Optics: measuring and testing – By light interference – Spectroscopy
Reexamination Certificate
2002-06-24
2004-06-08
Font, Frank G. (Department: 2877)
Optics: measuring and testing
By light interference
Spectroscopy
C356S452000, C356S451000, C356S519000, C356S486000
Reexamination Certificate
active
06747742
ABSTRACT:
FIELD OF THE INVENTION
This invention generally relates to absorption spectroscopy and more particularly relates to a micro spectrometer, which provides a profile of the transmission percentage versus wavelength for relatively small volume or low concentration samples.
BACKGROUND
Industry experts agree that the emerging requirements for biological and chemical warfare necessitates a small, portable device capable of detecting trace amounts of various chemicals in air. In some cases, the concentration in air of various biological and chemical reagents of interest may be approximately 0.1 to 10 ppm or less.
Conventionally, chemical detection may be accomplished using absorption spectroscopy. Spectroscopy is used to identify various unknown substances by reading spectroscopic patterns. Absorption spectroscopy relies on the consistent absorption or fluorescence by various compounds at specific wavelengths of light that produce a consistent pattern identifying the substance.
In practice, vibration bands within a molecule selectively absorb wavelengths corresponding to the energy level of the vibration bands. Thus, the absorption spectrum of a chemical compound will typically comprise a series of absorption bands, which are fixed with respect to wavelength and intensity. In practice, each of the absorption bands originates from an interatomic bond within the molecule.
For example,
FIG. 1
depicts a two-atom compound A—B having an absorption spectrum associated with the stretching of the bond A—B. In this example the absorption frequency is given by Eq. 1 as follows:
v
=
(
1
2
π
c
s
)
[
k
f
[
M
A
+
M
B
]
M
A
M
B
]
1
2
Eq
.
(
1
)
where &ngr; is the wavenumber in cm
−1
of the absorption band [&ngr; (cm
−1
)=10
4
/&lgr;, &lgr; is the wavelength, where &ngr; and &lgr; in cm
−1
and &mgr;m, respectively], c
s
, is the velocity of light (approximately 3×10
10
cm/s), M
A
and M
B
are the masses of the two atoms (A and B respectively), and k
f
is the spring constant of the bond. Thus, as the bond stiffness increases, the wavelength of the corresponding absorption band decreases. In general, a molecule with N atoms will comprise 3N-6 normal absorption bands, each with a distinct absorption frequency.
The intensity of the absorption band is governed by a number of factors as provided in Eq. 2:
∫
band
ln
(
I
o
I
)
ⅆ
v
=
A
s
cb
A
s
=
[
8
π
2
N
A
3
ℏ
c
s
]
v
&LeftBracketingBar;
∂
μ
∂
Q
s
&RightBracketingBar;
2
Eq
.
(
2
)
where, I
o
and I are the intensities of the incident and transmitted light, respectively, c is the concentration (moles/liter), b is the path length (cm), h is Planck's constant (approximately 6.63×10
−34
), N
A
is Avogadro's umber (6.23×10
23
) and &mgr; is the dipole moment, where the integration is taken over the entire absorption band and the partial derivative refers to the derivative in normal coordinate space.
Thus, Eq. 2 effectively states that the two non-atomic factors that affect the intensity of the absorption band are the sample concentration and the optical path length. However, the signal to noise ratios in typical absorption signals is relatively low making it difficult to provide instrumentation capable of detecting relatively weak absorption bands.
For example, absorption spectroscopy has historically been performed in the continuous wave spectroscopy (CW-SPEC) mode. In this instance a sample of interest is irradiated with white light and the transmitted light is spatially resolved into separate wavelengths (e.g. by the use of a Fiber Bragg grating, or by the use of dispersive prisms). A photodetector may measure the separate wavelengths providing the transmission spectrum. Alternately, the incident light is temporally resolved into different wavelengths (e.g., by the use of a rotating prism and a white light source), and the transmitted light is measured by a photodetector. This approach is limited in sensitivity because most of the energy generated by the light source is discarded by the dispersive mechanisms used.
More recently Fourier Transform absorption spectroscopy, (FT-SPEC), has been used to improve the measurement sensitivity by continuously detecting all the wavelengths. This technique was enabled by the development of the Michelson interferometer as illustrated in FIG.
2
. Generally a Michelson interferometer may comprise a fixed mirror
34
and a moving mirror
33
. In practice a light source
31
may be used to generate white light, which is collimated onto a sample
39
, and then onto a beamsplitter
32
.
The beamsplitter
34
divides the incident beam into two separate optical beams, one of which is incident on the moving mirror
33
, and the other is incident on the fixed mirror
34
. In practice each of the mirror are reflective at the wavelengths of interest and reflect the incident beams back to the beamsplitter where they are combined and forwarded to a detector
35
. In operation, the lengths of the two optical paths are different so that the intensity of the recombined light varies in accordance with the constructive and destructive interference of the two beams as given by Eq. 3.
I
x
=
∫
v
A
v
(
1
+
cos
{
2
π
vx
}
)
ⅆ
v
Eq
.
(
3
)
where A
&ngr;
is the intensity of the incident, unmodulated light, and x is the path length difference. Eq. 3 represents a Fourier transform of the intensity of the incident beam A
&ngr;
so that the intensity of the incident beam, A
&ngr;
, may be estimated from the inverse FFT of the intensity of the recombined optical beam I
x
. Typically a calibration interferometer having a monochromatic light source
36
, and a white light source
37
may be used to calibrate the Michelson interferometer as illustrated in FIG.
3
.
This technique is called Fourier transform spectroscopy because the transmission spectrum of the sample is obtained as the inverse Fourier transform of the raw detector output. Fourier transform spectroscopy typically provides improved sensitivity compared to CW-SPEC instruments (with similar detectors and light source instrumentation).
Both CW-SPEC and FT-SPEC instrumentation are widely available and used in the academia and industry. Unfortunately, both CW-SPEC and FT-SPEC are unsuitable for detection of samples in the small size limit (i.e. when the concentration in air is approximately 0.1 ppm, or the total sample size is approximately 1 nano-liter or less). The detection limit in absorption spectroscopy is given by the minimally detectable absorption determined by the signal-to-noise ratio of the measurement instrumentation.
Consider an optical radiation at a frequency v and power P incident on a collection of N molecules (the sample). If the N molecules absorb a fraction of the incident power &eegr; (&eegr;<<1), and the rest is transmitted to a detector of quantum efficiency &bgr;, and the incident power is below the saturation intensity, then the detector current is given by Eq. 4.
I
D
=
P
(
1
-
η
)
e
β
ℏ
v
Eq
.
(
4
)
and the signal I
s
(the change in detector current due to absorption) is given by Eq. 5 as follows:
I
S
=
P
η
e
β
ℏ
v
Eq
.
(
5
)
If absorption is due to an atomic transition with resonance frequency &ngr;
o
, then the fraction of the absorbed incident power &eegr; can be written as Eq. 6.
η
=
N
σ
A
Eq
.
(
6
)
where a &sgr;=&sgr;
o
K, &sgr;
o
is the resonant cross section of the particular transition of interest; and K is a factor less than one that represents the reduction in cross section due to the radiative decay of the transitions into atomic states other
Brown Khaled
Christie Parker & Hale LLP
Font Frank G.
Tanner Research, Inc.
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