Abstract

Shearing interferometers are very popular and have a growing range of applications, especially in the field of optical testing. We describe a new kind of a lateral shearing interferometer. The lateral shear is produced by two Ronchi phase gratings in series. The phase can be shifted by a lateral movement of one grating relative to the other, and the amount of shear can easily be adjusted by variation of the distance of the gratings. The simplicity of the device is an important advantage, especially in the near IR.

© 1997 Optical Society of America

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References

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  1. M. V. R. K. Murty, “Rotational shearing interferometry,” Appl. Opt. 5, 615–619 (1966).
    [CrossRef] [PubMed]
  2. H. Sickinger, O. Falkenstörfer, N. Lindlein, J. Schwider, “Characterization of microlenses using a phase-shifting shearing interferometer,” Opt. Eng. 33, 2680–2686 (1994).
    [CrossRef]
  3. M. C. Hutley, Diffraction Gratings (Academic, London, 1982).
  4. V. Ronchi, “On the phase grating interferometer,” Appl. Opt. 4, 1041–1042 (1965).
    [CrossRef]
  5. D. Malacara, ed., Optical Shop Testing (Wiley, New York, 1978).
  6. V. Ronchi, “Über die Schattenstreifen zum Studium der Lichtwellen,” Z. Instrumentenkunde 46, 553–560 (1926).
  7. D. Malacara, A. Cornejo, M. V. R. K. Murty, “A shearing interferometer for convergent or divergent beams,” Bol. Inst. Tomantzintla 1, 223–226 (1975).
  8. W. H. Steel, “A radial shear interferometer for testing microscope objectives,” J. Sci. Instrum. 42, 102 (1965).
    [CrossRef]
  9. V. Ronchi, “Forty years of history of a grating interferometer,” Appl. Opt. 3, 437–451 (1964).
    [CrossRef]

1994 (1)

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

1975 (1)

D. Malacara, A. Cornejo, M. V. R. K. Murty, “A shearing interferometer for convergent or divergent beams,” Bol. Inst. Tomantzintla 1, 223–226 (1975).

1966 (1)

1965 (2)

V. Ronchi, “On the phase grating interferometer,” Appl. Opt. 4, 1041–1042 (1965).
[CrossRef]

W. H. Steel, “A radial shear interferometer for testing microscope objectives,” J. Sci. Instrum. 42, 102 (1965).
[CrossRef]

1964 (1)

1926 (1)

V. Ronchi, “Über die Schattenstreifen zum Studium der Lichtwellen,” Z. Instrumentenkunde 46, 553–560 (1926).

Cornejo, A.

D. Malacara, A. Cornejo, M. V. R. K. Murty, “A shearing interferometer for convergent or divergent beams,” Bol. Inst. Tomantzintla 1, 223–226 (1975).

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]

Hutley, M. C.

M. C. Hutley, Diffraction Gratings (Academic, London, 1982).

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]

Malacara, D.

D. Malacara, A. Cornejo, M. V. R. K. Murty, “A shearing interferometer for convergent or divergent beams,” Bol. Inst. Tomantzintla 1, 223–226 (1975).

Murty, M. V. R. K.

D. Malacara, A. Cornejo, M. V. R. K. Murty, “A shearing interferometer for convergent or divergent beams,” Bol. Inst. Tomantzintla 1, 223–226 (1975).

M. V. R. K. Murty, “Rotational shearing interferometry,” Appl. Opt. 5, 615–619 (1966).
[CrossRef] [PubMed]

Ronchi, V.

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]

Steel, W. H.

W. H. Steel, “A radial shear interferometer for testing microscope objectives,” J. Sci. Instrum. 42, 102 (1965).
[CrossRef]

Appl. Opt. (3)

Bol. Inst. Tomantzintla (1)

D. Malacara, A. Cornejo, M. V. R. K. Murty, “A shearing interferometer for convergent or divergent beams,” Bol. Inst. Tomantzintla 1, 223–226 (1975).

J. Sci. Instrum. (1)

W. H. Steel, “A radial shear interferometer for testing microscope objectives,” J. Sci. Instrum. 42, 102 (1965).
[CrossRef]

Opt. Eng. (1)

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

Z. Instrumentenkunde (1)

V. Ronchi, “Über die Schattenstreifen zum Studium der Lichtwellen,” Z. Instrumentenkunde 46, 553–560 (1926).

Other (2)

D. Malacara, ed., Optical Shop Testing (Wiley, New York, 1978).

M. C. Hutley, Diffraction Gratings (Academic, London, 1982).

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Figures (5)

Fig. 1
Fig. 1

New interferometer, consisting of two Ronchi phase gratings in series.

Fig. 2
Fig. 2

Schematic setup of the shearing interferometer.

Fig. 3
Fig. 3

Interferogram of a silicon microlens.

Fig. 4
Fig. 4

Wave front 10% sheared in the x and the y directions.

Fig. 5
Fig. 5

Integrated wave front.

Equations (16)

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ΔW=Wx, y-Wx-s, y.
ΔWWxs.
βm=arcsinmλp+sinα,
fx=fpxm=-δxp-m  fpx:=expiθ:0x<p/2  1:p/2x<p  0:x<0, xp
Iw=fx2=fp·m=-δxp-m2=0p/2 expiθexp-i2πωxdx+p/2p1 exp-i2πωxdx1pm=-δωp-m2=cosθ+pπω2sinpπω22πω expiθ2-pπω×1pm=-δωp-m2=4π2m=-×cosθ+πm2sinπm21m expi θ2-πm2,
m=0limm0 sinπm21m=π2I0=cos2θ2,
m=2m, m0sin2πm2=0Im=0,
m=2m+1sin2πm2=1Im=cos2θ+π24m2π2,
Im=cos2θ20sin2θ24m2π2: m=0: m=2m: m=2m+1.
I0=0,  θ=2πλ dn-1d=λ2n-1.
I±1=4π240.5%
s=2l tanβ=2lλp+sinα1-λp+sinα21/2.
s=2lλp2-λ21/2,
Δϕ=2πpΔx.
Φ=ijai,jUi,j.
V=Φx+s,y-Φx,y-kx2+Φx,y+s-Φx,y-ky2,

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