Abstract

Derivative spectrophotometry has been shown to have many important applications: for example, studying composition and reaction processes; providing gas signatures; detecting trace chemicals. This technique can become a powerful means for analyzing isomers used in polymer production. In this report, practical examples are given which typify applications of the derivative spectra. Conventional absorption and emission spectra often present overlapping bands not easily resolved by conventional means; band resolution usually is facilitated by first-and second-derivative spectra obtained from spectrophotometric measurements. Numerical methods based on both off-line and on-line computer processing are presented for generating first- and second-derivative spectra, and these techniques are discussed fully. With these methods, the contribution of background noise is emphasized. Ways to reduce this noise are given.

© 1972 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Instrument News, Vol. 20, No. 1 (1969), The Perkin-Elmer Corporation, Norwalk, Connecticut.
  2. C. S. French, A. B. Church, R. W. Eppley, Carnegie Institution of Washington Yearbook No. 53 (1954), p. 182.
  3. A. T. Giese, C. S. French, Appl. Spectrosc. 9, 78 (1955).
    [CrossRef]
  4. A. M. Bartz, H. D. Ruhl, Appl. Opt. 9, 969 (1963).
  5. E. Gunders, B. Kaplam, J. Opt. Soc. Am. 55, 1094 (1955).
    [CrossRef]
  6. M. P. Klein, E. A. Dratz, Rev. Sci. Instrum. 39, 397 (1968).
    [CrossRef] [PubMed]
  7. F. R. Stauffer, H. Sakai, Appl. Opt. 7, 61 (1968).
    [CrossRef] [PubMed]
  8. D. T. Williams, R. N. Hager, Appl. Opt. 91, 1597 (1970).
    [CrossRef]
  9. G. Bonfigliori, P. Brovetto, G. Busca, S. LeVialdi, G. Palmieri, E. Wanke, Appl. Opt. 6, 447 (1967).
    [CrossRef]
  10. J. Overend, A. C. Gilby, J. W. Russell, C. W. Brown, J. Beutel, C. W. Bjork, H. G. Paulat, Appl. Opt. 6, 457 (1967).
    [CrossRef] [PubMed]
  11. F. Arhmu, A. Rucci, Rev. Sci. Instrum. 37, 1696 (1966).
    [CrossRef]
  12. B. L. Evans, K. T. Thompson, J. Sci. Instrum. 1, 327 (1969).
  13. I. Baslev, Phys. Rev. 143, 636 (1966).
    [CrossRef]
  14. R. N. Hager, R. C. Anderson, J. Opt. Soc. Am. 60, 1444 (1970).
    [CrossRef]
  15. R. Peden, F. Grum, Appl. Opt. 9, 2143 (1970).
    [CrossRef] [PubMed]
  16. W. Jennings, First Course in Numerical Methods (Macmillan, New York, 1964), pp. 105–106.
  17. N. Draper, H. Smith, Applied Regression Analysis (Wiley, New York, 1966), pp. 129–130.
  18. J. B. Hildebrand, Introduction to Numerical Analysis (McGraw-Hill, New York, 1956), pp. 295–302.
  19. E. Tannenbaur, E. M. Coffin, A. J. Harrison, J. Phys. Chem. 21, 311 (1953).
    [CrossRef]
  20. D. Lewis, P. B. Merkel, W. H. Hamill, J. Chem. Phys. 53, 2750 (1970).
    [CrossRef]

1970 (4)

D. T. Williams, R. N. Hager, Appl. Opt. 91, 1597 (1970).
[CrossRef]

R. N. Hager, R. C. Anderson, J. Opt. Soc. Am. 60, 1444 (1970).
[CrossRef]

R. Peden, F. Grum, Appl. Opt. 9, 2143 (1970).
[CrossRef] [PubMed]

D. Lewis, P. B. Merkel, W. H. Hamill, J. Chem. Phys. 53, 2750 (1970).
[CrossRef]

1969 (2)

B. L. Evans, K. T. Thompson, J. Sci. Instrum. 1, 327 (1969).

Instrument News, Vol. 20, No. 1 (1969), The Perkin-Elmer Corporation, Norwalk, Connecticut.

1968 (2)

M. P. Klein, E. A. Dratz, Rev. Sci. Instrum. 39, 397 (1968).
[CrossRef] [PubMed]

F. R. Stauffer, H. Sakai, Appl. Opt. 7, 61 (1968).
[CrossRef] [PubMed]

1967 (2)

1966 (2)

F. Arhmu, A. Rucci, Rev. Sci. Instrum. 37, 1696 (1966).
[CrossRef]

I. Baslev, Phys. Rev. 143, 636 (1966).
[CrossRef]

1963 (1)

1955 (2)

1954 (1)

C. S. French, A. B. Church, R. W. Eppley, Carnegie Institution of Washington Yearbook No. 53 (1954), p. 182.

1953 (1)

E. Tannenbaur, E. M. Coffin, A. J. Harrison, J. Phys. Chem. 21, 311 (1953).
[CrossRef]

Anderson, R. C.

Arhmu, F.

F. Arhmu, A. Rucci, Rev. Sci. Instrum. 37, 1696 (1966).
[CrossRef]

Bartz, A. M.

Baslev, I.

I. Baslev, Phys. Rev. 143, 636 (1966).
[CrossRef]

Beutel, J.

Bjork, C. W.

Bonfigliori, G.

Brovetto, P.

Brown, C. W.

Busca, G.

Church, A. B.

C. S. French, A. B. Church, R. W. Eppley, Carnegie Institution of Washington Yearbook No. 53 (1954), p. 182.

Coffin, E. M.

E. Tannenbaur, E. M. Coffin, A. J. Harrison, J. Phys. Chem. 21, 311 (1953).
[CrossRef]

Draper, N.

N. Draper, H. Smith, Applied Regression Analysis (Wiley, New York, 1966), pp. 129–130.

Dratz, E. A.

M. P. Klein, E. A. Dratz, Rev. Sci. Instrum. 39, 397 (1968).
[CrossRef] [PubMed]

Eppley, R. W.

C. S. French, A. B. Church, R. W. Eppley, Carnegie Institution of Washington Yearbook No. 53 (1954), p. 182.

Evans, B. L.

B. L. Evans, K. T. Thompson, J. Sci. Instrum. 1, 327 (1969).

French, C. S.

A. T. Giese, C. S. French, Appl. Spectrosc. 9, 78 (1955).
[CrossRef]

C. S. French, A. B. Church, R. W. Eppley, Carnegie Institution of Washington Yearbook No. 53 (1954), p. 182.

Giese, A. T.

Gilby, A. C.

Grum, F.

Gunders, E.

Hager, R. N.

R. N. Hager, R. C. Anderson, J. Opt. Soc. Am. 60, 1444 (1970).
[CrossRef]

D. T. Williams, R. N. Hager, Appl. Opt. 91, 1597 (1970).
[CrossRef]

Hamill, W. H.

D. Lewis, P. B. Merkel, W. H. Hamill, J. Chem. Phys. 53, 2750 (1970).
[CrossRef]

Harrison, A. J.

E. Tannenbaur, E. M. Coffin, A. J. Harrison, J. Phys. Chem. 21, 311 (1953).
[CrossRef]

Hildebrand, J. B.

J. B. Hildebrand, Introduction to Numerical Analysis (McGraw-Hill, New York, 1956), pp. 295–302.

Jennings, W.

W. Jennings, First Course in Numerical Methods (Macmillan, New York, 1964), pp. 105–106.

Kaplam, B.

Klein, M. P.

M. P. Klein, E. A. Dratz, Rev. Sci. Instrum. 39, 397 (1968).
[CrossRef] [PubMed]

LeVialdi, S.

Lewis, D.

D. Lewis, P. B. Merkel, W. H. Hamill, J. Chem. Phys. 53, 2750 (1970).
[CrossRef]

Merkel, P. B.

D. Lewis, P. B. Merkel, W. H. Hamill, J. Chem. Phys. 53, 2750 (1970).
[CrossRef]

Overend, J.

Palmieri, G.

Paulat, H. G.

Peden, R.

Rucci, A.

F. Arhmu, A. Rucci, Rev. Sci. Instrum. 37, 1696 (1966).
[CrossRef]

Ruhl, H. D.

Russell, J. W.

Sakai, H.

Smith, H.

N. Draper, H. Smith, Applied Regression Analysis (Wiley, New York, 1966), pp. 129–130.

Stauffer, F. R.

Tannenbaur, E.

E. Tannenbaur, E. M. Coffin, A. J. Harrison, J. Phys. Chem. 21, 311 (1953).
[CrossRef]

Thompson, K. T.

B. L. Evans, K. T. Thompson, J. Sci. Instrum. 1, 327 (1969).

Wanke, E.

Williams, D. T.

D. T. Williams, R. N. Hager, Appl. Opt. 91, 1597 (1970).
[CrossRef]

Appl. Opt. (6)

Appl. Spectrosc. (1)

Carnegie Institution of Washington Yearbook No. 53 (1)

C. S. French, A. B. Church, R. W. Eppley, Carnegie Institution of Washington Yearbook No. 53 (1954), p. 182.

Instrument News (1)

Instrument News, Vol. 20, No. 1 (1969), The Perkin-Elmer Corporation, Norwalk, Connecticut.

J. Chem. Phys. (1)

D. Lewis, P. B. Merkel, W. H. Hamill, J. Chem. Phys. 53, 2750 (1970).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Phys. Chem. (1)

E. Tannenbaur, E. M. Coffin, A. J. Harrison, J. Phys. Chem. 21, 311 (1953).
[CrossRef]

J. Sci. Instrum. (1)

B. L. Evans, K. T. Thompson, J. Sci. Instrum. 1, 327 (1969).

Phys. Rev. (1)

I. Baslev, Phys. Rev. 143, 636 (1966).
[CrossRef]

Rev. Sci. Instrum. (2)

M. P. Klein, E. A. Dratz, Rev. Sci. Instrum. 39, 397 (1968).
[CrossRef] [PubMed]

F. Arhmu, A. Rucci, Rev. Sci. Instrum. 37, 1696 (1966).
[CrossRef]

Other (3)

W. Jennings, First Course in Numerical Methods (Macmillan, New York, 1964), pp. 105–106.

N. Draper, H. Smith, Applied Regression Analysis (Wiley, New York, 1966), pp. 129–130.

J. B. Hildebrand, Introduction to Numerical Analysis (McGraw-Hill, New York, 1956), pp. 295–302.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1
Fig. 1

Output signals from the Cary 14 spectrophotometer.

Fig. 2
Fig. 2

Absorbance and normalized first-derivative spectra by on-line computation with a didymium glass; (A) 5-nm data collection interval: 1, original absorbance; 2, first derivative. (B) Same as A, except 1-nm data collection interval.

Fig. 3
Fig. 3

(A) Normalized, unsmoothed first-derivative spectrum by off-line computation for didymium glass; 5-nm data collection interval. (B) Normalized, unsmoothed first-derivative spectrum by off-line computation for didymium glass; 1-nm data collection interval by off-line computation for didymium glass; 1-nm data collection interval.

Fig. 4
Fig. 4

Normalized, unsmoothed second-derivative spectrum by off-line computation for didymium glass; 1-nm data collection interval.

Fig. 5
Fig. 5

Comparison of normalized) unsmoothed first-derivative spectrum by off-line computation vs equivalent derivative spectrum (circles) measured on a Perkin-Elmer 356 spectrophotometer.

Fig. 6
Fig. 6

Absorbance and normalized, unsmoothed first-derivative spectrum in visible region for rosamine-4 solution in methanol: 1, absorbance; 2, derivative.

Fig. 7
Fig. 7

Same as Fig. 6, curve 2, except with SE-13 data smoothing.

Fig. 8
Fig. 8

Same as Fig. 6, curve 2, except with SE-15 data smoothing.

Fig. 9
Fig. 9

Luminescent emission and normalized second-derivative spectrum in ultraviolet region for a biphenyl–styrene solution in cyclohexane; excitation wavelength is 275 nm. 1, luminescence emission; 2, second derivative.

Fig. 10
Fig. 10

Absorbance and normalized second-derivative spectrum in ultraviolet region for a car exhaust: 1, absorbance; 2, second derivative.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

Δ S ( λ ) = S ( λ 2 ) - S ( λ 1 ) .
λ = λ 0 + A sin ω t ,
g 1 ( λ ) = α 0 + α 1 λ + α 2 λ 2 ,
g 2 ( λ ) = β 0 + β 1 λ + β 2 λ 2 + β 2 λ 3 .
g ˙ 1 ( λ ) = α 1 + 2 α 2 λ             and             g 1 ( λ ) = 2 α 2 ,
g 2 ( λ ) = β 1 + 2 β 2 λ + 3 β 3 λ 2             and             g 2 ( λ ) = 2 β 2 + 6 β 3 λ .
Z i = { / 6 1 ( 5 y 1 + 2 y 2 - y 3 ) i = 1 , / 3 1 ( y i - 1 + y i + y i + 1 ) i = 2 , 3 , , n - 1 , / 6 1 ( - y n - 2 + 2 y n - 1 + 5 y n ) i = n .
Z i = { / 5 1 ( 3 y 1 + 2 y 2 + y 3 - y 5 ) i = 1 , / 10 1 ( 4 y 1 + 3 y 2 + 2 y 3 + y 4 ) i = 2 , / 5 1 ( y i - 2 + y i - 1 + y i + y i + 1 + y i + 2 ) i = 3 , 4 , , n - 2 , / 10 1 ( y n - 3 + 2 y n - 2 + 3 y n - 1 + 4 y n ) i = n - 1 , / 5 1 ( - y n - 4 + y n - 2 + 2 y n - 1 + 3 y n ) i = n .

Metrics