Abstract

We have developed a high-resolution alignment technique which utilizes the partial polarization property of fine period transmission gratings. It is especially useful when the grating period is sufficiently small so that there are no visible diffracted orders. This technique uses a photoelastic modulator (PEM) to produce an intensity signal that is proportional to the sine of twice the angle between the grating lines and the PEM crystal axis. The experimentally demonstrated resolution of this technique on 200-nm period gold transmission gratings is better than 1 sec of arc. This technique was developed to align x-ray transmission gratings for spectroscopy and interferometry applications.

© 1988 Optical Society of America

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References

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  1. H. I. Smith, E. H. Anderson, M. L. Schattenburg, “Planar Techniques for Fabricating X-Ray Diffraction Gratings and Zone Plates,” in Symposium on X-Ray Microscopy, Gottingen, 14–16 Sept. 1983, Springer Series in Optical Sciences, Vol. 43, X-Ray Microscopy, D. Rudolph, G. Schmahl, Eds. (Springer-Verlag, Berlin, 1984), pp. 51–61.
  2. N. M. Ceglio, R. L. Kauffman, A. M. Hawryluk, H. Medecki, “A Time Resolved X-ray Transmission Grating Spectrometer for Investigation of Laser Produced Plasmas,” Appl. Opt. 22, 318 (1983).
    [CrossRef] [PubMed]
  3. C. R. Canizares, M. L. Schattenburg, H. I. Smith, “The Medium and High Energy Transmission Grating Spectrometer for AXAF,” Proc. Soc. Photo-Opt. Instrum. Eng. 597, 253 (1985).
  4. P. Rockett, KMS Fusion, Inc., personal communication.
  5. H. E. Torberg, W. J. Rowan, J. R. Vyce, “Optical Instruments for Metrology,” in Handbook of Optics, W. G. Driscoll, W. Vaughn, Eds. (McGraw-Hill, New York, 1978), p. 16–42.
  6. J. C. Kemp, “Piezo-Optical Birefringence Modulators: New Use for a Long-Known Effect,” J. Opt. Soc. Am. 59, 950 (1969).
  7. S. N. Jasperson, S. E. Schnatterly, “An Improved Method for High Reflectivity Ellipsometry Based on a New Polarization Modulation Technique,” Rev. Sci. Instrum. 40, 761 (1969).
    [CrossRef]
  8. H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, NJ, 1984), p. 370.
  9. Melles Griot 3 FCG 167.
  10. Model PEM-80, Hinds International, Inc., Portland, OR.
  11. Model D656, Davidson Optronics, Inc., West Covina, CA.

1985 (1)

C. R. Canizares, M. L. Schattenburg, H. I. Smith, “The Medium and High Energy Transmission Grating Spectrometer for AXAF,” Proc. Soc. Photo-Opt. Instrum. Eng. 597, 253 (1985).

1983 (1)

1969 (2)

J. C. Kemp, “Piezo-Optical Birefringence Modulators: New Use for a Long-Known Effect,” J. Opt. Soc. Am. 59, 950 (1969).

S. N. Jasperson, S. E. Schnatterly, “An Improved Method for High Reflectivity Ellipsometry Based on a New Polarization Modulation Technique,” Rev. Sci. Instrum. 40, 761 (1969).
[CrossRef]

Anderson, E. H.

H. I. Smith, E. H. Anderson, M. L. Schattenburg, “Planar Techniques for Fabricating X-Ray Diffraction Gratings and Zone Plates,” in Symposium on X-Ray Microscopy, Gottingen, 14–16 Sept. 1983, Springer Series in Optical Sciences, Vol. 43, X-Ray Microscopy, D. Rudolph, G. Schmahl, Eds. (Springer-Verlag, Berlin, 1984), pp. 51–61.

Canizares, C. R.

C. R. Canizares, M. L. Schattenburg, H. I. Smith, “The Medium and High Energy Transmission Grating Spectrometer for AXAF,” Proc. Soc. Photo-Opt. Instrum. Eng. 597, 253 (1985).

Ceglio, N. M.

Haus, H. A.

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, NJ, 1984), p. 370.

Hawryluk, A. M.

Jasperson, S. N.

S. N. Jasperson, S. E. Schnatterly, “An Improved Method for High Reflectivity Ellipsometry Based on a New Polarization Modulation Technique,” Rev. Sci. Instrum. 40, 761 (1969).
[CrossRef]

Kauffman, R. L.

Kemp, J. C.

Medecki, H.

Rockett, P.

P. Rockett, KMS Fusion, Inc., personal communication.

Rowan, W. J.

H. E. Torberg, W. J. Rowan, J. R. Vyce, “Optical Instruments for Metrology,” in Handbook of Optics, W. G. Driscoll, W. Vaughn, Eds. (McGraw-Hill, New York, 1978), p. 16–42.

Schattenburg, M. L.

C. R. Canizares, M. L. Schattenburg, H. I. Smith, “The Medium and High Energy Transmission Grating Spectrometer for AXAF,” Proc. Soc. Photo-Opt. Instrum. Eng. 597, 253 (1985).

H. I. Smith, E. H. Anderson, M. L. Schattenburg, “Planar Techniques for Fabricating X-Ray Diffraction Gratings and Zone Plates,” in Symposium on X-Ray Microscopy, Gottingen, 14–16 Sept. 1983, Springer Series in Optical Sciences, Vol. 43, X-Ray Microscopy, D. Rudolph, G. Schmahl, Eds. (Springer-Verlag, Berlin, 1984), pp. 51–61.

Schnatterly, S. E.

S. N. Jasperson, S. E. Schnatterly, “An Improved Method for High Reflectivity Ellipsometry Based on a New Polarization Modulation Technique,” Rev. Sci. Instrum. 40, 761 (1969).
[CrossRef]

Smith, H. I.

C. R. Canizares, M. L. Schattenburg, H. I. Smith, “The Medium and High Energy Transmission Grating Spectrometer for AXAF,” Proc. Soc. Photo-Opt. Instrum. Eng. 597, 253 (1985).

H. I. Smith, E. H. Anderson, M. L. Schattenburg, “Planar Techniques for Fabricating X-Ray Diffraction Gratings and Zone Plates,” in Symposium on X-Ray Microscopy, Gottingen, 14–16 Sept. 1983, Springer Series in Optical Sciences, Vol. 43, X-Ray Microscopy, D. Rudolph, G. Schmahl, Eds. (Springer-Verlag, Berlin, 1984), pp. 51–61.

Torberg, H. E.

H. E. Torberg, W. J. Rowan, J. R. Vyce, “Optical Instruments for Metrology,” in Handbook of Optics, W. G. Driscoll, W. Vaughn, Eds. (McGraw-Hill, New York, 1978), p. 16–42.

Vyce, J. R.

H. E. Torberg, W. J. Rowan, J. R. Vyce, “Optical Instruments for Metrology,” in Handbook of Optics, W. G. Driscoll, W. Vaughn, Eds. (McGraw-Hill, New York, 1978), p. 16–42.

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

C. R. Canizares, M. L. Schattenburg, H. I. Smith, “The Medium and High Energy Transmission Grating Spectrometer for AXAF,” Proc. Soc. Photo-Opt. Instrum. Eng. 597, 253 (1985).

Rev. Sci. Instrum. (1)

S. N. Jasperson, S. E. Schnatterly, “An Improved Method for High Reflectivity Ellipsometry Based on a New Polarization Modulation Technique,” Rev. Sci. Instrum. 40, 761 (1969).
[CrossRef]

Other (7)

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, NJ, 1984), p. 370.

Melles Griot 3 FCG 167.

Model PEM-80, Hinds International, Inc., Portland, OR.

Model D656, Davidson Optronics, Inc., West Covina, CA.

P. Rockett, KMS Fusion, Inc., personal communication.

H. E. Torberg, W. J. Rowan, J. R. Vyce, “Optical Instruments for Metrology,” in Handbook of Optics, W. G. Driscoll, W. Vaughn, Eds. (McGraw-Hill, New York, 1978), p. 16–42.

H. I. Smith, E. H. Anderson, M. L. Schattenburg, “Planar Techniques for Fabricating X-Ray Diffraction Gratings and Zone Plates,” in Symposium on X-Ray Microscopy, Gottingen, 14–16 Sept. 1983, Springer Series in Optical Sciences, Vol. 43, X-Ray Microscopy, D. Rudolph, G. Schmahl, Eds. (Springer-Verlag, Berlin, 1984), pp. 51–61.

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Figures (2)

Fig. 1
Fig. 1

Unpolarized light from a lamp is polarized at 45° to the axis of the PEM. In the PEM a bar of fused silica is periodically stressed which produces a time variable retardation plate. The grating acts as a partial polarizer, and the modulated signal is measured with a photodiode detector.

Fig. 2
Fig. 2

SEM micrograph of a 200-nm period x-ray transmission grating with Au lines electroplated to ~1 μm and supported on a 1-μm thick polyimide membrane.

Equations (22)

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I out = I in ( α TE 2 cos 2 θ + α TM 2 sin 2 θ ) .
E = E 0 2 ( x ^ + y ^ ) ,
E = E 0 2 { x ^ + y ^ exp [ i ϕ ( t ) ] } ,
E out = α TE ( E · u ^ ) u ^ + α TM ( E · v ^ ) v ^ ,
v ^ = x ^ cos θ + y ^ sin θ ,
u ^ = - x ^ sin θ + y ^ cos θ .
I 1 2 μ 0 0 E 0 2 = α TM 2 + α TE 2 2 + ( α TM 2 - α TE 2 2 ) sin 2 θ cos ϕ ( t ) .
ϕ ( t ) = Φ 0 sin ( ω m t ) ,
cos [ Φ 0 sin ( ω m t ) ] = J 0 ( Φ 0 ) + 2 J 2 ( Φ 0 ) cos ( 2 ω m t ) + 2 J 4 ( Φ 0 ) cos ( 4 ω m t ) + .
I ( 2 ω m ) 1 2 μ 0 0 E 0 2 = 2 J 2 ( Φ 0 ) ( α TM 2 - α TE 2 2 ) sin 2 θ cos 2 ω m t .
( Δ i rms ) 2 = 2 e i dc B ,
Δ θ rms = [ d i ( 2 ω m ) d θ ] θ = 0 - 1 Δ i rms 2 ,
i dc = ( α TM 2 + α TE 2 2 ) e η h ν I 0 ,
[ d i ( 2 ω m ) d θ ] θ = 0 = 4 J 2 ( Φ 0 ) ( α TM 2 - α TE 2 2 ) e η h ν I 0 .
β = 1 i dc [ d i ( 2 ω m ) d θ ] θ = 0
= 4 J 2 ( Φ 0 ) ( α TM 2 - α TE 2 α TM 2 + α TE 2 ) .
β 2 ( α TM 2 - α TE 2 α TM 2 + α TE 2 ) .
Δ θ rms = 1 β e B i dc .
Δ i rms = 2 e i dc B
= 3 p A ,
[ d i ( 2 ω m ) d θ ] θ = 0 = 30 μ A rad - 1 .
Δ θ = 0.07 μ rad .

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