# US 2010/0165338 A1 · Time-Resolved Spectroscopy System and Methods for Multiple-Species Analysis in Fluorescence and Cavity-Ringdown Applications

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- Number: US 2010/0165338 A1
- Document ID: US20100165338A1
- Status: Published application
- Kind: A1
- Application number: 12/697,227
- Filed: 2010-01-30
- Published: 2010-07-01
- Earliest claimed: 2006-11-21
- Inventors: Ricardo Claps
- Web page: https://patentgrep.com/patent/US20100165338A1

## CPC

- G01N 21/64: Fluorescence; Phosphorescence
- G01J 3/02: Details
- G01J 3/0205: {Optical elements not provided otherwise, e.g. optical manifolds, diffusers, windows}
- G01J 3/0218: {using optical fibers}
- G01J 3/0256: {Compact construction}
- G01J 3/10: Arrangements of light sources specially adapted for spectrometry or colorimetry
- G01J 3/2889: {Rapid scan spectrometers; Time resolved spectrometry}
- G01J 3/4406: {Fluorescence spectrometry}
- G01N 21/6408: {with measurement of decay time, time resolved fluorescence}
- G06F 17/10: Complex mathematical operations {(function generation by table look-up G06F1/03; evaluation of elementary functions by calculation G06F7/544)}
- G01N: INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES (measuring or testing apparatus or processes other than immunoassay, involving enzymes or microorganisms C12M, C12Q)
- G01J: MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY (light sources F21, H01J, H01K, H05B; investigating properties of materials by optical means G01N)
- G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N)

## Abstract

A time-resolved spectroscopy system employing a time-division multiplexing optical device with no dispersive optical elements to perform lifetime and concentration measurements in multi-species samples, is disclosed. Some examples include fluorescence and cavity ring-down spectroscopy. The system is unique in its compactness and simplicity of operation. In one embodiment, the system makes use of only one photo-detector and an efficient linear regression algorithm. The system offers a measurement time for multiple species measurements of less than 1 s. The system can also be used to perform fluorescence correlation spectroscopy and fluorescence cross-correlation spectroscopy. Four methods to de-convolve a multi-component, exponentially decaying optical signal such as obtained with the system disclosed here, are presented. These methods may be applied to the measurement of fluorescence decay lifetimes and cavity ring-down times, the latter used extensively for the measurement of gas and trace-gas concentrations in complex mixtures, via absorption spectroscopy.

## Claims

### Claim 1

A time-resolved spectroscopy system comprising:
a light source for producing light to be directed at a sample, said sample comprising at least one light emitting or light absorbing compound:
a time-division multiplexing device for taking the radiation scattered or transmitted by the sample as a result of said light impinging on said sample and distributing that radiation to each of a plurality of optical channels; and
a detector for detecting the radiation carried by each of said optical channels; wherein
the light from the light source is directed through a waveguide and the radiation scattered or transmitted by the sample is collected from the same waveguide; and further comprising
an analyzer connected to said detector for analyzing one or more signals produced by said detector to determine the characteristics of the radiation carried by each of said optical channels.

### Claim 2 (depends on 1)

The system as in claim 1 further comprising:
a waveguide for transmitting light from the light source to said sample;
a routing element in communication with said waveguide for transmitting to said plurality of optical channels radiation from said sample in response to light from said light source being incident on said sample;
a filter mounted in series with said routing element to prevent light from said light source from being transmitted to the detector through the optical channels; and further comprising
a filter in series with each optical channel to allow the passage of selected radiation from the sample to the corresponding optical channel.

### Claim 3 (depends on 1)

The system as in claim 1 wherein said sample contains a luminescent material whose luminescence lifetime is quenched by a molecular oxygen concentration in said sample, thus enabling the measurement of said oxygen concentration.

### Claim 4 (depends on 1)

The system as in claim 1 wherein said sample contains a luminescent material whose luminescence is quenched by an ion concentration in said sample, such ions being one of H+, Na+, Ca+, Cu2+, Cl−, and H2PO4−.

### Claim 5

A method of using a time-resolved spectroscopy system to detect one or more compounds in a sample comprising:
producing light to be directed at a sample, said sample comprising at least one light emitting or light absorbing compound;
providing a plurality of optical channels;
distributing to each of said plurality of optical channels radiation scattered or transmitted by the sample as a result of said light impinging on said sample;
detecting the radiation carried by each of said optical channels; and further
wherein different concentrations of light emitting or light absorbing compounds in a given sample are expressed by a vector, χ, and said vector can be found using the equation:
χ=Z−1·σt·A; wherein
vector A corresponds to the measurements obtained with the time-resolved spectroscopy system, and Z−1 is a symmetric matrix.

### Claim 6 (depends on 5)

The method of claim 5, wherein matrix Z is:
Z=σt·σ.

### Claim 7 (depends on 6)

The method of claim 6, wherein the matrix, σ, is obtained by integration of the signal produced by a time-resolved spectroscopy system based on the design and fabrication specifications of said system, and of the light emitting or light absorbing compounds in the sample.

### Claim 8 (depends on 7)

The method of claim 7, wherein the elements of matrix σ are obtained by a convolution of an exponentially decaying function of a light emitting compound with an optical channel transmission function; wherein
a first index of matrix σ counts the number of optical channels in the time-resolved spectroscopy system, N; and wherein
a second index of matrix σ counts the total number of different compounds present in the sample; further wherein
each element in matrix σ is proportional to the absorbance and fluorescence quantum efficiency of a given compound in the sample;
the exponentially decaying function has a time constant related to a given compound in the sample; and further wherein
a selected speed and dwell time are included in the calculation of matrix σ.

### Claim 9

A method of using a time-resolved spectroscopy system to detect one or more compounds in a sample, said method comprising:
producing light to be directed at a sample, said sample comprising at least one light emitting or light absorbing compound;
providing a plurality of optical channels;
distributing to each of said plurality of optical channels radiation scattered or transmitted by the sample as a result of said light impinging on said sample;
detecting the radiation carried by each of said optical channels; and further wherein
the lifetime and concentration of multiple light emitting or light absorbing components of a sample are obtained essentially simultaneously by finding singular points of the variance of a function of two independent parameters.

### Claim 10 (depends on 9)

The method of claim 9, wherein said function of two independent parameters is obtained from the variance in the matrix product Z−1·σ; wherein
said two independent parameters are an intensity reference and a lifetime reference; wherein
Z is a nonsingular, symmetric matrix; and further wherein
Z=σt·σ.

### Claim 11 (depends on 10)

The method of claim 10, wherein said variance, ν, is a function dependent on two variables calculated using the following equation:
v
=
Max
[
∑
i

(
Z
-
1
·
σ
)
ij
]
;
wherein
ν is calculated for a lifetime reference ranging in selected increments from 0 to a maximum lifetime, and an intensity reference ranging in selected increments from 0 to a maximum intensity; and further wherein
ν has distinct poles at points having as coordinates the lifetimes and concentrations of the different compounds of the sample.

### Claim 12 (depends on 10)

The method of claim 10, wherein the elements of matrix σ are obtained by a convolution of a sum of two exponentially decaying functions with an optical channel transmission function; wherein
a first index of matrix σ counts the number of optical channels in the time-resolved spectroscopy system, N; and wherein
a second index of matrix σ counts the total number of different compounds present in the sample; further wherein
each element in matrix σ is proportional to the absorbance and fluorescence quantum efficiency of a given compound in the sample;
the exponentially decaying function has a time constant related to a given compound in the sample; and further wherein
a selected speed and dwell time are included in the calculation of matrix σ.

### Claim 13 (depends on 11)

The method of claim 11, wherein said two independent parameters are scanned by using an electronic circuit.

### Claim 14 (depends on 11)

The method of claim 11, wherein said two independent parameters are scanned optically, using a reference signal.

### Claim 15

A method for measuring the radiation decay lifetime and concentration of multiple light emitting or light absorbing components of a sample substantially at the same time, by approximating a discrete Laplace transform of the measurements obtained with a time-resolved spectroscopy system with a sum of rational functions of the Laplace parameter, s; wherein
the coefficients of each of said rational functions comprise concentration values of each of the light emitting or light absorbing components of said sample; and further wherein poles of each of said rational functions comprise the inverse of the radiation decay lifetime for each of the compounds of said sample.

### Claim 16 (depends on 15)

The method of claim 15, wherein said discrete Laplace transform is carried out using discrete voltage values measured with a time-resolved spectroscopy system at discrete intervals of time; and
further using values for the first time derivatives of said discrete voltage values at said discrete intervals of time; and
further using values for the second time derivatives of said discrete voltage values at said discrete intervals of time; wherein
said first time derivatives and said second time derivatives are obtained from said discrete voltage values measured with a time-resolved spectroscopy system at discrete time intervals, in combination with operational parameters of the time-resolved spectroscopy system; and
using a set of polynomials of the Laplace parameter, s, such that a specific polynomial is associated with a different time derivative of the signal.

### Claim 17 (depends on 15)

The method of claim 15, wherein said discrete Laplace transform is carried out using the following expression
L
s

(
I
)
=
∑
k


-
s


t
k

{
I
k
·
P
2
k

(
s
)
+

I
k

t
k
·
P
1
k

(
s
)
+

2

I
k

t
k
2
·
P
0
k

(
s
)
}
;
wherein
values for Ik are measured using the time-resolved spectroscopy system, and values for dIk/dtk, and d2Ik/dt2, are obtained from those of Ik, combined with operational parameters of the time-resolved spectroscopy system when operated at three different rotational speeds, ω+, ω, and, ω−, by using the following expression:

I
k

t
k
=
(
1
2
)
·
(
I
k
+
-
I
k
Δ


t
k
+
+
I
k
-
I
k
-
Δ


t
k
-
)
=
1
2

π

ω


n
Δω


k

(
ω
+

(
I
k
+
-
I
k
)
+
ω
-

(
I
k
-
I
k
-
)
)
,

2

I
k

t
k
2
=
(
2
t
k
+
-
t
k
-
)
·
(
I
k
+
-
I
k
Δ


t
k
+
-
I
k
-
I
k
-
Δ


t
k
-
)
=
2
π
2

(
ω


n
Δω


k
)
2

(
ω
+

ω
-
Δ


ω
)
·
(
ω
+

(
I
k
+
-
I
k
)
-
ω
-

(
I
k
-
I
k
-
)
)
;
wherein
P0k, P1k, and P2k are polynomials of the Laplace parameter, s, given by:
Δ
k
=
t
k
+
1
-
t
k
,

P
0
k

(
s
)
=
Δ
k
3
6
,

P
1
k

(
s
)
=
Δ
k
2
2
-
s

Δ
k
3
3
,

P
2
k

(
s
)
=
Δ
k
-
s
·
Δ
k
2
2
+
s
2
·
Δ
k
3
6
.

### Claim 18 (depends on 17)

The method of claim 17 wherein said sum of rational functions of the Laplace parameter, s, is given by the following formula:
L
s
δ

(
I
)
=
∑
i

ζ
i

{
1
(
s
+
1
/
τ
i
)
-
δ
+
(
s
+
1
/
τ
i
)
·
δ
2
2
}
.
wherein
each of the coefficients, ζi, correspond to the concentrations of each of the compounds in the sample; and wherein
the poles, 1/τi, correspond to the inverse of the lifetimes of all the compounds in the sample; and further wherein
δ is a parameter intrinsically associated with the design and operation of the time-resolved spectroscopy system; and further wherein
said approximate equalization of a discrete Laplace transform of said measurements is obtained from said sample with said time-resolved spectroscopy system, and said sum of rational functions of the Laplace parameter, s, is given by:
Lsδ(I)=Ls(I).

### Claim 19 (depends on 18)

The method of claim 18 wherein said parameter, δ, corresponds to a time-gap between a light source in said time-resolved spectroscopy system being directed at a sample and the detection of a resulting signal from the sample in a first optical channel, to start the measurement of the time-decaying radiation signal.

### Claim 20 (depends on 19)

The method of claim 19, wherein the parameter δ is adjustable by changing a spatial gap between an optical channel for directing light from a light source at a sample and a first optical collection optical channel in said time-resolved spectroscopy system.

### Claim 21 (depends on 15)

The method of claim 15, wherein said discrete Laplace transform of the measurements is obtained from said sample using said time-resolved spectroscopy system operating with a continuously varying rotational speed; and further comprises defining a function, IF, as:
I
F

(
t
)
=
∑
k

A

(
k
,
t
)
·
I
k

(
t
)
wherein
Ik(t), k varies from 1 to N, where N is an integer representing the number of optical channels in the time-resolved spectroscopy system; wherein
I1(t) to IN(t) are the time resolved measurements obtained from each of the individual optical channels in the time-resolved spectroscopy system; and wherein
A(1, t) to A(N, t), are selected to avoid overlapping of the signals coming from different optical channels; and further wherein
the values of compound concentration, ζi, and decay lifetimes, τi, for each of the different compounds that compose the sample are obtained from solving a non-linear regression problem expressed in the following equation:
∑
i

ζ
i

{
1
(
s
+
1
/
τ
i
)
-
δ
+
(
s
+
1
/
τ
i
)
·
δ
2
2
}
=
∑
k

∫
t
k
-
t
k
+

A

(
k
,
t
)


-
st

I
k

(
t
)


t

### Claim 22

A method of using a time-resolved spectroscopy system for use in cavity ring-down spectroscopy to detect one or more components in a sample, said method comprising:
producing light to be directed at a sample contained in a cavity ring-down system, said sample comprising at least one absorbing component;
providing a plurality of optical channels;
distributing to each of said plurality of optical channels radiation transmitted through the sample using a time-division multiplexing device;
detecting the radiation carried by each of said optical channels; and further
wherein
the signal lifetime is used to obtain the concentration of multiple absorbing components of a sample are obtained essentially simultaneously by finding singular points of the variance of a function of two independent parameters.