Absorptionsensitive diffuse reflection imaging of concealed powders using a terahertz quantum cascade laser.
ABSTRACT We report diffuse reflection imaging in air of concealed powdered samples using a terahertz quantum cascade laser. The sensitivity of the detection scheme to subsurface absorption within samples is confirmed using fullycharacterized powdered admixtures of polystyrene and polymethyl methacrylate (PMMA). Measurements of the backscattering intensity from these samples are then used in conjunction with KubelkaMunk scattering theory, as well as several models based on the quasicrystalline approximation, to extract the absorption coefficient of PMMA. Our research demonstrates the feasibility of highresolution frequencydomain terahertz imaging for the detection and identification of concealed powders in a reflection geometry.
 Citations (0)
 Cited In (12)

Conference Paper: Fast active THz camera with range detection by frequency modulation
[Show abstract] [Hide abstract]
ABSTRACT: We report on the realization of an active fully electronic THz camera operating at 645 GHz and room temperature. It currently acquires images with about 9000 pixels in 10 seconds. Each pixel contains the amplitude as well as the phase information of the reflected THz signal. Frequency modulation allows to select a specific working distance and to suppress spurious reflections. The typical image size is in the order of hundreds of cm<sup>2</sup>.Infrared, Millimeter and Terahertz Waves, 2008. IRMMWTHz 2008. 33rd International Conference on; 10/2008  SourceAvailable from: Edmund Harold Linfield[Show abstract] [Hide abstract]
ABSTRACT: We report terahertz (THz) diffuse reflectance measurements of bulk powdered samples at a frequency of 2.83 THz using a narrowband quantum cascade laser. Samples studied comprise polydisperse powders with absorption coefficients extending over two orders of magnitude from ∼3 cm(1) to >200 cm(1). Diffuse reflectance measurements are used to obtain the effective absorption coefficient of these samples from the backscattering crosssection, predicted under the quasicrystalline approximation (QCA) in the Tmatrix formulation and in conjunction with the PercusYevick pair distribution function. Results are compared with effective absorption coefficients obtained from THz timedomain spectroscopy measurements on pressed pellet samples, and show good agreement over the range of effective absorption coefficients studied. We observe that the backscattering crosssection predicted under the QCA is strongly dependent on both the real and imaginary components of the complex permittivity of the sample, and we show that reliable determination of the absorption coefficient from diffuse reflectance measurements therefore requires knowledge of the sample's refractive index. This work demonstrates the applicability of diffuse reflectance measurements, using a THz frequency quantum cascade laser, to the highresolution spectroscopic analysis of bulk powdered samples at THz frequencies.The Journal of Chemical Physics 04/2011; 134(13):134304. · 3.12 Impact Factor  Aleksandar D Rakić, Thomas Taimre, Karl Bertling, Yah Leng Lim, Paul Dean, Dragan Indjin, Zoran Ikonić, Paul Harrison, Alexander Valavanis, Suraj P Khanna, Mohammad Lachab, Stephen J Wilson, Edmund H Linfield, A Giles Davies[Show abstract] [Hide abstract]
ABSTRACT: The terahertz (THz) frequency quantum cascade laser (QCL) is a compact source of highpower radiation with a narrow intrinsic linewidth. As such, THz QCLs are extremely promising sources for applications including highresolution spectroscopy, heterodyne detection, and coherent imaging. We exploit the remarkable phasestability of THz QCLs to create a coherent sweptfrequency delayed selfhomodyning method for both imaging and materials analysis, using laser feedback interferometry. Using our scheme we obtain amplitudelike and phaselike images with minimal signal processing. We determine the physical relationship between the operating parameters of the laser under feedback and the complex refractive index of the target and demonstrate that this coherent detection method enables extraction of complex refractive indices with high accuracy. This establishes an ultimately compact and easytoimplement THz imaging and materials analysis system, in which the local oscillator, mixer, and detector are all combined into a single laser.Optics Express 09/2013; 21(19):2219422205. · 3.55 Impact Factor
Page 1
Absorptionsensitive diffuse reflection imaging of
concealed powders using a terahertz quantum
cascade laser
Paul Dean,1* Muhammad U. Shaukat,1 Suraj P. Khanna,1 Subhasish Chakraborty,2
Mohammad Lachab,1 Andrew Burnett,1 Giles Davies1 and Edmund H. Linfield1
1School of Electronic and Electrical Engineering, University of Leeds, Leeds, LS2 9JT, UK
2School of Electrical and Electronic Engineering, University of Manchester, Manchester, M60 1QD, UK
*Corresponding author: p.dean@leeds.ac.uk
Abstract: We report diffuse reflection imaging in air of concealed
powdered samples using a terahertz quantum cascade laser. The sensitivity
of the detection scheme to subsurface absorption within samples is
confirmed using fullycharacterized powdered admixtures of polystyrene
and polymethyl methacrylate (PMMA). Measurements of the
backscattering intensity from these samples are then used in conjunction
with KubelkaMunk scattering theory, as well as several models based on
the quasicrystalline approximation, to extract the absorption coefficient of
PMMA. Our research demonstrates the feasibility of highresolution
frequencydomain terahertz imaging for the detection and identification of
concealed powders in a reflection geometry.
©2008 Optical Society of America
OCIS codes: (110.6795) Terahertz imaging; (140.5965) Semiconductor lasers, quantum cascade
(280.1350) Backscattering; (300.1030) Absorption
References and links
1.
2.
3.
B. B. Hu and M. C. Nuss, “Imaging with THz waves,” Opt. Lett. 20, 17161718 (1995).
D. Mittleman, Sensing with THz Radiation (Springer, Berlin, 2003).
K. Kawase, Y. Ogawa, Y. Watanabe, and H. Inoue, “Nondestructive terahertz imaging of illicit drugs
using spectral fingerprints,” Opt.
http://www.opticsinfobase.org/abstract.cfm?URI=oe11202549.
Y. C. Shen, T. Lo, P. F. Taday, B. E. Cole, R. Tribe, and M. C. Kemp, “Detection and identification of
explosives using THz pulsed spectroscopic imaging,” Appl. Phys. Lett. 86, 241116241118 (2005).
D. J. Cook, B. K. Decker, G. Dadusc, and M. G. Allen, “Through container THz sensing: applications for
bio detection,” in Int. Soc. Opt. Eng. Proc. SPIE 5268, 3642 (2004).
V. P. Wallace, R. M. Woodward, A. J. Fitzgerald, E. Pickwell, R. J. Pye, and D. D. Arnone, “Terahertz
pulsed imaging of basal cell carcinoma ex vivo and in vivo,” Br. J. Dermatol. 151, 424432 (2004).
S. M. Kim, F. Hatami, J. S. Harris, A. W. Kurian, J. Ford, D. King, G. Scalari, M. Giovannini, N. Hoyler,
J. Faist, and G. Harris, “Biomedical terahertz imaging with a quantum cascade laser,” Appl. Phys. Lett. 88,
153903153905 (2006).
E. Pickwell, B. E. Cole, A. J. Fitzgerald, and V. P. Wallace, “Simulation of terahertz pulse propagation in
biological systems,” Appl. Phys. Lett. 84, 21902192 (2004).
J. Chen, Y. Chen, H. Zhao, G. J. Bastiaans, and X.C. Zhang, “Absorption coefficients of selected
explosives and related compounds in the range of 0.12.8 THz,” Opt. Express 15, 1206012067 (2007),
http://www.opticsinfobase.org/abstract.cfm?URI=oe151912060.
10. A. Burnett, W. Fan, P. Upadhya, J. Cunningham, E. H. Linfield, A. G. Davies, H. Edwards, T. Munshi, and
A. O’Neil, “Analysis of drugs of abuse and explosives using terahertz timedomain and Raman
spectroscopy,” Int. Soc. Opt. Eng. Proc. SPIE 6549, 61200 (2007).
11. A. J. Fitzgerald, E. Berry, N. N. Zinovev, G. C. Walker, M. A. Smith, and J. M. Chamberlain, “An
introduction to medical imaging with coherent terahertz frequency radiation,” Phys. Med. Biol. 47, R6784
(2002).
12. T. KleineOstmann, P. Knobloch, M. Koch, S. Hoffman, M. Breede, M. Hofmann, G. Hein, K. Pierz,
M. Sperling, and K. Donhuijsen, “Continuouswave THz imaging,“ Electron. Lett. 37, 14611463 (2001).
13. A. Dobroiu, M. Yamashita, Y. N. Oshima, Y. Morita, C. Otani, and K. Kawase, “Terahertz imaging system
based on a backwardwave oscillator,” Appl. Opt. 43, 56375646 (2004).
Express
11, 25492554 (2003),
4.
5.
6.
7.
8.
9.
#92353  $15.00 USD
(C) 2008 OSA
Received 1 Feb 2008; revised 5 Mar 2008; accepted 5 Mar 2008; published 14 Apr 2008
28 April 2008 / Vol. 16, No. 9 / OPTICS EXPRESS 5997
Page 2
14. Y. Watanabe, K. Kawase, T. Ikari, H. Ito, Y. Ishikawa, and H. Minamide, “Component spatial pattern
analysis of chemicals using terahertz spectroscopic imaging,” Appl. Phys. Lett. 83, 800802 (2003).
15. B. Williams, S. Kumar, Q. Hu, and J. L. Reno, “Highpower quantum cascade lasers,” Electron. Lett. 42,
8990 (2006).
16. A. W. M. Lee, Q. Qin, S. Kumar, B. S. Williams, Q. Hu, and J. L. Reno, “Realtime terahertz imaging over
a standoff distance (>25 meters),” Appl. Phys. Lett. 89, 141125141127 (2006).
17. A. W. M. Lee and Q. Hu, “Realtime, continuouswave terahertz imaging by use of a microbolometer focal
plane array,” Opt. Lett. 30, 25632565 (2005).
18. M. A. Belkin, J. A. Fan, S. Hormoz, F. Capasso, S. P. Khanna, M. Lachab, A. G. Davies, and E. H.
Linfield, “Terahertz quantum cascade lasers with copper metalmetal waveguides operating up to 178 K,”
Opt. Express 16, 32423248 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe1653242.
19. HB. Liu, Y. Chen, G. J. Bastiaans, and X.C. Zhang, “Detection and identification of explosive RDX by
THz diffuse reflection spectroscopy,”
http://www.opticsinfobase.org/abstract.cfm?URI=oe141415.
20. J. Pearce and D. M. Mittleman, “Propagation of singlecycle terahertz pulses in random media,” Opt.
Lett. 26, 20022004 (2001).
21. J. Pearce, Z. Jian, and D. M. Mittleman, “Statistics of multiply scattered broadband terahertz pulses,” Phys.
Rev. Lett. 91, 04390314 (2003).
22. S. Barbieri, J. Alton, H. E. Beere, J. Fowler, E. H. Linfield, and D. A. Ritchie, “2.9 THz quantum cascade
laser operating at 70 K in continuous wave,” Appl. Phys. Lett. 85, 16741676 (2004).
23. M. Naftaly, A. Malcoci, and H. Eisele, “A sensitive broadband detector for roomtemperature operation of
a simple terahertz Fouriertransform spectrometer,” The Joint 31st International Conference on Infrared and
Millimeter Waves and 14th International Conference on Terahertz Electronics, p.35 (2006).
24. K. L. Nguyen, M. L. Johns, L. F. Gladden, C. H. Worrall, P. Alexander, H. E. Beere, M. Pepper,
D. A. Ritchie, J. Alton, S. Barbieri, and E. H. Linfield, “Threedimensional imaging with a terahertz
quantum cascade laser,” Opt.
http://www.opticsinfobase.org/abstract.cfm?URI=oe1462123.
25. S. Barbieri, J. Alton, C. Baker, T. Lo, H. E. Beere, and D. Ritchie, “Imaging with THz quantum cascade
lasers using a Schottky diode mixer,”
http://www.opticsinfobase.org/abstract.cfm?URI=oe13176497.
26. J. Coltman, “The specification of imaging properties by response to a sine wave input,” J. Opt. Soc.
Am. 46, 46872 (1954).
27. J. R. Birch, “The farinfrared optical constants of polypropylene, PTFE and polystyrene,” Infrared Phys. 33,
3338 (1992).
28. L. Tsang, J. A. Kong, and R. T. Shin, Theory of Microwave Remote Sensing (New York, Wiley, 1985)
29. G. Kortum, Reflectance Spectroscopy (Springer, Berlin, 1969).
30. P. Kubelka and F. Munk, “Ein beitrag zur optic der fabanstriche,” Z. Tech. Physik 12, 593601 (1931).
31. J. D. Lindberg, R. E. Douglass, and D. M. Garvey, “Absorptioncoefficientdetermination method for
particulate materials,” Appl. Opt. 33, 43144319 (1994).
32. J. D. Lindberg, “Absolute diffuse reflectance from relative reflectance measurements,” Appl. Opt. 26,
29002905 (1987).
33. L. L. Foldy, “The multiple scattering of waves. I. General theory of isotropic scattering by randomly
distributed scatterers” Phys. Rev. 67, 107119 (1945).
34. M. Lax, “Multiple scattering of waves. II. The effective field in dense systems,” Phys. Rev. 85, 621629
(1952).
35. M. S. Wertheim, “Exact solution of the PercusYevick integral equation for hard spheres,” Phys. Rev.
Lett. 10, 321323 (1963).
36. L. Tsang and J. A. Kong, “Scattering of electromagnetic waves from a half space of densely distributed
dielectric scatterers,” Radio Science 18, 12601272 (1963).
37. P. R. Siqueira and K. Sarabandi, “Method of moments evaluation of the twodimensional quasicrystalline
approximation,” IEEE Trans. Antenn. Prop. 44, 10671077 (1996).
Opt. Express
14, 415423 (2006),
Express
14, 21232129 (2006),
Opt. Express
13, 64976503 (2005),
1. Introduction
Over recent years there has been a great deal of interest in terahertz (THz) imaging
applications, particularly in the fields of nondestructive inspection, security screening and
biomedicine [18]. The suitability of THz radiation to such applications stems primarily from
the transparency of many nonpolar materials at THz frequencies. THz radiation is also
sensitive to absorption arising from molecularlyspecific vibrational modes in a wide range of
organic and inorganic chemicals including explosives and drugsofabuse [9,10]. THz
#92353  $15.00 USD
(C) 2008 OSA
Received 1 Feb 2008; revised 5 Mar 2008; accepted 5 Mar 2008; published 14 Apr 2008
28 April 2008 / Vol. 16, No. 9 / OPTICS EXPRESS 5998
Page 3
imaging is therefore particularly wellsuited to chemical fingerprinting and sensing
applications.
A range of THz imaging systems have been previously reported [18]. Many of these
employ broadband photoconductive sources alongside timedomain detection, enabling
frequencydependent imaging over a broad spectrum [11]. However, systems of this type
suffer from low THz powers (∼10100 μW) as well as the reliance on an expensive ultrafast
nearinfrared/visible laser source. Incoherent imaging using a narrowband tuneable source
has also been demonstrated [1213] and applied to component spatial pattern analysis of
chemical mixtures [3,14]. Whilst such systems offer potential for chemical sensing
applications, in addition to the practical advantage of not requiring optical gating of the
detector, performance is again limited by only moderate THz powers and the limited
availability of widelytuneable sources. Conversely, terahertz quantum cascade lasers (QCLs)
deliver high output powers, which can exceed 100 mW in continuouswave operation [15].
Standoff imaging over a distance of 25 m has been previously reported using such sources
[16], as has realtime imaging through use of a microbolometer array [17]. To date, emission
frequencies range from 1.2 to 5.0 THz and operating temperatures as high as 178 K have been
achieved [18]. Their narrowband emission and tunability also indicate that these sources offer
great potential for the development of fast spectroscopic standoff imaging systems with high
sensitivity and chemical specificity.
Owing to the relative practical simplicity, the majority of THz imaging systems reported
to date employ a transmission geometry. However, this geometry is only applicable when the
sample under investigation is suitably thin and exhibits low absorption at THz frequencies. In
order to perform imaging of bulky or highlyabsorbing samples, one is restricted to a
reflective geometry in which radiation reflected or backscattered from the sample is detected.
For standoff imaging, however, the exact alignment required for collection of specular
reflections cannot be guaranteed in practice. A practical standoff imaging system should
therefore monitor diffuse radiation returning from the sample. Diffuse imaging also enables
the detection of samples contained within packaging that would adversely affect
measurements in a specular geometry, as well as samples from which there is a strong
component of subsurface scattered radiation such as powders. Sensitivity to such radiation is
essential for spectroscopic identification of materials when a narrowband source and
incoherent detection are employed. A diffuse sensing scheme is thus highly applicable for
drug and explosivefingerprinting applications using THz QCLs.
In this paper we report diffuse reflection imaging in air using a QCL at 2.8 THz. The
detection of concealed powdered samples is demonstrated, including the detection of powders
concealed within a container from which there is a strong specular reflection. The sensitivity
of the detection scheme to subsurface absorption of radiation is confirmed using fully
characterized admixtures of polystyrene and polymethyl methacrylate (PMMA) powders.
These measurements are then used to assess the suitability of KubelkaMunk theory, and a
number of backscattering theories based on the quasicrystalline approximation (QCA), to
describe diffuse reflection from absorbing samples at THz frequencies. In particular, these
theories are used to extract the absorption coefficient of PMMA and these predictions are
compared with measurements obtained using THz timedomain spectroscopy (TDS). To the
best of our knowledge, this work represents the first demonstration of absorptionsensitive
reflection imaging using a THz QCL. Our investigation also demonstrates the applicability of
frequencydomain THz imaging to the detection and identification of concealed powdered
materials such as drugs and explosives.
2. Background
The interaction between radiation and bulk powdered samples can be described in terms of
three mechanisms: directional specular reflection from powder surfaces, nondirectional
‘diffuse Fresnel reflection’ from rough sample surfaces [19], and subsurface scattering and
absorption of radiation by the powdered medium. The relative strengths of these mechanisms
depend on the degree of surface roughness, the complex refractive index of the material, as
#92353  $15.00 USD
(C) 2008 OSA
Received 1 Feb 2008; revised 5 Mar 2008; accepted 5 Mar 2008; published 14 Apr 2008
28 April 2008 / Vol. 16, No. 9 / OPTICS EXPRESS 5999
Page 4
well as the mean particle size of the powder. For smooth samples (rootmeansquare surface
roughness much smaller than the radiation wavelength λ), the specular reflection at the air
powder interface is strongly directional and can be discriminated against with the use of off
axis collection optics. For larger particle sizes, this reflection becomes increasingly non
directional owing to reflections from small randomly orientated mirrorlike microfacets on
the sample surface. For both rough and smooth surfaces, a portion of the incident radiation
penetrates beneath the surface of the sample where it experiences both scattering and
absorption by the particles of the medium. Scattering is strongest when the particle size is
comparable to the radiation wavelength whereas the degree of absorption is dictated by the
wavelengthdependent complex refractive index of the material. Terahertz propagation in the
presence of multiple scattering has been investigated elsewhere [20,21].
For chemical fingerprinting applications, the measurement scheme should be sensitive to
the absorption coefficient of the material under analysis. When a coherent detection scheme
is used, the imaginary part of the refractive index can be deduced from the diffuse Fresnel
reflections through use of the measured or inferred phase delays [19]. When incoherent
detection is used, only the amplitude of the diffuse Fresnel reflection is measured and this is
only weakly dependent on the imaginary part of the refractive index for most materials. For
chemical fingerprinting applications, incoherent diffuse measurements must therefore make
use of subsurface scattered radiation, the amplitude of which is strongly influenced by
absorption within the sample.
3. Terahertz imaging system
3.1 Experimental setup
Figure 1 shows a schematic diagram of the imaging apparatus used for this work. The laser
was a 2.5mmlong boundtocontinuum QCL emitting at 2.8 THz [22], which was cooled to
∼5 K in a closedcycle pulse tube refrigerator. Radiation from the QCL was collimated with
an f/1.7 parabolic reflector and focused onto the sample at a 30° angle of incidence using an
f/4.3 reflector. The focal length of this reflector provided a working distance of 33 cm. A
second f/4.3 parabolic was used to collect specular reflections from the sample surface, which
were coupled onto a room temperature Murata pyroelectric sensor [23] (D1). Diffusely
scattered and nondirectional reflected radiation was collected using a 90° f/2 parabolic
reflector and coupled into a heliumcooled silicon bolometer (D2). The offaxis configuration
of this reflector ensured that no direct specular reflection was collected. Our system thus
permits simultaneous detection of both scattered and specularly reflected THz radiation.
Whilst a cryogenicallycooled detector was used in this system, we note that a usable
detection sensitivity could be achieved using a roomtemperature Golay cell [24] or Schottky
diode mixer [25].
Current pulses were supplied to the QCL at a frequency of 50 kHz and a duty cycle of
40%. These pulses were electronically modulated at a frequency of 160 Hz with lockin
detection being employed to improve the detection sensitivity. This lockin modulation
frequency was selected to allow simultaneous lockin detection from both detectors.
Measurements indicate that the signaltonoise ratio of the pyroelectric sensor is optimised at
∼20 Hz whereas that of the bolometer is optimised at ∼200 Hz. Both detectors are therefore
operated in a nonoptimised regime. Under normal operation both detectors were susceptible
to noise induced by the highfrequency current pulses driving the QCL. This noise source
was reduced, with only a small sacrifice in output power, by use of a 5pole lowpass filter
with a 1 MHz 3dB point on the output of the current source. Under the conditions described.
the peak power incident on the sample is estimated to be ∼1 mW. For image acquisition, the
sample was mounted on a twoaxis translation stage that was raster scanned with a 250μm
stepsize. No purging of the system was used.
#92353  $15.00 USD
(C) 2008 OSA
Received 1 Feb 2008; revised 5 Mar 2008; accepted 5 Mar 2008; published 14 Apr 2008
28 April 2008 / Vol. 16, No. 9 / OPTICS EXPRESS 6000
Page 5
Fig. 1. Experimental apparatus for simultaneous specular (red) and diffuse (blue) imaging using
a THzfrequency quantum cascade laser (QCL). D1 – roomtemperature pyroelectric sensor;
D2 – heliumcooled silicon bolometer.
3.2 System resolution
The spatial resolution of the system was analysed using a series of goldonglass resolution
targets. With the resolution target positioned in the object plane of the system, line profiles
were recorded for both horizontal and vertical orientations using a 10μm stepsize. For each
line scan the squarewave modulation depth was measured and the Coltman expansion [26]
applied to deduce the sinusoidal modulation depth. The modulation transfer function (MTF)
was then obtained by normalising to the modulation for an infiniteperiod sinusoidal target.
Figure 2 shows the horizontal and vertical MTFs measured for our system. Defining the
resolution limit at the 20% modulation threshold indicates spatial resolutions equal to 350 μm
and 305 μm along horizontal and vertical directions, respectively. These values are consistent
with a circularly symmetric beam projected onto the sample plane at an incidence angle of
30°.
Fig. 2. Measurement of the modulation transfer function (MTF) of the imaging setup using
vertically (blue) and horizontally (red) oriented targets. The lines are intended only to guide
the eye. The 20% modulation threshold indicates spatial resolutions equal to 350 μm and
305 μm respectively.
QCL
D1
D2
Sample
#92353  $15.00 USD
(C) 2008 OSA
Received 1 Feb 2008; revised 5 Mar 2008; accepted 5 Mar 2008; published 14 Apr 2008
28 April 2008 / Vol. 16, No. 9 / OPTICS EXPRESS 6001
Page 6
4. Results
4.1 Diffuse imaging of concealed powders
The detection of powdered samples using a diffuse imaging scheme was initially
demonstrated using 800 mg of loose polyethylene powder contained within a 35 mm x 50 mm
resealable polythene bag. Figure 3 shows a THz image of this sample concealed behind a
fibrous HDPE FedEx® envelope and taken with a 250μm stepsize. As can be seen, the
powder is clearly imaged and the obscuring layer has little effect other than a weak
contribution arising from reflections off its surface. The regions of high intensity are specular
highlights arising from creases in the front surface of the polythene bag.
Fig. 3. Diffuse image of polyethylene powder enclosed inside a polythene bag and concealed
behind a HDPE FedEx® envelope, taken with a 250μm pixel size.
The image acquisition time for this 180 x 108 pixel image was 27 minutes (∼12 pixels per
second (pps)), which is limited by the ∼75 ms traveling time for the translation stage used in
this measurement. For comparison, the signal averaging time and computer processing time
amounted to ∼6 ms per pixel. The peak THz power coupled into the detector after scattering
from this lowabsorbing sample was estimated to be ~1 μW. This provides a measurement
dynamic range of 20 dB at this maximum imaging rate. We note that greater dynamic ranges
can be achieved at the expense of imaging speed with longer timeaveraging of each pixel.
For example, at 5 pps the dynamic range was measured to be 30 dB.
4.2 Absorptionsensitive imaging of powders
The sensitivity of our system to absorption within powdered samples was demonstrated using
polystyrene and PMMA as model compounds. Polystyrene is known to exhibit low
absorption at THz frequencies [27] whereas PMMA is strongly absorbing. Powders were
selected that had wellcharacterised and closely matched particle sizes; the polystyrene and
PMMA had manufacturerspecified particle sizes of 6.06 ± 0.08 μm and 5.4 ± 0.5 μm,
respectively. Nine sample admixtures were prepared with mass fractions ranging from 0 to 1
in equal steps of 0.125. These were then loosely packed inside a sample holder comprising a
polystyrene box divided into separate compartments, each measuring approximately 10 mm x
10 mm x 10 mm, with a removable polystyrene lid (see Fig. 4(a)); the dimensions of each
powder sample measured approximately 9 mm x 9 mm x 9 mm. Measurements of the volume
filling fraction indicate a value of 0.4 for these uncompressed powders.
Figure 4(b) shows the specular image of this sample taken with a 250μm pixel size. As
can be seen, the image is dominated by strong reflections off the surface of the lid and the
powders cannot be resolved. The corresponding diffuse image is shown in Fig. 4(c). In this
case, there is a negligible contribution from specular reflections and the powders are clearly
imaged. In addition, there is a strong correlation between the image intensity and the fraction
10 mm
#92353  $15.00 USD
(C) 2008 OSA
Received 1 Feb 2008; revised 5 Mar 2008; accepted 5 Mar 2008; published 14 Apr 2008
28 April 2008 / Vol. 16, No. 9 / OPTICS EXPRESS 6002
Page 7
of strongly absorbing material. This correlation is investigated in more detail in Sec. 5. The
peak powers measured at the detectors D1 and D2 were ∼15 μW and ∼400 nW, respectively, in
the case of the lowest absorbing samples.
The image intensity for each powder admixture was measured by sampling over a
5 mm x 5 mm (20 x 20 pixels) region in the centre of each compartment in order to reduce the
effects of laser speckle and structural variation. Five independent sets of measurements were
performed and averaged to yield the reflectivity for each sample, measured relative to a PTFE
powder reference. Measurements performed on pressed pellets using TDS [10] reveal that the
refractive index of the two materials is almost identical at 2.8 THz; 1.42 ± 0.02 for
polystyrene and 1.38 ± 0.02 in the case of PMMA. By virtue of this and the closely matched
particle sizes, the scattering meanfreepath and angular distribution within these nine samples
are expected to be almost identical. Furthermore, the small particle sizes used here ensure a
small contribution to the collected radiation from diffuse surface reflections. The observed
differences in the measured image intensities for the nine mixture compositions can therefore
be solely attributed to different degrees of absorption within these samples.
(c)
Fig. 4. (a) Photograph of the sample holder (lid removed) loaded with powder admixtures.
The % mass of PMMA is shown for each admixture. (b) Specular THz image of the sample
shown in (a). (c) Diffuse THz image of the sample shown in (a). The nonuniform intensity
distributions observed here are attributed to the presence of diffuse surface reflections and
scattering from microcavities formed within the samples. Such effects are averagedout with
repeated measurements. All three images are displayed on the same scale. The THz images
have a pixel size of 250 μm.
(a)
(b)
10 mm
0 % 25.0 % 12.5 %
37.5 %
62.5 %
50.0 %
75.0 %
100 %
87.5 %
#92353  $15.00 USD
(C) 2008 OSA
Received 1 Feb 2008; revised 5 Mar 2008; accepted 5 Mar 2008; published 14 Apr 2008
28 April 2008 / Vol. 16, No. 9 / OPTICS EXPRESS 6003
Page 8
5. Analysis
5.1 KubelkaMunk theory
A number of theoretical models have been developed for describing the backscattering of
radiation from a dense medium of randomly distributed dielectric particles [28,29]. The most
commonly applied of these is KubelkaMunk (KM) theory owing to the simplicity of its
formulism [30]. This model is derived from the radiative transport equation and describes the
propagation of a uniform, diffuse irradiance through a onedimensional semiinfinite isotropic
slab.
KM theory relates the diffuse reflectivity R∞ of an infinitely thick absorbing sample to the
KM absorption coefficient K and scattering coefficient S according to the remission function
(
RF
=
∞
2
()
)
S
K
R
R
=
−
∞
∞
1
2
. (1)
For the admixtures measured in this investigation, the scattering coefficient S is independent
of the mixture composition owing to the matched particle size and matched real refractive
indices of the two powders. Therefore, for the present case, Eq. (1) can be written as [29]:
()()
α
[]
21
2
1
2
3
α
cc
Sn
RF
−+≈
∞
. (2)
Here K has been expressed in terms of the volume fraction c of species 1 (PMMA), relative to
the total volume fraction of powder, and the Lambert’s law absorption coefficients α1 and α2
of both materials using the approximation
K
index [31].
The remission function F(R∞) is extremely sensitive to changes in reflectivity for small
values of R∞. Care must therefore be taken to ensure correct calculation of R∞ from the
measurement data. In theory, the reference sample should be completely diffusing and non
absorbing  conditions unachievable in practice. However, in the present case we can make
use of the fact that, according to Eq. (2) and assuming α1>>α2,
[29,32]. Here, R∞ has been written in terms of a constant γ to be determined, and the
reflectivity R measured relative to a PTFE reference. By fitting this relationship to the
experimental data, the value of γ can be estimated. The resulting values for R∞, calculated
from the measured values of R and the fitted value of γ using the relation R∞=γR, are shown in
Fig. 5 as a function of the volume fraction of PMMA.
Also shown in Fig. 5 are the corresponding values of the remission function F(R∞). As
expected, we observe a clear linear relationship between F(R∞) and the volume fraction of
PMMA. Figure 5 also shows a fit of this data to Eq. (2), for which a value α2=4 cm1 has been
used, as measured using THz TDS. The intercept of the fitted line predicts a value
S=5±1 cm1 and the slope yields the estimate α1=42±11 cm1 for the absorption coefficient of
PMMA. The uncertainties in these values reflect the distribution of measured image
intensities for each sample as well as the sensitivity of F(R∞) to small changes in R∞.
2
23
n
α≈
, where n is the real refractive
( )
R
γ
()
[]
( )
c
[] 1
≈
ln ln
dFd
#92353  $15.00 USD
(C) 2008 OSA
Received 1 Feb 2008; revised 5 Mar 2008; accepted 5 Mar 2008; published 14 Apr 2008
28 April 2008 / Vol. 16, No. 9 / OPTICS EXPRESS 6004
Page 9
Fig. 5. Measurement of the sample reflectivity R∞ (black, right axis) as a function of volume
fraction of PMMA. The corresponding values of the KubelkaMunk remission function F(R∞)
are also shown (red, left axis). The lines represent fits of the data to Eq. (2), in which the
estimated value of γ=1.6 is used, and S=5±1 cm1 and α1= 42±11 cm1are treated as free
parameters.
5.2 Quasicrystalline approximation
More rigorous scattering models that include the effects of phase coherence have been based
on wave theory and the multiple scattering equations [28]. One of the simplest of these
models describes multiple scattering from isotropic point scatterers and neglects any
correlation between particle positions. This is known as the effective field approximation
(EFA) [33] and is most applicable to low concentrations of scatterers. A higher order
approximation to the EFA that does account for correlated particle positions is the quasi
crystalline approximation (QCA) [34]. For a sparse concentration of scatterers it is reasonable
to assume that the particle positions are independent of each other. Hence, in this limit the
QCA reduces to the EFA. For larger concentrations, the QCA can be used in conjunction
with realistic pair distribution functions such as the PercusYevick (PY) distribution for
spherical particles [35]. A further correction to the QCAPY model is the coherent potential
(QCACP) formulism [28], which more accurately accounts for the effective electrical
permittivity that a wave experiences in a dense medium of particles.
A closedform expression for the backscattering crosssection σ of electromagnetic waves
scattered from a half space of densely distributed dielectric scatterers under the QCA has been
previously reported [28,36]. Derivation of this expression assumes a polarized plane wave
obliquely incident on the scattering medium, and is valid only in the lowfrequency limit
(λ >> particle size) and under the distorted Born approximation. In our case we use an
incident angle of 30° and take the backscattered power to be proportional to σ for this
geometry. The absorption coefficient of polystyrene is again taken to be 4 cm1.
Figure 6 show fits of the measured image intensities, cast in terms of the backscattering
crosssection, as a function of volume fraction of PMMA under the EFA, QCAPY and
QCACP. The magnitude of σ is significantly larger in the case of the EFA, which is to be
expected owing to the assumption of uncorrelated particle positions. Nevertheless, it can be
seen that the EFA, QCAPY and QCACP all predict a similar functional dependence of σ on
the volume fraction of PMMA. The values of α1 obtained from these fits are 19.7±2.3 cm1,
18.1±2.1 cm1 and 17.9±1.9 cm1, respectively. For comparison, measurements performed on
pressed pellets using THz TDS predict a value α1=41 cm1 at the QCL radiation wavelength.
#92353  $15.00 USD
(C) 2008 OSA
Received 1 Feb 2008; revised 5 Mar 2008; accepted 5 Mar 2008; published 14 Apr 2008
28 April 2008 / Vol. 16, No. 9 / OPTICS EXPRESS 6005
Page 10
Hence, we note that these scattering models consistently underestimate the absorption
coefficient for the experimental conditions employed here.
(a)
Fig. 6. Measurement of the backscattering crosssection as a function of volume fraction of
PMMA under the (a) EFA (black), (b) QCAPY (blue) and QCACP (red; data points not
shown).
6. Discussion
All four of the scattering models evaluated in this paper successfully reproduce the
experimental observation that the diffuse reflectivity decreases for increasing absorption
strength of the sample material. The absorption coefficient obtained from KM theory agrees
well with the value measured using THz TDS. In the case of the QCAbased backscattering
models, the absorption coefficient is underestimated by a factor of ∼2. This difference could
be attributed to the collection of additional diffuse surface reflections from the samples, which
leads to underestimation of the absorption coefficient in the case of the QCAbased models,
but overestimation of both K and S using the KM analysis presented here. This difference
could also indicate the inadequacy of the QCAbased models at larger volume fractions, as
has been reported elsewhere [37].
The consistency between the values of α1 predicted by the three QCAbased models is a
result of the small size parameter (∼0.03) and small relative permittivity of the powdered
samples used. Under these conditions, the implementation of the PY pair distribution function
has the primary effect of uniformly reducing the backscattering crosssections predicted. In
the limit of very small particle size, the effective permittivity calculated under QCAPY
approaches that calculated under EFA. Therefore, in this limit, the two methods yield similar
values of α1. Comparing the QCAPY and QCACP models, their internal consistency can be
explained by the similarity between the effective relative permittivity (∼1.33) used in the latter
model with that of air, which is a consequence of the small permittivity of the powder
materials [28].
It should be noted that measurement of the absolute absorption coefficient of an unknown
powered material would not, in general, be possible using KM theory without prior calibration
of the image intensity using either the method described above or a suitable reflection
standard. For reflection measurements from a single powder, the relationship between K and
S demonstrated by Eq. (1) would then permit only a qualitative assessment of the material
absorption coefficient. This is also true in the case of the QCAbased models since the sample
parameters such as particle size and packing density would not be known in general.
Nevertheless, we note that for chemical fingerprinting applications one is concerned only with
the ratio of image intensities measured from the same sample at two or more known
wavelengths. The analysis presented in Sec. 5 suggests that all four of the models evaluated
would enable a qualitative assessment of wavelengthdependent absorption within samples,
(b)
#92353  $15.00 USD
(C) 2008 OSA
Received 1 Feb 2008; revised 5 Mar 2008; accepted 5 Mar 2008; published 14 Apr 2008
28 April 2008 / Vol. 16, No. 9 / OPTICS EXPRESS 6006
Page 11
and thus provide fingerprint information for sensing applications. With careful selection of
the imaging wavelengths, specific materials could thus be targeted. Since application of the
QCAbased models do not require knowledge of the absolute sample reflectivity, perhaps
these hold greater promise for the analysis of multiwavelength diffuse reflection
measurements. It should be noted, however, that the present analytical formulism of the
QCAbased models is applicable only in the limit λ >> particle size. Further diffuse
measurements on samples with larger particle sizes, as well as implementation of a complete
QCAbased model that does not adopt the lowfrequency approximation, would be required to
assess fully the performance of these models outside this limit.
7. Conclusions
In summary, we have demonstrated diffuse reflection imaging of powdered samples in air
using a terahertz quantum cascade laser. For a weaklyabsorbing polyethylene powder
enclosed inside a plastic bag and concealed behind a HDPE FedEx® envelope, a dynamic
range of ∼20dB was measured at the maximum imaging rate of ∼12 pps, which was limited by
translation of the sample in our apparatus. The sensitivity of the detection scheme to
absorption within samples was confirmed using measurements of the backscattered intensity
for a range of characterized polystyrenePMMA powdered admixtures. These measurements
have been fitted to a number of scattering theories and the absorption coefficient of PMMA
extracted in each case. KubelkaMunk theory yielded a value of 42±11 cm1 whereas theories
based on the quasicrystalline approximation consistently underestimated this value by a
factor ∼2. Measurements obtained using THz TDS yield a value of 41 cm1. These results
confirm that such models could enable qualitative assessment of wavelengthdependent
absorption within powdered samples, sufficient to provide fingerprinting information. Our
research therefore demonstrates the potential of multiwavelength frequencydomain THz
imaging for the detection and identification of materials in a reflection geometry.
Acknowledgements
We acknowledge support from the Research Councils (UK) Basic Technology Programme,
the Engineering and Physical Sciences Research Council (EPSRC, UK), and Her Majesty’s
Government Communication Centre (HMGCC, UK).
#92353  $15.00 USD
(C) 2008 OSA
Received 1 Feb 2008; revised 5 Mar 2008; accepted 5 Mar 2008; published 14 Apr 2008
28 April 2008 / Vol. 16, No. 9 / OPTICS EXPRESS 6007