Abstract

Piezoelectric materials used in mechanical scanning of Fabry-Perot spectrometers are found to have measurable nonlinearities. Dynamic scanning has been used in the present investigation in order to decrease the effects of some of the variables, such as creep, of the piezoelectric material in static operation. The results show mainly a decrease in the distance between corresponding maxima, or apparent free spectral range, as the driving voltage increases to higher values. A relationship between this voltage and displacement (in terms of orders) has been derived, and it is given by νi = ln {1 − (xix0)/[a/(1 − b) − x0]}/ln b, where νi is the displacement in orders from an arbitrary starting point, xi is a quantity directly proportional to the voltage, while x0 is also a quantity proportional to the voltage at the arbitrary reference point, a is the distance between the arbitrary reference point and the next order, and b is the nonlinearity constant for a given piezoelectric material. Examples are given for emission and absorption measurements where the usually large effects of the piezoelectric material nonlinearities are derived, as well as schemes to minimize or altogether remove the effects by suitable handling of the data or by changing the experiment such that the scanning is forced to be linear.

© 1978 Optical Society of America

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References

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  1. J. V. Ramsay, Appl. Opt. 1, 411 (1962).
    [CrossRef]
  2. J. V. Ramsay, Appl. Opt. 5, 1297 (1966).
    [CrossRef] [PubMed]
  3. G. Hernandez, Appl. Opt. 9, 1225 (1970).
    [CrossRef] [PubMed]
  4. R. Dupeyrat, J. Phys. Rad. 19, 290 (1958).
    [CrossRef]
  5. V. G. Koloshnikov, M. A. Mazing, S. C. Mandelstam, Y. P. Marasanov, Opt. Spectrosc. 11, 302 (1961).
  6. J. Cooper, J. R. Greig, J. Sci. Instrum. 40, 433 (1963).
    [CrossRef]
  7. K. D. Mielenz, R. B. Stephens, K. F. Nefflen, J. Res. Nat. Bur. Stand. Sect. C: 68, 1 (1964).
  8. G. Hesse, Feingeratetechnick 12, 535 (1965).
  9. M. Gadsden, H. M. Williams, J. Res. Nat. Bur. Stand. Sect. C: 70, 159 (1966).
  10. J. R. Johnson, Appl. Opt. 6, 1930 (1967).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  12. J. R. Johnson, Appl. Opt. 7, 1061 (1968).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  15. J. Brannon, Appl. Opt. 8, 1977 (1971).
    [CrossRef]
  16. G. Hernandez, O. A. Mills, Appl. Opt. 12, 126 (1973).
    [CrossRef] [PubMed]
  17. G. Hernandez, Appl. Opt.17, 0000 in press (1978).
    [PubMed]
  18. G. Hernandez, R. G. Roble, J. Geophys. Res. 81, 2065 (1976).
    [CrossRef]
  19. G. Hernandez, R. G. Roble, J. Geophys. Res. 81, 5173 (1976).
    [CrossRef]
  20. G. Hernandez, R. G. Roble, J. Geophys. Res. 83, 5505 (1977).
    [CrossRef]

1977 (1)

G. Hernandez, R. G. Roble, J. Geophys. Res. 83, 5505 (1977).
[CrossRef]

1976 (2)

G. Hernandez, R. G. Roble, J. Geophys. Res. 81, 2065 (1976).
[CrossRef]

G. Hernandez, R. G. Roble, J. Geophys. Res. 81, 5173 (1976).
[CrossRef]

1973 (1)

1971 (1)

J. Brannon, Appl. Opt. 8, 1977 (1971).
[CrossRef]

1970 (2)

G. F. Kirkbright, M. Sargent, Spectrochim. Acta. Part B: 5, 577 (1970).
[CrossRef]

G. Hernandez, Appl. Opt. 9, 1225 (1970).
[CrossRef] [PubMed]

1968 (3)

1967 (1)

1966 (2)

J. V. Ramsay, Appl. Opt. 5, 1297 (1966).
[CrossRef] [PubMed]

M. Gadsden, H. M. Williams, J. Res. Nat. Bur. Stand. Sect. C: 70, 159 (1966).

1965 (1)

G. Hesse, Feingeratetechnick 12, 535 (1965).

1964 (1)

K. D. Mielenz, R. B. Stephens, K. F. Nefflen, J. Res. Nat. Bur. Stand. Sect. C: 68, 1 (1964).

1963 (1)

J. Cooper, J. R. Greig, J. Sci. Instrum. 40, 433 (1963).
[CrossRef]

1962 (1)

1961 (1)

V. G. Koloshnikov, M. A. Mazing, S. C. Mandelstam, Y. P. Marasanov, Opt. Spectrosc. 11, 302 (1961).

1958 (1)

R. Dupeyrat, J. Phys. Rad. 19, 290 (1958).
[CrossRef]

Brannon, J.

J. Brannon, Appl. Opt. 8, 1977 (1971).
[CrossRef]

Cooper, J.

J. R. Greig, J. Cooper, Appl. Opt. 7, 2166 (1968).
[CrossRef] [PubMed]

J. Cooper, J. R. Greig, J. Sci. Instrum. 40, 433 (1963).
[CrossRef]

Dupeyrat, R.

R. Dupeyrat, J. Phys. Rad. 19, 290 (1958).
[CrossRef]

Gadsden, M.

M. Gadsden, H. M. Williams, J. Res. Nat. Bur. Stand. Sect. C: 70, 159 (1966).

Greig, J. R.

J. R. Greig, J. Cooper, Appl. Opt. 7, 2166 (1968).
[CrossRef] [PubMed]

J. Cooper, J. R. Greig, J. Sci. Instrum. 40, 433 (1963).
[CrossRef]

Hercher, M.

Hernandez, G.

G. Hernandez, R. G. Roble, J. Geophys. Res. 83, 5505 (1977).
[CrossRef]

G. Hernandez, R. G. Roble, J. Geophys. Res. 81, 2065 (1976).
[CrossRef]

G. Hernandez, R. G. Roble, J. Geophys. Res. 81, 5173 (1976).
[CrossRef]

G. Hernandez, O. A. Mills, Appl. Opt. 12, 126 (1973).
[CrossRef] [PubMed]

G. Hernandez, Appl. Opt. 9, 1225 (1970).
[CrossRef] [PubMed]

G. Hernandez, Appl. Opt.17, 0000 in press (1978).
[PubMed]

Hesse, G.

G. Hesse, Feingeratetechnick 12, 535 (1965).

Johnson, J. R.

Kirkbright, G. F.

G. F. Kirkbright, M. Sargent, Spectrochim. Acta. Part B: 5, 577 (1970).
[CrossRef]

Koloshnikov, V. G.

V. G. Koloshnikov, M. A. Mazing, S. C. Mandelstam, Y. P. Marasanov, Opt. Spectrosc. 11, 302 (1961).

Mandelstam, S. C.

V. G. Koloshnikov, M. A. Mazing, S. C. Mandelstam, Y. P. Marasanov, Opt. Spectrosc. 11, 302 (1961).

Marasanov, Y. P.

V. G. Koloshnikov, M. A. Mazing, S. C. Mandelstam, Y. P. Marasanov, Opt. Spectrosc. 11, 302 (1961).

Mazing, M. A.

V. G. Koloshnikov, M. A. Mazing, S. C. Mandelstam, Y. P. Marasanov, Opt. Spectrosc. 11, 302 (1961).

Mielenz, K. D.

K. D. Mielenz, R. B. Stephens, K. F. Nefflen, J. Res. Nat. Bur. Stand. Sect. C: 68, 1 (1964).

Mills, O. A.

Nefflen, K. F.

K. D. Mielenz, R. B. Stephens, K. F. Nefflen, J. Res. Nat. Bur. Stand. Sect. C: 68, 1 (1964).

Ramsay, J. V.

Roble, R. G.

G. Hernandez, R. G. Roble, J. Geophys. Res. 83, 5505 (1977).
[CrossRef]

G. Hernandez, R. G. Roble, J. Geophys. Res. 81, 2065 (1976).
[CrossRef]

G. Hernandez, R. G. Roble, J. Geophys. Res. 81, 5173 (1976).
[CrossRef]

Sargent, M.

G. F. Kirkbright, M. Sargent, Spectrochim. Acta. Part B: 5, 577 (1970).
[CrossRef]

Stephens, R. B.

K. D. Mielenz, R. B. Stephens, K. F. Nefflen, J. Res. Nat. Bur. Stand. Sect. C: 68, 1 (1964).

Williams, H. M.

M. Gadsden, H. M. Williams, J. Res. Nat. Bur. Stand. Sect. C: 70, 159 (1966).

Appl. Opt. (9)

Feingeratetechnick (1)

G. Hesse, Feingeratetechnick 12, 535 (1965).

J. Geophys. Res. (3)

G. Hernandez, R. G. Roble, J. Geophys. Res. 81, 2065 (1976).
[CrossRef]

G. Hernandez, R. G. Roble, J. Geophys. Res. 81, 5173 (1976).
[CrossRef]

G. Hernandez, R. G. Roble, J. Geophys. Res. 83, 5505 (1977).
[CrossRef]

J. Phys. Rad. (1)

R. Dupeyrat, J. Phys. Rad. 19, 290 (1958).
[CrossRef]

J. Res. Nat. Bur. Stand. Sect. C (2)

M. Gadsden, H. M. Williams, J. Res. Nat. Bur. Stand. Sect. C: 70, 159 (1966).

K. D. Mielenz, R. B. Stephens, K. F. Nefflen, J. Res. Nat. Bur. Stand. Sect. C: 68, 1 (1964).

J. Sci. Instrum. (1)

J. Cooper, J. R. Greig, J. Sci. Instrum. 40, 433 (1963).
[CrossRef]

Opt. Spectrosc. (1)

V. G. Koloshnikov, M. A. Mazing, S. C. Mandelstam, Y. P. Marasanov, Opt. Spectrosc. 11, 302 (1961).

Spectrochim. Acta. Part B (1)

G. F. Kirkbright, M. Sargent, Spectrochim. Acta. Part B: 5, 577 (1970).
[CrossRef]

Other (1)

G. Hernandez, Appl. Opt.17, 0000 in press (1978).
[PubMed]

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Figures (4)

Fig. 1
Fig. 1

Nonlinearity of the piezoelectric material shown as the location of the i + 1 fringe maxima as a function of the ith fringe maxima for the indicated types of material. Unity slope or linear behavior is also shown as comparison.

Fig. 2
Fig. 2

Unshifted spectra for (a) background spectrum and (b) absorption and (c) the product of (a) and (b) or absorption spectrum.

Fig. 3
Fig. 3

Shifted absorption spectra (left) and (right) resultant absorption obtained from the ratio of the shifted absorption spectra to the unshifted background spectrum. The amount of operating point shift (in orders) is indicated in the right-hand side panels (see text for details).

Fig. 4
Fig. 4

Schematic diagram of circuit to linearize the scan of the piezoelectric materials.

Tables (1)

Tables Icon

Table I Apparent Winds Caused by Shifting the Spectrometer Operating Point

Equations (28)

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V = l t / ( L α ) ,
x 1 = x 0 b + a ; x 2 = x 1 b + a ; x 3 = x 2 b + a ; etc .,
x n = x 0 b n + a ( b n 1 ) / ( b 1 ) .
n = ln { 1 ( x n x 0 ) / [ a / ( 1 b ) x 0 ] } / ln b ,
( x n 1 x n ) = b n ( b 01 x 0 ) ,
x n + Δ x n = x n + b n Δ x 0 = ( x 0 + Δ x 0 ) b n + a ( b n 1 ) / ( b 1 ) .
n + ln ( 1 c + c b ) / ln b = ln { 1 + ( x n + Δ x n x 0 ) / [ x 0 + a / ( b 1 ) ] } / ln b .
ln ( 1 c + b c ) / ln b = ν ; 0 ν 1 , c = ( b ν 1 ) / ( b 1 ) .
σ i = ln { 1 ( x i x 0 ) / [ a / ( 1 b ) x 0 ] } / ln b ,
( x i x 0 ) = [ a / ( 1 b ) x 0 ] ( 1 b σ i ) .
lim b 1 ( x i x 0 ) = a σ i ,
lim σ i ( x i x 0 ) = a / ( 1 b ) x 0 .
δ x = σ o υ Δ σ x / ( c Δ σ ) ,
x x ref = [ a / ( 1 b ) x 0 ] ( 1 b c ) b ν 0 b d .
x x ref = ( x x ref ) 0 b d ,
δ = ( 1 b d ) ( b t 1 ) / ( 1 b ) ,
δ + = ( 1 b d ) ( b t b ) / ( 1 b ) ,
δ ave = ( 1 b d ) [ b t ( 1 + b ) / 2 ] / ( 1 b ) .
R = ( x x ref ) / ( x + x ref ) = ( b t 1 ) / ( b t b ) ,
t = ln [ b + ( b 1 ) / R 1 ] / ln b .
w x / Δ σ x = ( b f b f ) / ( 1 b ) ,
w x + / Δ σ x = b ( b f b f ) / ( 1 b ) ,
w x / Δ σ x = ( 1 + b ) ( b f b f ) / [ 2 ( 1 b ) ] .
lim b 1 ( w x i / Δ σ x ) = 2 f
I B = I 0 i = 1 N exp [ k ( ν i ) Y i ] ,
I A = { I 0 i = 1 N exp [ k ( ν i ) Y i ] } exp [ k ( ν A ) Y A ] = I B exp [ k ( ν A ) Y A ] .
k ( v j ) = k 0 j exp [ ( ν ν j ) / G j ] 2 ,
ν = ln { 1 ( x i x 0 ) b c / [ a / ( 1 b ) x 0 ] } / ln b .

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