# US 11,994,430 B2 · Method for determining a correction value function and method for generating a frequency-corrected hyperspectral image

> Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt

- Number: US 11,994,430 B2
- Document ID: US11994430B2
- Status: Granted
- Kind: B2
- Application number: 17/474,431
- Filed: 2021-09-14
- Published: 2021-12-30
- Granted: 2024-05-28
- Earliest claimed: 2019-03-15
- Assignees: Bruker Optics GmbH & Co. KG
- Applicants: Bruker Optik GmbH
- Inventors: Roland Harig; Stephan Luettjohann
- Web page: https://patentgrep.com/patent/US11994430B2

## CPC

- G01J 3/45: Interferometric spectrometry
- G01J 5/10: using electric radiation detectors
- G01J 3/0208: {using focussing or collimating elements, e.g. lenses or mirrors; performing aberration correction}
- G01J 3/021: {using plane or convex mirrors, parallel phase plates, or particular reflectors}
- G01J 3/0243: {having a through-hole enabling the optical element to fulfil an additional optical function, e.g. a mirror or grating having a throughhole for a light collecting or light injecting optical fiber}
- G01N 21/274: {Calibration, base line adjustment, drift correction}
- G01N 21/35: using infrared light (G01N21/39 takes precedence)
- G01J 5/80: Calibration (using comparison with reference sources G01J5/52)
- G01J 2003/4534: {Interferometer on illuminating side}
- G01J 2005/0077: {Imaging}
- G01N 2021/1772: {Array detector}
- G01N 2021/3595: {using FTIR}
- 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)
- 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)

## Abstract

A method for determining a correcting quantity function kF(x, y) for calibrating an FTIR measurement arrangement with an IR detector. The IR detector includes a plurality of sensor elements, which are each located at a position (x, y), and the method includes: (a) recording interferograms IFGRxy of a reference sample using the sensor elements of the IR detector, (b) calculating spectra Rxy of the reference sample by Fourier transforming the interferograms of the reference sample for at least four sensor elements, (c) calculating correcting quantities kxy by comparing each spectrum Rxy of the reference sample calculated in step b) with a reference data set of the reference sample, and (d) determining the correcting quantity function kF(x, y) using the correcting quantities kxy calculated in step c). This permits frequency shifts that occur in FTIR spectrometers with extensive detectors to be effectively corrected regardless of the position of the sensor element.

## Claims

### Claim 1

A method for generating a frequency-corrected hyperspectral image of a sample with a Fourier Transform infrared (FTIR) measurement arrangement including an infrared detector having a plurality of sensor elements, the method comprising, for each of the plurality of sensor elements which are respectively located at a position (x,y) of the IR detector:
recording an interferogram IFGPxy with an equidistant sampling grid axy with the sensor element;
Fourier transforming the interferogram IFGPxy, to determine a spectrum Sxy(ν) with a frequency axis;
wherein the spectrum Sxy(ν) for each of the plurality of sensor elements is corrected with a correcting quantity function kF(x,y) for calibrating the FTIR measurement arrangement with the IR detector,
wherein the correcting quantity function kF(x,y) is determined with a method which comprises:
a) recording interferograms IFGRxy of a reference sample with the plurality of sensor elements of the IR detector;
b) calculating spectra R of the reference sample by Fourier transforming the interferograms IFGRxy of the reference sample for at least four sensor elements;
c) calculating correcting quantities kxy by comparing each spectrum of the spectra Rxy of the reference sample calculated in said step b) with a reference data set of the reference sample, wherein the reference data set comprises a target position ν1 of a selected absorption peak P of the reference sample;
d) determining the correcting quantity function kF(x, y) based on the correcting quantities kxy calculated in said step c),
wherein the correcting quantity function kF(x,y) is determined by stretching or compressing the spectra Rxy of the reference sample calculated in said step b), or by dividing the target position vL and an actual position νxy, wherein the interferogram IFGPxy is recorded with the equidistant sampling grid axy=a0/kF(x, y) and wherein spectra of the sample are subsequently generated by a Fourier transform of corrected interferograms, where a0 provides a value for the equidistant sampling grid axy when calculating values for the frequency axis.

### Claim 2 (depends on 1)

The method as claimed in claim 1, wherein the reference data set comprises a simulated spectrum Ssim with a plurality of absorption peaks of the reference sample and said calculating of the correcting quantities kxy in said step c) is implemented by comparing the spectra Rxy of the reference sample calculated in said step b) with the simulated spectrum Ssim.

### Claim 3 (depends on 2)

The method as claimed in claim 2, wherein the correcting quantities kxy are determined by maximizing a correlation, by varying the correcting quantities kxy between the simulated spectrum Ssim(ν) and the spectra Rxy(ν/kxy) stretched or compressed by 1/kxy.

### Claim 4 (depends on 1)

The method as claimed in claim 1, wherein the correcting quantity function kF(x,y) is given by
k
F
⁡
(
x
,
y
)
=
k
c
⁢
⁢
cos
(
arctan
(
(
c
y
-
y
)
2
+
(
c
x
-
x
)
2
f
eff
)
)
where cy, cx, feff and kc are parameters for matching the correcting quantity function kF(x,y) to the calculated correcting quantities kxy.

### Claim 5 (depends on 4)

The method as claimed in claim 4, wherein the correcting quantity function kF(x,y) is matched to the calculated correcting quantities kxy by minimizing an error function:
Σxy(kF(x,y)−kxy)2.

### Claim 6 (depends on 4)

The method as claimed in claim 4, wherein the parameters required for the matching are determined by setting up equations with the correcting quantities kxy calculated in said step c) for the at least four sensor elements to produce a system of equations and by solving the system of equations through curve fitting.

### Claim 7 (depends on 1)

The method as claimed in claim 1, wherein the correcting quantity function kF(x,y) is given by
kF(x,y)=a*(x2+y2)+b*x+c*y+d
where a, b, c and d are parameters for matching the correcting quantity function kF(x,y) to the calculated correcting quantities kxy.

### Claim 8 (depends on 7)

The method as claimed in claim 7, wherein the correcting quantity function kF(x,y) is matched to the calculated correcting quantities kxy by minimizing an error function:
Σxy(kF(x,y)−kxy)2.

### Claim 9 (depends on 7)

The method as claimed in claim 7, wherein the parameters required for the matching are determined by setting up equations with the correcting quantities kxy calculated in said step c) for the at least four sensor elements to produce a system of equations and by solving the system of equations through curve fitting.

### Claim 10

A method for generating a frequency-corrected hyperspectral image of a sample with a Fourier Transform infrared (FTIR) measurement arrangement including an infrared detector having a plurality of sensor elements, the method comprising, for each of the plurality of sensor elements which are respectively located at a position (x,y) of the IR detector:
recording an interferogram IFGPxy with an equidistant sampling grid axy with the sensor element;
Fourier transforming the interferogram IFGPxy, to determine a spectrum Sxy(ν) with a frequency axis;
wherein the spectrum Sxy(ν) for each of the plurality of sensor elements is corrected with a correcting quantity function kF(x,y) for calibrating the FTIR measurement arrangement with the IR detector,
wherein the correcting quantity function kF(x,y) is determined with a method which comprises:
a) recording interferograms IFGRxy of a reference sample with the plurality of sensor elements of the IR detector;
b) calculating spectra Rxy of the reference sample by Fourier transforming the interferograms IFGRxy of the reference sample for at least four sensor elements;
c) calculating correcting quantities kxy by comparing each spectrum of the spectra Rxy of the reference sample calculated in said step b) with a reference data set of the reference sample, wherein the reference data set comprises a target position ν1 of a selected absorption peak P of the reference sample;
d) determining the correcting quantity function kF(x, y) based on the correcting quantities kxy calculated in said step c),
wherein the correcting quantity function kF(x,y) is determined by stretching or compressing the spectra Rxy of the reference sample calculated in said step b), or by dividing the target position vL and an actual position νxy, wherein the interferogram IFGPxy is recorded with the equidistant sampling grid axy=a0 and wherein spectra of the sample are subsequently generated by a Fourier transform of interferograms, where a0*kF(x,y) provides a value for the equidistant sampling grid axy when calculating values for the frequency axis.

### Claim 11 (depends on 10)

The method as claimed in claim 10, wherein the reference data set comprises a simulated spectrum Ssim with a plurality of absorption peaks of the reference sample and said calculating of the correcting quantities kxy in said step c) is implemented by comparing the spectra Rxy of the reference sample calculated in said step b) with the simulated spectrum Ssim.

### Claim 12 (depends on 10)

The method as claimed in claim 10, wherein the correcting quantities kxy are determined by maximizing a correlation, by varying the correcting quantities kxy, between the simulated spectrum Ssim(ν) and the spectra Rxy(ν/kxy) stretched or compressed by 1/kxy.

### Claim 13 (depends on 10)

The method as claimed in claim 10, wherein the correcting quantity function kF(x,y) is given by
k
F
(
x
,
y
)
=
k
c
⁢
cos
⁡
(
arctan
⁡
(
(
c
y
-
y
)
2
+
(
c
x
-
x
)
2
f
eff
)
)
where cy, cx, feff and kc are parameters for matching the correcting quantity function kF(x,y) to the calculated correcting quantities kxy.

### Claim 14 (depends on 13)

The method as claimed in claim 13, wherein the correcting quantity function kF(x,y) is matched to the calculated correcting quantities kxy by minimizing an error function:
Σxy(kF(x,y)−kxy)2.

### Claim 15 (depends on 13)

The method as claimed in claim 13, wherein the parameters required for the matching are determined by setting up equations with the correcting quantities kxy calculated in said step c) for the at least four sensor elements to produce a system of equations and by solving the system of equations through curve fitting.

### Claim 16 (depends on 10)

The method as claimed in claim 10, wherein the correcting quantity function kF(x,y) is given by
kF(x,y)=a*(x2+y2)+b*x+c*y+d
where a, b, c and d are parameters for matching the correcting quantity function kF(x,y) to the calculated correcting quantities kxy.

### Claim 17 (depends on 16)

The method as claimed in claim 16, wherein the correcting quantity function kF(x,y) is matched to the calculated correcting quantities kxy by minimizing an error function:
Σxy(kF(x,y)−kxy)2.

### Claim 18 (depends on 16)

The method as claimed in claim 16, wherein the parameters required for the matching are determined by setting up equations with the correcting quantities kxy calculated in said step c) for the at least four sensor elements to produce a system of equations and by solving the system of equations through curve fitting.