Abstract

We have investigated the possibility of using transparent stretchable diffraction gratings for spectrometric applications. The gratings were fabricated by replication of a triangular-groove master into a transparent viscoelastic. The sample length, and hence the spatial period, can be reversibly changed by mechanical stretching. When used in a monochromator with two slits, the stretchable grating permits scanning the spectral components over the output slit, converting the monochromator into a scanning spectrometer. The spectral resolution of such a spectrometer was found to be limited mainly by the wave-front aberrations due to the grating deformation. A model relating the deformation-induced aberrations in different diffraction orders is presented. In the experiments, a 12-mm long viscoelastic grating with a spatial frequency of 600 line pairs/mm provided a full-width at half-maximum resolution of up to ~1.2 nm in the 580–680 nm spectral range when slowly stretched by a micrometer screw and ~3 nm when repeatedly stretched by a voice coil at 15 Hz. Comparison of aberrations in transmitted and diffracted beams measured by a Shack-Hartmann wave-front sensor showed that astigmatisms caused by stretch-dependent wedge deformation are the main factors limiting the resolution of the viscoelastic-grating-based spectrometer.

© 2007 Optical Society of America

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References

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  1. M.  Born and E.  Wolf, Principles of optics (Cambridge University Press, 2002), Chaps. 8 and 11.
  2. M.  Bass, ed., Handbook of optics (McGraw-Hill Inc., 1995), vol. I - Chap. 3 and vol. II - Chap. 19.
  3. J.F.  James and R.S.  Sternberg, The design of optical spectrometers (Chapman and Hall Ltd., London, 1969).
  4. P.  Bousquet, Spectroscopy and its instrumentation, (Hilger, London, 1972).
  5. M.C.  Hutley, Diffraction Gratings, (Academic Press, London, 1982).
  6. E.G.  Loewen and E.  Popov, Diffraction gratings and applications, (Marcel Dekker Inc., New York, 1997).
  7. A.N.  Simonov, O.  Akhzar-Mehr, and G.  Vdovin, "Light scanner based on a viscoelastic stretchable grating," Opt. Lett. 30, 949-951 (2005).
    [CrossRef] [PubMed]
  8. P.M  Morse, and H.  Feshbach, Methods of Theoretical Physics, Part II, (McGraw-Hill, New York, 1953).
  9. W.N.  Findley, K.  Onaran and J.S.  Lai, Creep and Relaxation of Nonlinear Viscoelastic Materials: With an Introduction to Linear Viscoelasticity, (Dover Publications, Mineola, New York, 1990).
    [PubMed]
  10. R.M.  Christensen, Theory of viscoelasticity, (Dover Publications, Mineola, New York, 2003).
  11. http://www.okotech.com.
  12. R.J.  Noll, "Zernike polynomials and atmospheric turbulence," J. Opt. Soc. Am. 66, 207-211 (1976).
    [CrossRef]
  13. T.  Harada and T.  Kita, "Mechanically ruled aberration-corrected concave gratings," Appl. Opt. 19, 3987-3993 (1980).
    [CrossRef] [PubMed]
  14. V.N.  Mahajan, "Aberrations of diffracted wave fields. II. Diffraction gratings," J. Opt. Soc. Am. A 17, 2223-2228 (2000).
    [CrossRef]
  15. W.E.  Blass and G.W.  Halsey, Deconvolution of Spectra, (Academic Press, New York, 1981).
  16. P.A.  Jansson, ed. Deconvolution with Applications in Spectroscopy, (Academic Press, New York, 1984).

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Other (12)

P.M  Morse, and H.  Feshbach, Methods of Theoretical Physics, Part II, (McGraw-Hill, New York, 1953).

W.N.  Findley, K.  Onaran and J.S.  Lai, Creep and Relaxation of Nonlinear Viscoelastic Materials: With an Introduction to Linear Viscoelasticity, (Dover Publications, Mineola, New York, 1990).
[PubMed]

R.M.  Christensen, Theory of viscoelasticity, (Dover Publications, Mineola, New York, 2003).

http://www.okotech.com.

M.  Born and E.  Wolf, Principles of optics (Cambridge University Press, 2002), Chaps. 8 and 11.

M.  Bass, ed., Handbook of optics (McGraw-Hill Inc., 1995), vol. I - Chap. 3 and vol. II - Chap. 19.

J.F.  James and R.S.  Sternberg, The design of optical spectrometers (Chapman and Hall Ltd., London, 1969).

P.  Bousquet, Spectroscopy and its instrumentation, (Hilger, London, 1972).

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

E.G.  Loewen and E.  Popov, Diffraction gratings and applications, (Marcel Dekker Inc., New York, 1997).

W.E.  Blass and G.W.  Halsey, Deconvolution of Spectra, (Academic Press, New York, 1981).

P.A.  Jansson, ed. Deconvolution with Applications in Spectroscopy, (Academic Press, New York, 1984).

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Figures (7)

Fig. 1.
Fig. 1.

Spectrometer with stretchable grating: S1, S2, slits; L1, L2, lenses; LS, light source; D, photodiode; G, generator; VC, voice coil. Inset shows the Lissajous figure obtained by illuminating the input slit S1 with three lasers at 633 nm, 656 nm and 670 nm.

Fig. 2.
Fig. 2.

Spectrum obtained with three lasers at 633 nm, 656 nm and 670 nm.

Fig. 3.
Fig. 3.

Spectrum of a neon lamp measured by the viscoelastic-grating-based spectrometer (blue curve with circles) and reference spectrum of the lamp (red curve).

Fig. 4.
Fig. 4.

Spectrum of a neon lamp measured by the scanning viscoelastic-based spectrometer (blue curve with circles) and reference spectrum obtained with the untstretched grating (red curve).

Fig. 5.
Fig. 5.

Wave-front aberrations measured in (a) the transmitted and (b) the diffracted beams of the viscoelastic grating (solid figures). Dashed lines with open figures in panel b are calculations based on the grating deformation model described in the text.

Fig. 6.
Fig. 6.

Geometry of light diffraction by the transmission viscoelastic grating subjected to stretching. The origin O of the reference frame coincides with center of the grating.

Fig. 7.
Fig. 7.

Comparison of the neon lamp spectrum measured by the scanning viscoelastic-based spectrometer (blue curve with circles) with convoluted reference spectrum obtained with the untstretched grating (red curve).

Equations (14)

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R s = λ δ λ = λ F q δ S q Λ cos θ q ,
Δ d ( x , y ) = d 0 v Δ L L 0 u ( x , y ) n 1 ,
Λ ( x , y ) Λ 0 Λ 0 = 1 v Δ d ( x , y ) d 0 ,
Λ ( x , y ) = Λ 0 × { 1 + Δ L L + u ( x , y ) v d 0 ( n 1 ) } ,
u ( x , y ) = λ i a i ( t ) Z i ( r r 0 ) ,
u ( x , y ) λ { a 2 ( t ) Z 2 ( r r 0 ) + a 3 ( t ) Z 3 ( r r 0 ) + a 6 ( t ) Z 6 ( r r 0 ) } .
Λ ( x , y ) = Λ 0 × ( 1 + Δ L L ) × { 1 + γ i a i ( t ) Z i ( r r 0 ) } ,
S = AB + BC + CD m λ q ,
m λ q = m λ 0 x dx Λ ( x , y ) m λ Λ 0 ( 1 + Δ L L ) 0 x { 1 γ i a i ( t ) Z i ( r r 0 ) + } dx ' ,
w ( x , y ) = λ i a i ( d ) Z i ( r r 0 ) ,
C + i a i ( d ) Z i ( r r 0 ) = m Λ 0 ( 1 + Δ L L ) 0 x { 1 γ i a i ( t ) Z i ( r r 0 ) + } dx + i a i ( t ) Z i ( r r 0 ) ,
S A ( λ ) = S 0 ( λ ) × U ( λ λ , λ ) d λ ,
U ( λ λ , λ ) H ( δ S 2 , λ ) ,
δ S 2 = ( λ λ ) F 2 ( Λ cos θ 2 ) .

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