörfer, N. Lindlein, J. Schwider, “Characterization of microlenses using a phase shifting shearing interferometer,” Opt. Eng. 33, 2680–2686 (1994).
[CrossRef]

Freischlad, K. R.

Harbers, G.

G. W. R. Leibbrandt, G. Harbers, P. J. Kunst, “Wave-front analysis with high accuracy by use of a double-grating lateral shearing interferometer,” Appl. Opt. 31, 6151–6161 (1996).
[CrossRef]

Hutley, M. C.

D. Daly, R. F. Stevens, M. C. Hutley, N. Davies, “The manufacture of microlenses by melting photoresist,” Meas. Sci. Technol. 1, 759–766 (1990).
[CrossRef]

Koliopoulos, C. L.

Kunst, P. J.

G. W. R. Leibbrandt, G. Harbers, P. J. Kunst, “Wave-front analysis with high accuracy by use of a double-grating lateral shearing interferometer,” Appl. Opt. 31, 6151–6161 (1996).
[CrossRef]

Leibbrandt, G. W. R.

G. W. R. Leibbrandt, G. Harbers, P. J. Kunst, “Wave-front analysis with high accuracy by use of a double-grating lateral shearing interferometer,” Appl. Opt. 31, 6151–6161 (1996).
[CrossRef]

Lindlein, N.

H. Sickinger, O. Falkenstörfer, N. Lindlein, J. Schwider, “Characterization of microlenses using a phase shifting shearing interferometer,” Opt. Eng. 33, 2680–2686 (1994).
[CrossRef]

Murty, M. V. R. K.

M. V. R. K. Murty, “Lateral shearing interferometers,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1978), pp. 105–148.

Popovic, Z. D.

Schwider, J.

H. Sickinger, O. Falkenstörfer, N. Lindlein, J. Schwider, “Characterization of microlenses using a phase shifting shearing interferometer,” Opt. Eng. 33, 2680–2686 (1994).
[CrossRef]

Sickinger, H.

H. Sickinger, O. Falkenstörfer, N. Lindlein, J. Schwider, “Characterization of microlenses using a phase shifting shearing interferometer,” Opt. Eng. 33, 2680–2686 (1994).
[CrossRef]

Sprague, R. A.

Stevens, R. F.

D. Daly, R. F. Stevens, M. C. Hutley, N. Davies, “The manufacture of microlenses by melting photoresist,” Meas. Sci. Technol. 1, 759–766 (1990).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1986), pp. 464–466.

Appl. Opt.

Z. D. Popovic, R. A. Sprague, G. A. N. Connell, “Technique for monolithic fabrication of microlens arrays,” Appl. Opt. 27, 1281–1284 (1988).
[CrossRef] [PubMed]

G. W. R. Leibbrandt, G. Harbers, P. J. Kunst, “Wave-front analysis with high accuracy by use of a double-grating lateral shearing interferometer,” Appl. Opt. 31, 6151–6161 (1996).
[CrossRef]

J. Opt. Soc. Am. A

Meas. Sci. Technol.

D. Daly, R. F. Stevens, M. C. Hutley, N. Davies, “The manufacture of microlenses by melting photoresist,” Meas. Sci. Technol. 1, 759–766 (1990).
[CrossRef]

Opt. Eng.

L. Erdmann, D. Efferenn, “Technique for monolithic fabrication of silicon microlenses with selectable rim angles,” Opt. Eng. 36, 1094–1098 (1997).
[CrossRef]

H. Sickinger, O. Falkenstörfer, N. Lindlein, J. Schwider, “Characterization of microlenses using a phase shifting shearing interferometer,” Opt. Eng. 33, 2680–2686 (1994).
[CrossRef]

Other

M. V. R. K. Murty, “Lateral shearing interferometers,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1978), pp. 105–148.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1986), pp. 464–466.

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Figures (14)

Fig. 1
Fig. 1

Scanning electron microscopy micrograph of a silicon microlens. The silicon lens is monolithically integrated in a system with V grooves for the hybrid integration of a single-mode fiber and a Pyrex mirror.

Fig. 2
Fig. 2

Schematic diagram of the lateral shearing interferometer. The arrangement is described in detail in Ref. 5.

Fig. 3
Fig. 3

Flow diagram for calculating the wave front from the interferometer data.

Fig. 4
Fig. 4

Normalized camera output versus pin diode signal.

Fig. 5
Fig. 5

Ideal input-wave front with 0.5λ defocus and -1λ spherical aberration. (80% of the exit pupil, 153 mλ p.v.)

Fig. 6
Fig. 6

Error contribution of the shear ratio due to wave-front reconstruction: p.v. values of the differences between the input wave fronts and the output wave fronts for a varying shear.

Fig. 7
Fig. 7

Difference of the ideal wave front and the wave front after the simulation (systematic wave-front error) of the measurement process with the linear camera response and a shear ratio of 5% of the exit pupil.

Fig. 8
Fig. 8

Difference of the systematic wave-front error plotted in Fig. 7 with the best-fit sphere.

Fig. 9
Fig. 9

Difference between the output wave front for a linear response and the output wave front for a nonlinear response, (shear ratio: 5%, ϕ0 = π/4, and V = 0.4).

Fig. 10
Fig. 10

Difference between the output wave front for a linear response and the output wave front for a nonlinear response, (shear ratio: 5%, ϕ0 = 3π/4, and V = 0.4).

Fig. 11
Fig. 11

Zernike coefficients for varying defocus.

Fig. 12
Fig. 12

Measured wave front of a hyperbolic silicon microlens. The corners of the quadratic area represent 89% of the exit pupil (shear ratio, 5%; p.v., 0.17λ).

Fig. 13
Fig. 13

Measured wave front after the silicon microlens in Fig. 12 is tilted ∼90°. The detail in the central annular structure detected in Fig. 12 is rotated ∼90°.

Fig. 14
Fig. 14

Measured wave front of a hyperbolic silicon microlens with a conic constant of -11.6. The corners of the quadratic area represent 89% of the exit pupil (shear ratio, 5%; p.v., 0.21λ).

Tables (1)

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Table 1 Symmetric Zernike Coefficients for Measurements of a Microlens with Varying Defocus in Module A

Equations (3)

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I n = 1 2 1 + V   cos Δ ϕ + ϕ 0 + n π 2 , n = 0 ,   1 3 ,
I NL = a 0 + a 1 I n + a 2 I n 2 ,
s n Δ ϕ = int 255 I NL I n Δ ϕ ,

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