Abstract

A new kind of lateral shearing interferometer, called the three-wave lateral shearing interferometer, was previously described [ Appl. Opt. 32, 6242 ( 1993)]. As this instrument was monochromatic and its usable light efficiency was poor, the proposed setup was well suited only for a class of wave-front sensing problems, such as optical testing, in which the source can be easily adapted. A new achromatic setup adapted to low light level applications is presented. Three replicas of the analyzed wave front are obtained by Fourier filtering of the orders diffracted by a microlens array. An important feature of these new devices is their great similarity to another class of wave-front sensors based on the Hartmann test.

© 1995 Optical Society of America

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References

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  1. V. Ronchi, “Forty years of history of a grating interferometer,” Appl. Opt. 3, 437–451 (1967).
    [CrossRef]
  2. J. C. Wyant, “White light extended source shearing interferometer,” Appl. Opt. 13, 200–202 (1974),
    [CrossRef] [PubMed]
  3. C. L. Koliopoulos, “Radial grating lateral shear heterodyne interferometer,” Appl. Opt. 19, 1523–1528 (1980).
    [CrossRef] [PubMed]
  4. J. Schwider, “Continuous lateral shearing interferometer,” Appl. Opt. 23, 4403–4409 (1984).
    [CrossRef] [PubMed]
  5. J. Primot, “Three-wave lateral shearing interferometer,” Appl. Opt. 32, 6242–6249 (1993).
    [CrossRef] [PubMed]
  6. M. C. Hutley, “Optical techniques for the generation of microlens arrays,” J. Mod. Opt. 37, 253–265 (1990).
    [CrossRef]
  7. F. Roddier, “Wavefront sensing and the irradiance transport equation,” Appl. Opt. 29, 1402–1404 (1990).
    [CrossRef] [PubMed]
  8. K. Ichikawa, A. Lohmann, M. Tadeka, “Phase retrieval based on the irradiance transport equation and the Fourier transform method: experiments,” Appl. Opt. 27, 3433–3436 (1988).
    [CrossRef] [PubMed]
  9. N. Streibl, “Phase imaging by the transport equation of intensity,” Opt. Commun. 49, 6–9 (1984)
    [CrossRef]
  10. J. C. Wyant, C. L. Koliopoulos, “Phase measurement systems for adaptive optics,” AGARD Conf. Proc. No. 300, Special Topics in Optical Propagation (1981), Ref. 48, pp. 48-1–48-12.
  11. F. Roddier, “Variations on a Hartmann theme,” Opt. Eng. 29, 1239–1242 (1990).
    [CrossRef]

1993 (1)

1990 (3)

M. C. Hutley, “Optical techniques for the generation of microlens arrays,” J. Mod. Opt. 37, 253–265 (1990).
[CrossRef]

F. Roddier, “Wavefront sensing and the irradiance transport equation,” Appl. Opt. 29, 1402–1404 (1990).
[CrossRef] [PubMed]

F. Roddier, “Variations on a Hartmann theme,” Opt. Eng. 29, 1239–1242 (1990).
[CrossRef]

1988 (1)

1984 (2)

N. Streibl, “Phase imaging by the transport equation of intensity,” Opt. Commun. 49, 6–9 (1984)
[CrossRef]

J. Schwider, “Continuous lateral shearing interferometer,” Appl. Opt. 23, 4403–4409 (1984).
[CrossRef] [PubMed]

1981 (1)

J. C. Wyant, C. L. Koliopoulos, “Phase measurement systems for adaptive optics,” AGARD Conf. Proc. No. 300, Special Topics in Optical Propagation (1981), Ref. 48, pp. 48-1–48-12.

1980 (1)

1974 (1)

1967 (1)

Hutley, M. C.

M. C. Hutley, “Optical techniques for the generation of microlens arrays,” J. Mod. Opt. 37, 253–265 (1990).
[CrossRef]

Ichikawa, K.

Koliopoulos, C. L.

J. C. Wyant, C. L. Koliopoulos, “Phase measurement systems for adaptive optics,” AGARD Conf. Proc. No. 300, Special Topics in Optical Propagation (1981), Ref. 48, pp. 48-1–48-12.

C. L. Koliopoulos, “Radial grating lateral shear heterodyne interferometer,” Appl. Opt. 19, 1523–1528 (1980).
[CrossRef] [PubMed]

Lohmann, A.

Primot, J.

Roddier, F.

Ronchi, V.

Schwider, J.

Streibl, N.

N. Streibl, “Phase imaging by the transport equation of intensity,” Opt. Commun. 49, 6–9 (1984)
[CrossRef]

Tadeka, M.

Wyant, J. C.

J. C. Wyant, C. L. Koliopoulos, “Phase measurement systems for adaptive optics,” AGARD Conf. Proc. No. 300, Special Topics in Optical Propagation (1981), Ref. 48, pp. 48-1–48-12.

J. C. Wyant, “White light extended source shearing interferometer,” Appl. Opt. 13, 200–202 (1974),
[CrossRef] [PubMed]

AGARD Conf. Proc. No. 300, Special Topics in Optical Propagation (1)

J. C. Wyant, C. L. Koliopoulos, “Phase measurement systems for adaptive optics,” AGARD Conf. Proc. No. 300, Special Topics in Optical Propagation (1981), Ref. 48, pp. 48-1–48-12.

Appl. Opt. (7)

J. Mod. Opt. (1)

M. C. Hutley, “Optical techniques for the generation of microlens arrays,” J. Mod. Opt. 37, 253–265 (1990).
[CrossRef]

Opt. Commun. (1)

N. Streibl, “Phase imaging by the transport equation of intensity,” Opt. Commun. 49, 6–9 (1984)
[CrossRef]

Opt. Eng. (1)

F. Roddier, “Variations on a Hartmann theme,” Opt. Eng. 29, 1239–1242 (1990).
[CrossRef]

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Figures (13)

Fig. 1
Fig. 1

Geometrical demonstration of the independence of the interference figure with respect to the longitudinal position of the observation plane.

Fig. 2
Fig. 2

Three-wave interferogram observed in the replication plane for a large spherical aberration.

Fig. 3
Fig. 3

Three-wave interferogram observed in a distant plane of the replication plane for a large spherical aberration. Note that the experimental setup is identical to that of Fig. 2 but for a longitudinal translation of the camera.

Fig. 4
Fig. 4

New replication device.

Fig. 5
Fig. 5

Microlens array observed in the exit pupil of the afocal system.

Fig. 6
Fig. 6

Microlens array observed in the microlens focal plane.

Fig. 7
Fig. 7

Microlens array observed in an extrafocal plane.

Fig. 8
Fig. 8

Three-wave interferogram observed in the exit pupil of the afocal system.

Fig. 9
Fig. 9

Three-wave interferogram observed in the above-defined microlens focal plane (see Fig. 6). Note the similarity with Fig. 8 but for the blurred outline.

Fig. 10
Fig. 10

Six-wave interferogram observed in the above-defined extrafocal plane (see Fig. 7). Note the similarity with Figs. 8 and 9; blur of the outline is now important.

Fig. 11
Fig. 11

Six-wave interferogram observed in the exit pupil of the afocal system.

Fig. 12
Fig. 12

Six-wave interferogram observed in the above-defined microlens focal plane (see Fig. 6).

Fig. 13
Fig. 13

Six-wave interferogram observed in the above-defined extrafocal plane (see Fig. 7).

Equations (8)

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A ( x ) = exp [ i W ( x ) ] .
A i ( x ) = exp { i [ W ( x ) + k i x ] } ,
I 0 ( x ) = | i = 1 3 A i ( x ) | 2 = 3 + i , j = 1 i j 3 exp [ i ( k i k j ) x ] .
I L ( x ) = I 0 ( x ) L k [ I 0 ( x ) W ( x ) + I 0 ( x ) 2 W ( x ) ] ,
I L ( x ) = 3 [ 1 L k 2 W ( x ) ] + i , j = 1 i j 3 { [ 1 L k 2 W ( x ) ] i L k ( k i k j ) W ( x ) } exp [ i ( k i k j ) x ] .
FT ( I L ) ( u ) = 3 FT [ 1 L k 2 W ( x ) ] + i , j = 1 i j 3 FT { [ 1 L k 2 W ( x ) ] i L k ( k i k j ) W ( x ) } * δ [ ( k i k j ) u ] ,
FT ( G ) ( u ) = n = 1 3 δ ( u u n ) ,
G ( x ) = n = 1 3 exp ( 2 i π u n x ) .

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