Abstract

A technique for calculating the optical constants of powdered materials that have been pressed into pellets along with a diluent such as polyethylene, as is commonly used in the spectroscopy community, is introduced. The simple Beer–Lambert law typically used to calculate the optical constants has the inherent weakness that it treats the absorbing medium as a single nonporous solid, as opposed to a dielectric material embedded within a medium. This leads to a systematic underestimation of both the absorption coefficient and the refractive index, especially at low filling factors. Effective medium theory provides a way to calculate more accurate optical constants and produces similar optical constants across a wide range of filling factors, including crucially at the low filling factors commonly used experimentally. The technique can also be extended to estimate the porosity of the samples and provide a true, preparation-independent value for the optical properties of the sample material.

© 2009 Optical Society of America

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  1. J. A. Zeitler, P. F. Taday, D. A. Newnham, M. Pepper, K. C. Gordon, and T. Rades, J. Pharm. Pharmacol. 59, 209 (2007).
    [CrossRef] [PubMed]
  2. E. P. J. Parrott, J. A. Zeitler, T. Friščić, M. Pepper, W. Jones, G. M. Day, and L. F. Gladden, Cryst. Growth Des. 9, 1452 (2009).
    [CrossRef]
  3. B. M. Fischer, M. Walther, and P. U. Jepsen, Phys. Med. Biol. 47, 3807 (2002).
    [CrossRef] [PubMed]
  4. A. Markelz, A. Roitberg, and E. J. Heilweil, Chem. Phys. Lett. 320, 42 (2000).
    [CrossRef]
  5. T. D. Dorney, R. G. Baraniuk, and D. M. Mittleman, J. Opt. Soc. Am. A 18, 1562 (2001).
    [CrossRef]
  6. R. Wilk, I. Pupeza, R. Cernat, and M. Koch, IEEE J. Sel. Top. Quantum Electron. 14, 392 (2008).
    [CrossRef]
  7. E. P. J. Parrott, J. A. Zeitler, L. F. Gladden, S. N. Taraskin, and S. R. Elliott, J. Non-Cryst. Solids 355, 1824 (2009).
    [CrossRef]
  8. P. U. Jepsen and B. M. Fischer, Opt. Lett. 30, 29 (2005).
    [CrossRef] [PubMed]
  9. J. C. Maxwell-Garnett, Philos. Trans. R. Soc. London Ser. A 203, 385 (1904).
    [CrossRef]
  10. E. P. J. Parrott, J. A. Zeitler, J. McGregor, S.-P. Oei, H. E. Unalan, S.-C. Tan, W. I. Milne, J.-P. Tessonnier, R. Schlögl, and L. F. Gladden, J. Phys. Chem. C 113, 10554 (2009).
    [CrossRef]
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    [CrossRef]
  12. M. Franz, B. M. Fischer, and M. Walther, Appl. Phys. Lett. 92, 021107 (2008).
    [CrossRef]
  13. J. A. Zeitler and L. F. Gladden, Eur. J. Pharm. Biopharm. 71, 2 (2009).
    [CrossRef]

2009 (4)

E. P. J. Parrott, J. A. Zeitler, T. Friščić, M. Pepper, W. Jones, G. M. Day, and L. F. Gladden, Cryst. Growth Des. 9, 1452 (2009).
[CrossRef]

E. P. J. Parrott, J. A. Zeitler, L. F. Gladden, S. N. Taraskin, and S. R. Elliott, J. Non-Cryst. Solids 355, 1824 (2009).
[CrossRef]

E. P. J. Parrott, J. A. Zeitler, J. McGregor, S.-P. Oei, H. E. Unalan, S.-C. Tan, W. I. Milne, J.-P. Tessonnier, R. Schlögl, and L. F. Gladden, J. Phys. Chem. C 113, 10554 (2009).
[CrossRef]

J. A. Zeitler and L. F. Gladden, Eur. J. Pharm. Biopharm. 71, 2 (2009).
[CrossRef]

2008 (3)

R. Wilk, I. Pupeza, R. Cernat, and M. Koch, IEEE J. Sel. Top. Quantum Electron. 14, 392 (2008).
[CrossRef]

Y. C. Shen, P. F. Taday, and M. Pepper, Appl. Phys. Lett. 92, 051103 (2008).
[CrossRef]

M. Franz, B. M. Fischer, and M. Walther, Appl. Phys. Lett. 92, 021107 (2008).
[CrossRef]

2007 (1)

J. A. Zeitler, P. F. Taday, D. A. Newnham, M. Pepper, K. C. Gordon, and T. Rades, J. Pharm. Pharmacol. 59, 209 (2007).
[CrossRef] [PubMed]

2005 (1)

2002 (1)

B. M. Fischer, M. Walther, and P. U. Jepsen, Phys. Med. Biol. 47, 3807 (2002).
[CrossRef] [PubMed]

2001 (1)

2000 (1)

A. Markelz, A. Roitberg, and E. J. Heilweil, Chem. Phys. Lett. 320, 42 (2000).
[CrossRef]

1904 (1)

J. C. Maxwell-Garnett, Philos. Trans. R. Soc. London Ser. A 203, 385 (1904).
[CrossRef]

Baraniuk, R. G.

Cernat, R.

R. Wilk, I. Pupeza, R. Cernat, and M. Koch, IEEE J. Sel. Top. Quantum Electron. 14, 392 (2008).
[CrossRef]

Day, G. M.

E. P. J. Parrott, J. A. Zeitler, T. Friščić, M. Pepper, W. Jones, G. M. Day, and L. F. Gladden, Cryst. Growth Des. 9, 1452 (2009).
[CrossRef]

Dorney, T. D.

Elliott, S. R.

E. P. J. Parrott, J. A. Zeitler, L. F. Gladden, S. N. Taraskin, and S. R. Elliott, J. Non-Cryst. Solids 355, 1824 (2009).
[CrossRef]

Fischer, B. M.

M. Franz, B. M. Fischer, and M. Walther, Appl. Phys. Lett. 92, 021107 (2008).
[CrossRef]

P. U. Jepsen and B. M. Fischer, Opt. Lett. 30, 29 (2005).
[CrossRef] [PubMed]

B. M. Fischer, M. Walther, and P. U. Jepsen, Phys. Med. Biol. 47, 3807 (2002).
[CrossRef] [PubMed]

Franz, M.

M. Franz, B. M. Fischer, and M. Walther, Appl. Phys. Lett. 92, 021107 (2008).
[CrossRef]

Frišcic, T.

E. P. J. Parrott, J. A. Zeitler, T. Friščić, M. Pepper, W. Jones, G. M. Day, and L. F. Gladden, Cryst. Growth Des. 9, 1452 (2009).
[CrossRef]

Gladden, L. F.

E. P. J. Parrott, J. A. Zeitler, T. Friščić, M. Pepper, W. Jones, G. M. Day, and L. F. Gladden, Cryst. Growth Des. 9, 1452 (2009).
[CrossRef]

E. P. J. Parrott, J. A. Zeitler, L. F. Gladden, S. N. Taraskin, and S. R. Elliott, J. Non-Cryst. Solids 355, 1824 (2009).
[CrossRef]

E. P. J. Parrott, J. A. Zeitler, J. McGregor, S.-P. Oei, H. E. Unalan, S.-C. Tan, W. I. Milne, J.-P. Tessonnier, R. Schlögl, and L. F. Gladden, J. Phys. Chem. C 113, 10554 (2009).
[CrossRef]

J. A. Zeitler and L. F. Gladden, Eur. J. Pharm. Biopharm. 71, 2 (2009).
[CrossRef]

Gordon, K. C.

J. A. Zeitler, P. F. Taday, D. A. Newnham, M. Pepper, K. C. Gordon, and T. Rades, J. Pharm. Pharmacol. 59, 209 (2007).
[CrossRef] [PubMed]

Heilweil, E. J.

A. Markelz, A. Roitberg, and E. J. Heilweil, Chem. Phys. Lett. 320, 42 (2000).
[CrossRef]

Jepsen, P. U.

P. U. Jepsen and B. M. Fischer, Opt. Lett. 30, 29 (2005).
[CrossRef] [PubMed]

B. M. Fischer, M. Walther, and P. U. Jepsen, Phys. Med. Biol. 47, 3807 (2002).
[CrossRef] [PubMed]

Jones, W.

E. P. J. Parrott, J. A. Zeitler, T. Friščić, M. Pepper, W. Jones, G. M. Day, and L. F. Gladden, Cryst. Growth Des. 9, 1452 (2009).
[CrossRef]

Koch, M.

R. Wilk, I. Pupeza, R. Cernat, and M. Koch, IEEE J. Sel. Top. Quantum Electron. 14, 392 (2008).
[CrossRef]

Markelz, A.

A. Markelz, A. Roitberg, and E. J. Heilweil, Chem. Phys. Lett. 320, 42 (2000).
[CrossRef]

Maxwell-Garnett, J. C.

J. C. Maxwell-Garnett, Philos. Trans. R. Soc. London Ser. A 203, 385 (1904).
[CrossRef]

McGregor, J.

E. P. J. Parrott, J. A. Zeitler, J. McGregor, S.-P. Oei, H. E. Unalan, S.-C. Tan, W. I. Milne, J.-P. Tessonnier, R. Schlögl, and L. F. Gladden, J. Phys. Chem. C 113, 10554 (2009).
[CrossRef]

Milne, W. I.

E. P. J. Parrott, J. A. Zeitler, J. McGregor, S.-P. Oei, H. E. Unalan, S.-C. Tan, W. I. Milne, J.-P. Tessonnier, R. Schlögl, and L. F. Gladden, J. Phys. Chem. C 113, 10554 (2009).
[CrossRef]

Mittleman, D. M.

Newnham, D. A.

J. A. Zeitler, P. F. Taday, D. A. Newnham, M. Pepper, K. C. Gordon, and T. Rades, J. Pharm. Pharmacol. 59, 209 (2007).
[CrossRef] [PubMed]

Oei, S.-P.

E. P. J. Parrott, J. A. Zeitler, J. McGregor, S.-P. Oei, H. E. Unalan, S.-C. Tan, W. I. Milne, J.-P. Tessonnier, R. Schlögl, and L. F. Gladden, J. Phys. Chem. C 113, 10554 (2009).
[CrossRef]

Parrott, E. P. J.

E. P. J. Parrott, J. A. Zeitler, T. Friščić, M. Pepper, W. Jones, G. M. Day, and L. F. Gladden, Cryst. Growth Des. 9, 1452 (2009).
[CrossRef]

E. P. J. Parrott, J. A. Zeitler, L. F. Gladden, S. N. Taraskin, and S. R. Elliott, J. Non-Cryst. Solids 355, 1824 (2009).
[CrossRef]

E. P. J. Parrott, J. A. Zeitler, J. McGregor, S.-P. Oei, H. E. Unalan, S.-C. Tan, W. I. Milne, J.-P. Tessonnier, R. Schlögl, and L. F. Gladden, J. Phys. Chem. C 113, 10554 (2009).
[CrossRef]

Pepper, M.

E. P. J. Parrott, J. A. Zeitler, T. Friščić, M. Pepper, W. Jones, G. M. Day, and L. F. Gladden, Cryst. Growth Des. 9, 1452 (2009).
[CrossRef]

Y. C. Shen, P. F. Taday, and M. Pepper, Appl. Phys. Lett. 92, 051103 (2008).
[CrossRef]

J. A. Zeitler, P. F. Taday, D. A. Newnham, M. Pepper, K. C. Gordon, and T. Rades, J. Pharm. Pharmacol. 59, 209 (2007).
[CrossRef] [PubMed]

Pupeza, I.

R. Wilk, I. Pupeza, R. Cernat, and M. Koch, IEEE J. Sel. Top. Quantum Electron. 14, 392 (2008).
[CrossRef]

Rades, T.

J. A. Zeitler, P. F. Taday, D. A. Newnham, M. Pepper, K. C. Gordon, and T. Rades, J. Pharm. Pharmacol. 59, 209 (2007).
[CrossRef] [PubMed]

Roitberg, A.

A. Markelz, A. Roitberg, and E. J. Heilweil, Chem. Phys. Lett. 320, 42 (2000).
[CrossRef]

Schlögl, R.

E. P. J. Parrott, J. A. Zeitler, J. McGregor, S.-P. Oei, H. E. Unalan, S.-C. Tan, W. I. Milne, J.-P. Tessonnier, R. Schlögl, and L. F. Gladden, J. Phys. Chem. C 113, 10554 (2009).
[CrossRef]

Shen, Y. C.

Y. C. Shen, P. F. Taday, and M. Pepper, Appl. Phys. Lett. 92, 051103 (2008).
[CrossRef]

Taday, P. F.

Y. C. Shen, P. F. Taday, and M. Pepper, Appl. Phys. Lett. 92, 051103 (2008).
[CrossRef]

J. A. Zeitler, P. F. Taday, D. A. Newnham, M. Pepper, K. C. Gordon, and T. Rades, J. Pharm. Pharmacol. 59, 209 (2007).
[CrossRef] [PubMed]

Tan, S.-C.

E. P. J. Parrott, J. A. Zeitler, J. McGregor, S.-P. Oei, H. E. Unalan, S.-C. Tan, W. I. Milne, J.-P. Tessonnier, R. Schlögl, and L. F. Gladden, J. Phys. Chem. C 113, 10554 (2009).
[CrossRef]

Taraskin, S. N.

E. P. J. Parrott, J. A. Zeitler, L. F. Gladden, S. N. Taraskin, and S. R. Elliott, J. Non-Cryst. Solids 355, 1824 (2009).
[CrossRef]

Tessonnier, J.-P.

E. P. J. Parrott, J. A. Zeitler, J. McGregor, S.-P. Oei, H. E. Unalan, S.-C. Tan, W. I. Milne, J.-P. Tessonnier, R. Schlögl, and L. F. Gladden, J. Phys. Chem. C 113, 10554 (2009).
[CrossRef]

Unalan, H. E.

E. P. J. Parrott, J. A. Zeitler, J. McGregor, S.-P. Oei, H. E. Unalan, S.-C. Tan, W. I. Milne, J.-P. Tessonnier, R. Schlögl, and L. F. Gladden, J. Phys. Chem. C 113, 10554 (2009).
[CrossRef]

Walther, M.

M. Franz, B. M. Fischer, and M. Walther, Appl. Phys. Lett. 92, 021107 (2008).
[CrossRef]

B. M. Fischer, M. Walther, and P. U. Jepsen, Phys. Med. Biol. 47, 3807 (2002).
[CrossRef] [PubMed]

Wilk, R.

R. Wilk, I. Pupeza, R. Cernat, and M. Koch, IEEE J. Sel. Top. Quantum Electron. 14, 392 (2008).
[CrossRef]

Zeitler, J. A.

E. P. J. Parrott, J. A. Zeitler, L. F. Gladden, S. N. Taraskin, and S. R. Elliott, J. Non-Cryst. Solids 355, 1824 (2009).
[CrossRef]

E. P. J. Parrott, J. A. Zeitler, J. McGregor, S.-P. Oei, H. E. Unalan, S.-C. Tan, W. I. Milne, J.-P. Tessonnier, R. Schlögl, and L. F. Gladden, J. Phys. Chem. C 113, 10554 (2009).
[CrossRef]

E. P. J. Parrott, J. A. Zeitler, T. Friščić, M. Pepper, W. Jones, G. M. Day, and L. F. Gladden, Cryst. Growth Des. 9, 1452 (2009).
[CrossRef]

J. A. Zeitler and L. F. Gladden, Eur. J. Pharm. Biopharm. 71, 2 (2009).
[CrossRef]

J. A. Zeitler, P. F. Taday, D. A. Newnham, M. Pepper, K. C. Gordon, and T. Rades, J. Pharm. Pharmacol. 59, 209 (2007).
[CrossRef] [PubMed]

Appl. Phys. Lett. (2)

Y. C. Shen, P. F. Taday, and M. Pepper, Appl. Phys. Lett. 92, 051103 (2008).
[CrossRef]

M. Franz, B. M. Fischer, and M. Walther, Appl. Phys. Lett. 92, 021107 (2008).
[CrossRef]

Chem. Phys. Lett. (1)

A. Markelz, A. Roitberg, and E. J. Heilweil, Chem. Phys. Lett. 320, 42 (2000).
[CrossRef]

Cryst. Growth Des. (1)

E. P. J. Parrott, J. A. Zeitler, T. Friščić, M. Pepper, W. Jones, G. M. Day, and L. F. Gladden, Cryst. Growth Des. 9, 1452 (2009).
[CrossRef]

Eur. J. Pharm. Biopharm. (1)

J. A. Zeitler and L. F. Gladden, Eur. J. Pharm. Biopharm. 71, 2 (2009).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

R. Wilk, I. Pupeza, R. Cernat, and M. Koch, IEEE J. Sel. Top. Quantum Electron. 14, 392 (2008).
[CrossRef]

J. Non-Cryst. Solids (1)

E. P. J. Parrott, J. A. Zeitler, L. F. Gladden, S. N. Taraskin, and S. R. Elliott, J. Non-Cryst. Solids 355, 1824 (2009).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Pharm. Pharmacol. (1)

J. A. Zeitler, P. F. Taday, D. A. Newnham, M. Pepper, K. C. Gordon, and T. Rades, J. Pharm. Pharmacol. 59, 209 (2007).
[CrossRef] [PubMed]

J. Phys. Chem. C (1)

E. P. J. Parrott, J. A. Zeitler, J. McGregor, S.-P. Oei, H. E. Unalan, S.-C. Tan, W. I. Milne, J.-P. Tessonnier, R. Schlögl, and L. F. Gladden, J. Phys. Chem. C 113, 10554 (2009).
[CrossRef]

Opt. Lett. (1)

Philos. Trans. R. Soc. London Ser. A (1)

J. C. Maxwell-Garnett, Philos. Trans. R. Soc. London Ser. A 203, 385 (1904).
[CrossRef]

Phys. Med. Biol. (1)

B. M. Fischer, M. Walther, and P. U. Jepsen, Phys. Med. Biol. 47, 3807 (2002).
[CrossRef] [PubMed]

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Figures (2)

Fig. 1
Fig. 1

(a) α and (b) n calculated by using the BL technique and MG1 and MG2 model techniques. The error bars for each technique represent the standard deviation of the values observed among the 21 different measurements.

Fig. 2
Fig. 2

Evolution of the absorption coefficient for the peak at 0.56 THz . The horizontal lines at 40 cm 1 and 47.5 cm 1 correspond to α extracted by using the BL technique and the MG1 model for the pure lactose pellet. The shaded regions represent the measured standard deviation in these values.

Equations (2)

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ε eff ε PE ε eff + 2 ε PE = f ε lac ε PE ε lac + 2 ε PE + g ε air ε PE ε air + 2 ε PE ,
f = m lac ρ lac ( m lac ρ lac ) + ( m PE ρ PE ) .

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