CN1361861A

CN1361861A - Method and system for adaptive interpretation of spectrometric data comobined with continual re-calibration

Info

Publication number: CN1361861A
Application number: CN 00810649
Authority: CN
Inventors: A·巴维茨; M·P·维斯尼夫斯基; R·Z·莫劳斯基; M·本斯利马
Original assignee: Bookham Technology PLC
Priority date: 1999-05-21
Filing date: 2000-05-23
Publication date: 2002-07-31
Also published as: WO2000071980A1; WO2000071980A9; EP1183505A1; JP2003500639A; AU4903000A

Abstract

A method for adaptive reconstruction and interpretation of spectra combined with re-calibration of a device providing spectrometric data, consist in carrying out an automatic calibration using the external reference light spectrum and its corresponding digital reference data stored in the internal memory of the device. The continual re-calibration procedure allows for automatic adaptation of the values of the coefficients in a reconstruction sub-procedure as well as the estimation of the values of the coefficients in an interpretation sub-procedure on the bases of a current shape of spectrometric data.

Description

Method and system for adaptive interpretation of spectral data combined with continuous recalibration

Technical Field

The present invention relates generally to spectral measurement and, more particularly, to compact spectral measurement systems that are portable and field applicable.

Background

Spectroscopy is an analytical technique involving the measured identification of the interaction of radiant energy with a substance, and it consists of an instrument designed for this purpose, the so-called spectrometer, and a corresponding device for interpreting the interaction both at the basic level and in the actual analysis. The distribution of radiant energy absorbed or emitted by a sample of the substance under investigation is called the substance's spectrum. Interpretation of spectra (interpretation) can provide fundamental information on the energy levels of atoms and molecules, i.e., the distribution of various types of atoms and molecules within these energy levels, the nature of the associated process of changing one energy level to another, the geometry of the molecules, chemical bonds, and interactions of molecules in solution. On a practical level, comparisons between spectra may provide a basis for qualitative determinations and chemical quantitative analyses of chemical compositions and chemical structures.

The spectrum to be measured has two common characteristics: they are all non-negative and they can all be separated into fairly flat regions and peaks of varying widths. Interpretation of the data representative of these spectral features obtained by means of spectrometers frequently involves the estimation of certain parameters of these peaks, namely: estimation of the position and size (i.e., area or height) of these peaks. The parameters of these peaks are particularly useful for qualitative and quantitative analysis of complex chemicals:

● the position of the peak can be used to identify the various compounds present in the sample of material under investigation;

● the size of the peak can be used to estimate the concentration of the identified compound.

Estimating the parameters of the spectrometric peaks directly from the obtained spectrometric data is problematic in many practical situations due to the following reasons:

● instrument defects (implfection) of the spectrometer,

● some inherent phenomenon in the sample of the substance under investigation.

Defects in the spectrometer can produce blurring of peaks and noise-like interference in the data representing the measured spectral features. On the other hand, some quantum phenomena in matter can increase the width of the peak significantly. Both instrumental blurring of peaks and natural increase in width can cause overlapping and merging of peaks, making correct identification of peaks impossible. Several different deconvolution algorithms (algorithm of deconvolution) have been proposed to mitigate instrument blur; an overview of these algorithms can be found in the following works: jansson P.A. (Ed.), cancellation with application in Spectroscopy, Academic Press, 1984 and Morawski R.Z.,

ski L., Barwicz A, "deconvo Algorithmsfor Instrument Applications-A Comparative Study," J.Chemometrics, 1995, Vol.9, pp.3-20. These algorithms are designed and evaluated using a quality criterion, such as approximate root mean square error, that is not deconvolution specific to spectroscopy. Therefore, the estimate of the spectral peak size determined from these results of deconvolution may become poor. On the other hand, curve fitting algorithms may be inefficient if they do not provide a good initial guess for the estimates sought. These two observations have independently motivated many researchers to later estimate peak locations using deconvolution algorithms and spectral peak sizes using curve fitting algorithms.

Both the spectral reconstruction (reconstruction) algorithm and the spectral parameter estimation algorithm require a considerable amount of information about the mathematical model of the spectral measurement data. This information is obtained during initial calibration of the spectrometer.

The numerical algorithms required for calibration of the spectrometer, reconstruction of the spectra, and estimation of the spectral parameters are available in many software libraries, for example some MATLAB Toolbox are software libraries that contain specialized libraries for processing spectral data, such as GRAMS/32 from the dairy industry (galenic Industries). In the patent context, there is only a partial methodology for spectral Deconvolution, such as U.S. patent No. 5247175 to Alan e schoen et al, issued on 21.9.1993, "Method and Apparatus for the deconstruction of Unresolved Data", and U.S. patent No. 4941101 to Paul b crilly, issued on 10.7.1990, which is specific to the chromatographic context, "Method for analyzingchromatography". On the other hand, there is a good example of a complete methodology for interpreting spectroscopic measurement data, see U.S. patent No. 5991023, "Method of interpreting spectroscopic data", issued 11/23.1999, to r.z.

However, in all of the above listed references, none of the methodologies provide complete support for on-line continuous re-calibration and adaptive spectral data interpretation, primarily due to the absence of such a closed-loop process of re-calibration and adaptive interpretation.

The need for high resolution and self-calibrating spectroscopic devices comes from everyday practice. U.S. patent No.5040889 to Thomas j.keane, published on 21/8/1991: "Spectrometers with Combined visual and ultrasound Sample Illumination" describes a Spectrometer that automatically calibrates the light detector by using a pivotable standard white Sample placed in the light path and controlled by a computer system. For each photodetector, a calibration factor is calculated and recalibrated whenever the temperature within the spectrometer changes, and this factor is then multiplied with the output signal of the photodetector. However, this is a partial static calibration, since it only calibrates the effects of the photodetector and does not take into account the effects produced by the light diffractive elements and slits. Thus, another dynamic calibration procedure is needed to eliminate these instrument errors and improve spectral resolution. In the field of telecommunications, and in particular for monitoring the optical performance of networks, there is a need for spectrometric devices that are small, operate under a wide range of environmental conditions, and more particularly are self-calibrating. In Miller c, Pelz l: an add-on for improving the performance of an Optical Channel analyzer is described in "Fabry-Perot tunable Filters", Lightwavi, March1999, Vol.16, No.3, which is based on Fabry-Perot tunable Filters using Optical fibers. This device uses an optical switch to alternately scan the spectrum (e.g., from a DWDM system) and a reference light source of known wavelength. This latter is used to continuously calibrate the device to correct for thermal drift, actuator non-linearity, and voltage variations. Deconvolution algorithms are also used to remove the effects of the spectral response of the tunable filter in order to improve the resolution of the measured spectrum. The main disadvantage of this device is that it measures only one wavelength or path length difference at a time, and therefore it takes a long time to process all optical channels. Thus, there remains a need for a low cost, miniaturized, self-calibrating spectral measuring device that has resolution comparable to that of conventional spectrum analyzers, and that is capable of measuring spectral characteristics of a wide variety of spectra in situ.

In the field of spectroscopy, the need for an adaptive reconstruction and interpretation procedure combined with continuous recalibration arises from the need for a spectroscopic measuring device that is compact, highly reliable to self-control, self-calibrating, capable of operating in a wide range of environmental conditions, and inexpensive to use widely, etc. The main object of the present invention is to respond to this need.

Object of the Invention

The invention aims to provide a method for carrying out self-adaptive interpretation on a spectrum according to spectral measurement data.

It is an object of the present invention to provide a method of integrating calibration and continuous recalibration of a spectroscopic measuring device, which provides for miniaturization and low-cost mass production of miniature spectroscopic analyzers.

Summary of The Invention

It is an object of the present invention to provide a program for interpreting spectral data representative of a sample characteristic of a substance of interest, the program comprising the steps of:

● performing initial calibration of the spectral measuring device;

● continuously recalibrates the spectral measuring device;

● adaptive reconstruction (adaptive reconstruction) of the spectra studied;

● adaptive interpretation (adaptive interpretation) of the spectra studied is performed.

The present invention also provides a method of calibrating and continuously calibrating the spectral measuring device, i.e., a method of confirming a numerical relationship between measurements produced by the spectral measuring device and established spectral measurement standards.

The present invention also provides a method of continuously recalibrating the spectroscopic measuring device which allows for the method to automatically adapt to instrument imperfections and possible changes in the shape of the spectroscopic data due to aging and/or thermal drift of the device, and non-linear behavior of the detector.

The invention also provides a method for numerical adaptive reconstruction of a study spectrum, i.e. a method for partially eliminating the effects of noise and blurring that corrupt spectral data, in combination with continuous recalibration of the spectral measurement apparatus.

The invention also provides a method for numerical adaptive interpretation, namely a method for estimating the position and size of some peaks forming the spectrum.

According to the invention, the calibration of the spectrometer is performed using an auxiliary light whose spectrum is considered to be known and can represent the characteristics of the measured spectrum in a series of experiments following the calibration. The result of this calibration has the form of two operators defined with the following numerical algorithm:

● an algorithm (projection operator) for simulating the spectral measurement data to give the measured spectrum

● an algorithm for estimating spectra and providing data (reconstruction operators)

The first algorithm is a pattern recognition algorithm, which involves the selection or estimation of model structural parameters, and the estimation of their functional parameters. The second algorithm is a deconvolution algorithm, or a generalized deconvolution algorithm, or a numerical solution algorithm of the first kind of integral equations.

According to the invention, the continuous recalibration of the spectrometer is carried out using a spectrum of the external reference light and digital reference data representative of the reference light characteristics, which data are stored in the computer or internal memory of the spectroscopic measuring device when obtained. The purpose of the recalibration of the device is to update the parameters of the operator.

According to the invention, the processing of the data representative of the study light comprises two main operations:

● use a reconstruction operator based on the spectral measurement data obtained

Estimating the unknown spectrum or its ideal model;

● use projection operators based on the spectral measurement data obtainedAnd a curve fitting algorithm estimates the parameters of the spectrum.

Adaptive interpretation methods of spectrometric data are useful for providing qualitative measurements of spectra, particularly in the case of small, integrated intelligent spectrometric devices. When combined with continuous or from time to time automatic recalibration, the spectral measuring device can maintain optimum performance, particularly for telecommunications applications.

The proposed method allows for automatic calibration of a particularly compact integrated spectral measurement device during manufacturing and in the absence of physical adjustments to the devices. The calibration will compensate for many forms of manufacturing variations without changing the physical device.

It therefore facilitates the solution of low-cost, flexible, high-quality spectroscopic measurement problems, particularly at the chip level, which can be easily adapted to a wide variety of applications by customizing a specific set of algorithms.

Brief description of the drawings

Exemplary embodiments will now be described in conjunction with the following figures:

FIG. 1 illustrates an exemplary measurement system;

FIG. 2 shows a flow chart of an adaptive reconstruction and interpretation procedure;

a) the program is an AI-RC program which,

b) the sub-routine AI-RC _ cal,

c) the sub-routine AI-RC _ record,

d) the sub-routine AI-RC rec,

e) subroutine AI-RC _ int;

FIG. 3 illustrates the exemplary measurement system;

fig. 4 gives the spectra of the test samples:

a) the actual spectrum x (lambda) is,

b) test data

Fig. 5 gives the spectra of the samples used for calibration:

a) actual spectrum x^cal(λ)，

b) Data of

Fig. 6 shows the outputs of the following filters:

a) a rational filter (ratio filter),

b) a spline function based Kalman filter;

FIG. 7 shows the final results of interpretation of the spectral measurement data;

FIG. 8 shows the exemplary measurement system, MMmicroOSA;

FIG. 9 shows MMmicroOSA^TMPossible applications in Dense Wavelength Division Multiplexing (DWDM) systems;

the spectrum of this test light is given in fig. 10:

a) the idealized spectrum s (lambda) of this light at the input of the DWDM transmitter,

b) the test data

FIG. 11 shows the emission spectrum of the laser;

fig. 12 illustrates the final result of the adaptive reconstruction and interpretation of telecommunications data.

Detailed Description

An example of a spectral adaptive reconstruction and interpretation program (AI-RC) combined with continuous recalibration of the apparatus providing the spectral measurement data is designed for a measurement system, which is shown in fig. 1 and comprises:

● a spectral measuring device in the form of a spectrometer or an essential part thereof, or in the form of a miniature spectral analyzer, which converts the optical signal carrying the measured spectral information into a digital code representing the spectrum;

● A processing device for processing the digital representation may be in the form of a general purpose computer, a microprocessor, or a general purpose digital signal processor. Or a dedicated digital signal processor;

● other functional elements required for measuring the spectrum.

The following notation is used to describe the procedure AI-RC:

lambda-wavelength; lambda belongs to [ lambda ]_min，λ_max]；

N-the number of data obtained by the spectral measurement device;

Δ λ -wavelength discretization step size; Δ λ ═ λ_min-λ_max)/(N-1)；

λ_n-nth data obtained by the spectroscopic measuring device; lambda [ alpha ]_n＝λ_min+(n-1)Δλ，n＝1，...，N；

x (λ) -the actual spectrum of the light under investigation;

i-position vector of spectral peak in spectrum x (λ), which is formed as I ═ l₁l₂...l_k]^T；

 -I;

a-a vector of magnitudes of spectral peaks in the spectrum x (λ), which is formed as a ═ a₁a₂...a_k]^T；

 -a estimate;

s (λ; I, a) -idealized spectrum of the light under investigation, assumed in the preferred embodiment to have the form:

wherein v is_s(λ, l) is an isolated normalized peak in s (λ; I, a) whose maximum is located at λ ═ l;

-is spectroscopic measurement data representative of x (λ) obtained by means of a spectroscopic measurement device;

<math> <mrow> <mo>{</mo> <msub> <mover> <mi>y</mi> <mo>~</mo> </mover> <mi>n</mi> </msub> <mo>}</mo> <mo>&equiv;</mo> <mo>{</mo> <msub> <mover> <mi>y</mi> <mo>~</mo> </mover> <mi>n</mi> </msub> <mo>|</mo> <mi>n</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <mi>N</mi> <mo>}</mo> <mo>;</mo> </mrow> </math>

x^cal(λ) -the actual spectrum of light used to calibrate the spectral measuring device; s (lambda; I)^cal，a^cal) -an idealized spectrum of light used to calibrate the spectral measuring device;

representing the actual spectrum x used to calibrate the spectroscopic measuring device^cal(λ) spectroscopic measurement data;

<math> <mrow> <mo>{</mo> <msubsup> <mover> <mi>y</mi> <mo>~</mo> </mover> <mi>n</mi> <mi>cal</mi> </msubsup> <mo>}</mo> <mo>&equiv;</mo> <mo>{</mo> <msubsup> <mover> <mi>y</mi> <mo>~</mo> </mover> <mi>n</mi> <mi>cal</mi> </msubsup> <mo>|</mo> <mi>n</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msup> <mi>N</mi> <mi>cal</mi> </msup> <mo>}</mo> <mo>;</mo> </mrow> </math>

x^recal(λ) -the actual spectrum of the external reference light used to recalibrate the spectral measurement device;is the spectral data measured by the spectral measuring device, which represents the actual spectrum x used to recalibrate the device^recal(λ)；

<math> <mrow> <mo>{</mo> <msubsup> <mover> <mi>y</mi> <mo>~</mo> </mover> <mi>n</mi> <mi>recal</mi> </msubsup> <mo>}</mo> <mo>&equiv;</mo> <mo>{</mo> <msubsup> <mover> <mi>y</mi> <mo>~</mo> </mover> <mi>n</mi> <mi>recal</mi> </msubsup> <mo>|</mo> <mi>n</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msup> <mi>N</mi> <mi>recal</mi> </msup> <mo>}</mo> <mo>;</mo> </mrow> </math>

s(λ；I^recal，a^recal) -is an idealized spectrum of light used to recalibrate the spectroscopic measuring device; g-is a projection operator (transform) that transforms the idealized spectrum s (λ; I, a) into the data space:

wherein, P_GIs a vector or matrix of parameters of the operator G which will be determined during calibration of the spectroscopic measuring device; p is a radical of_G＝[p_G，1p_G，2...]^TOr

R-is the reconstruction and interpretation operator (transform):

R＝R^roRⁱR^ris a reconstruction operator (transform), in the form of a generalized deconvolution method, for transforming the data

Conversion into an estimate of x (λ)

WhereinIs operator R^rIncluding regularization parameters determined during calibration of the spectral measurement device.

RⁱIs an interpreter (transform) in the form of a generalized deconvolution method to convert the data { x }_nIs converted into an estimate of s (lambda; I, a)

Wherein,

is operator RⁱIncluding the rule parameters determined during the calibration process.

2. Functional description of a preferred embodiment of the invention

2.1 general description of the procedure AI-RC

The main purpose of the procedure AI-RC is to obtain spectral measurement data

To estimate the position I and the size a of the spectral peaks contained in the spectrum of study x (λ). The feasibility of such an operation is critically governed by the reference data

And corresponding reference spectrum x^cal(λ) is determined by an auxiliary operation, which is referred to as calibration of the spectral measuring apparatus. This operation aims at obtaining information on a mathematical model of the relationship between the spectrometric data and the idealized spectrometric data to be known, which is the basis of the method chosen for estimating the parameters I and a. Although it is not necessary to begin processing each spectral measurement data sequence or sample at the very beginning

The calibration is performed before, but preferably valid calibration results are always available during the spectral processing.

The main difficulties associated with the estimation of the position and size of the spectrometric peaks within the detection spectrum are the blurring of these peaks caused by physical phenomena in the sample and their presence in the data caused by imperfect spectrometric devices

The ambiguity represented by (a). This difficulty can be overcome in the program AI-RC by applying a series of adaptive reconstruction and adaptive interpretation steps on the idealized-hypothetical spectrum s (λ; I, a) in order to correct (correct) the detection data so as to reduce the two ambiguities; if s (λ; I, a) is considered as an approximation of x (λ), only the (correct) instrument ambiguity needs to be corrected.

In accordance with the general functional description above, the AI-RC includes the following roughly defined steps:

●, the device providing the spectrometric data is initially calibrated, i.e. the spectrometric device, or the spectrometric detector, or the spectrometric sensor is initially calibrated (subroutine AI-RC-cal),

●, the device is continuously recalibrated on the basis of auxiliary reference data obtained by exciting the device with reference light (subroutine AI-RC-real),

● spectra studied { x }_nI.e. from a signal representing the spectrum x_nSpectral measurement data of featuresTo estimate the spectrum (subroutine AI-RC rec),

● based on an estimate of the actual spectrum obtained by means of the subroutine AI-RC _ rec

To adaptively estimate the position l of the spectral peak constituting the spectrum₁，l₂,., and size a₁，a₂,.. for the study spectrum (x)_nCarry on the self-adaptation interpretation (subroutine AI-RC _ int).

2.2 detailed description of subroutine AI-RC _ cal

This subroutine AI-RC _ cal comprises the following operations:

a) selecting a method of optimising the spectrum, i.e. selecting the optimised spectrum s_nThe form of the peak of };

b) the form of the reconstruction operator R of the idealized spectrum is chosen:

in which P is_RIs a vector of parameters;

c) from a library { P } of parameters to be determined during an initial calibration process, and updated during successive recalibration processes_R ^(j)J, a parameter is selected for the parameter P, 1_RAnd is selectedOf the study spectrum { x_nOr data

Characteristic F of₁，F₂,... compliant rules;

d) selecting a reference optical signal for initial calibration: { x_n ^cal(j) And associated s_n ^cal(j) J, where J is 1.. J; obtain a representation { x_n ^cal(j) Data of the characteristics of

J, where J is 1.. J;

e) for the data

Preprocessing, including removing outliers, subtracting baselines, smoothing, obtaining priori information for operation 2.g (i.e., an estimated value of variance of error in the calibration data), normalization, etc.;

f) according to the three groups:

，{x_n ^cal(j) and { s }_n ^cal(j) } to determine the parameter vector P_R ^(j)J, where J is 1.. J;

g) for the parameter P controlling the adaptation_RAnd feature F₁，F₂,..

2.3 detailed description of subroutine AI-RC _ real

This subroutine AI-RC _ real includes the following operations:

a) some reference optical signals for recalibration are selected: { x_n ^recal(j) And associated s_n ^recal(j) J, where J is 1.. J;

b) obtaining a representation s_n ^recal(j) Data of } in the same manner as described above

J, where J is 1.. J;

c) for the data

Preprocessing, including removing outliers, subtracting baselines, smoothing, obtaining priori information for operation 3.d (i.e., an estimated value of error variance in the calibration data), normalizing, etc.;

d) according to the following three arrays:

，{x_n ^recal(j) and { s }, and_n ^recal(j) }, updating the parameter vector P_R ^(j)J, where J is 1.. J;

e) for the parameter P controlling the adaptation_RAnd feature F₁，F₂,.. updating an approximation of the relationship;

2.4 detailed description of subroutine AI-RC _ rec

The subroutine AI-RC _ rec includes the following operations:

a) acquisition of a representative spectrum of interest { x }_nData of } in the same manner as described above

b) For the data

Performing a pretreatment comprising: eliminating abnormal values; deducting the baseline; smoothing; acquiring prior information for estimating spectral peak parameters in a mode of budgeting data errors; to be based on the measured spectrumDetermines the manner of manufacturing defects of the device, acquires the prior information for the reconstruction; detecting the ambient temperature with a temperature detector; and aging of working device components; normalization; and the like;

c) by having parameters

Operator R of^rAccording toData to estimate the spectrum of interest x_n-a library of parameters determined at initial calibration and updated during successive recalibrations, said parameters being continuously adapted to characteristics of said data.

2.5 detailed description of subroutine AI-RC _ int

This subroutine AI-RC int comprises the following operations:

a) evaluation of the spectra of the study at operation 2.4(c)

Performing self-adaptive smoothing processing;

b) obtaining the estimated value of the absorption peak width and the number of the absorption peaks for the pairPriori information for interpretation;

c) by means of band parameters

Operator ofBased on the data

An idealized spectrum s (λ) is estimated, the parameters being continuously adapted to the shape of the data according to a library of parameters determined during the interpretation calibration.

d) Estimating the position and size of each spectral peak within the study spectrum;

e) using a maximum detection algorithm, the maximum value of s (λ; i, an) estimate

Estimating the position I of each spectrum peak;

f) estimating the size of each spectral peak by means of an adaptive algorithm fitted with a curve of one of:

data selected in step 2.2(a)

、v_s(lambda, l) selected in step 2.2(a) with the parameter P determined in 2.2(f)_GOperator of

And the estimate  from step 2.5 (e);

the estimated value obtained in step 2.4(c)

V at 2.2(a) selection_s(λ, l), and an estimate  derived from 2.5 (e);

g) iteratively calibrating the estimates of the spectral peak parameters obtained at 2.5(e) and 2.5 (f);

h) the results of the parameter estimation are adapted to the requirements of the user, for example, converting them into some predefined parameters of the analyte substance.

A flow chart of the entire AI-RC process is shown in FIG. 2.

3. Exemplary embodiments of the invention

Example 1

A specific version of the AI-RC program has been designed for the measurement system shown in fig. 3, which includes: model S1000-absorption micro-spectrophotometer produced by Ocean Optics ; and a personal computer PC.

The following measurement parameters were selected for calibration and for acquisition of test data:

● wavelength range: lambda [ alpha ]_min＝450nm，λ_max＝675nm，

● number of data obtained from the spectrophotometer: n1024;

● wavelength discrete intervals: Δ λ ═ λ_min-λ_max)/(N-1)＝0.22nm。

Test data were obtained for a solution sample of holmium perchlorate (holmium perchlorate); the actual spectrum x (λ) is shown in fig. 4 a. The parameters of the spectrum are as follows:

● position vector of spectral peak: i ═ 452.2468.2473.1485537.3541.3543.7639.8644.2652.2656.4]^T

● magnitude vector of spectral peak: a ═ 1.170.190.20.4610.9880.410.2970.8210.4060.2460.263]^TIt has been assumed that the idealized spectrum of the study sample has the following form:

the spectral peaks are specified by the following formula:

v_s(λ) ═ δ (λ -l), where l ∈ [ λ ] - ]_min，λ_max]The set of data representing the x (lambda) characteristic obtained with the aid of a spectrophotometer,shown in fig. 4 b.

Some calibration data was obtained for a standard holmium oxide filter sample; actual spectrum x of the sample^cal(λ) is shown in FIG. 5 a. The parameters of this spectrum are as follows:

● position vector of spectral peak: i is^cal＝[450.7 454.5 460.4 463.5 473.9 0.483.9 488.8536.4 547.5 633.4 636.5 648.4]^T；

● magnitude vector of spectral peak: a is^cal＝[0.486 0.799 0.949 0.58 0.125 0.117 0.1140.284 0.106 0.129 0.149 0.109]^T(ii) a Calibration of an idealized spectrum s (. lamda.; I) of the sample used^cal，a^cal) It is assumed to have the following form:

the set of representatives x obtained with the aid of the spectrophotometer^cal(lambda) data of the characteristic of the light,

shown in fig. 5 b.

The selected projection operator (transform) transforms the idealized spectrum s (λ; I, a) into the data space:

the operator is defined by the following operations:

<math> <mrow> <mi>x</mi> <mrow> <mo>(</mo> <mi>λ</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>exp</mi> <mo>[</mo> <msubsup> <mo>&Integral;</mo> <mrow> <mo>-</mo> <mo>∞</mo> </mrow> <mrow> <mo>+</mo> <mo>∞</mo> </mrow> </msubsup> <msub> <mi>g</mi> <mi>sx</mi> </msub> <mrow> <mo>(</mo> <mi>λ</mi> <mo>-</mo> <msup> <mi>λ</mi> <mo>′</mo> </msup> <mo>)</mo> </mrow> <mi>ln</mi> <mo>[</mo> <mi>s</mi> <mrow> <mo>(</mo> <msup> <mi>λ</mi> <mo>′</mo> </msup> <mo>;</mo> <mi>I</mi> <mo>,</mo> <mi>a</mi> <mo>)</mo> </mrow> <mo>]</mo> <mi>d</mi> <msup> <mi>λ</mi> <mo>′</mo> </msup> <mo>]</mo> </mrow> </math>

<math> <mrow> <mi>y</mi> <mrow> <mo>(</mo> <mi>λ</mi> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mo>&Integral;</mo> <mrow> <mo>-</mo> <mo>∞</mo> </mrow> <mrow> <mo>+</mo> <mo>∞</mo> </mrow> </msubsup> <msub> <mi>g</mi> <mi>xy</mi> </msub> <mrow> <mo>(</mo> <mi>λ</mi> <mo>-</mo> <msup> <mi>λ</mi> <mo>′</mo> </msup> <mo>)</mo> </mrow> <mi>x</mi> <mrow> <mo>(</mo> <msup> <mi>λ</mi> <mo>′</mo> </msup> <mo>)</mo> </mrow> <mi>d</mi> <msup> <mi>λ</mi> <mo>′</mo> </msup> </mrow> </math>

function g_xy(λ) has been assumed to have the form of a Gauss function:

. Thus, the parameter vector P of the operator G_GComprises g_xyDiscrete values of (λ) and a parameter σ_xy。

The selected reconstruction operator (algorithm) transforms the data

Conversion into an estimate of s (lambda; I, a)

The operator can be defined as follows:

finding an estimate of x (lambda) by means of a rational filterThe filter has been already

ski L. is described in his doctor paper and is applied to data

The doctor thesis is as follows: "M subjects non-specific in terms of signals in terms of signal x points in terms of application specific properties", Ph.D. thesis, Universal du Qu bec-institut national de 1a Rasche scientific "Telecommunications, Montre al 1997.

● calculating an estimate of s (λ; I, a) by means of an adaptive rational filter

The filter is described in the following paper to be published by winsniwski m.p., Morawski r.z., Barwicz a.et al 1999 and applied to

The method comprises the following steps: instru.& Meas.“An Adaptive Ratuonal Filter ForInterpretation of Spectrometric Data”。

Operator R^rParameter vector ofCoefficients comprising the rational filter, and a function g_sxDiscrete values of (λ), as described in the following paper: ben SlimaM, Szczecinski L, Massicotte D, Morawski R.Z, Barwicz A, "Algorithmic Specification of a Specialized Processor for Spectrometric Applications", Proc.& Meas.Technology Conf.(Ottawa，Canada，May 19-21，1997)，pp.90-95；Ben Slima M.，Morawski R.Z.，Barwicz A.，“Kalman-filter-based Algorithms of Spectrophotometric DataCorrection-Part II：Use of Splines for Approximation ofSpectra”，IEEE Trans.Instrum.& Meas.，Vol.46，No.3，June1997，pp.685-689。

The following operations are done in the initial calibration:

● confirming function g using the iterative algorithm introduced by Jansson_sx(λ)；

● from the actual spectrum x^cal(λ) estimating the function g using an optimization algorithm_xyParameter σ of (λ)_xy；

● the coefficients of the rational filter are estimated using an optimization algorithm.

The following operations are performed in successive recalibrations:

● updating the coefficients of the rational filter using an optimization algorithm;

● the coefficients of the adaptive rational filter are estimated using an optimization method and morphology of the spectral measurement data.

Typical results of interpretation of the spectrometric data obtained by means of the described preferred embodiment are shown in fig. 6a, 6b and 7.

The following errors were defined in order to evaluate the accuracy of the program AI-RC:

● Relative Root Mean Square Error (RRMSE)

● Normalized Maximum Error (NME):

errors in the estimation of the position and height of spectral peaksThe difference is:

<math> <mrow> <msubsup> <mo>&PartialD;</mo> <mn>2</mn> <mi>l</mi> </msubsup> <mo>=</mo> <mn>0</mn> <mo>.</mo> <mn>0015</mn> <mo>,</mo> <msubsup> <mo>&PartialD;</mo> <mo>∞</mo> <mi>l</mi> </msubsup> <mo>=</mo> <mn>0</mn> <mo>.</mo> <mn>0024</mn> <mo>;</mo> <msubsup> <mo>&PartialD;</mo> <mn>2</mn> <mi>a</mi> </msubsup> <mo>=</mo> <mn>0</mn> <mo>.</mo> <mn>20</mn> <mo>,</mo> <msubsup> <mo>&PartialD;</mo> <mo>∞</mo> <mi>a</mi> </msubsup> <mo>=</mo> <mn>0</mn> <mo>.</mo> <mn>23</mn> <mo>;</mo> </mrow> </math>

example 2

An embodiment of an AI-RC program has been designed for a measurement system represented by an integrated MM microOSA (Optical Spectrum analyzer-Spectrum analyzer), which is shown in fig. 8. The analyzer is shown to monitor the optical channels in the DWDM network shown in figure 9.

The following DWDM system parameters were selected to calibrate and acquire test data:

● number of optical channels: 81;

● wavelength range: lambda [ alpha ]_min＝1530.77nm，λ_max＝1562.68nm；

● channel spacing: Δ λ ═ 0.4nm (50 GHz);

● laser source, has a known FWHM of 0.2nm, where FWHM denotes the full width at half maximum.

Obtaining test data for a telecommunications bandwidth; the actual spectrum x (λ) is shown in fig. 10 a. The parameters of the spectrum are as follows:

● peak position (carrier frequency) vector:

l_k＝1530.28+(k-1)Δλ+dl_k(k＝1，...，81)，

wherein dl_kAre some exactly the sameThe independent random variables of (a) are uniformly distributed at intervals of [ -0.05 nm; 0.05nm]The embodiment of i.e. dl_k∝∪(-0.05，0.05)；

● peak height vector a, which is considered to be a uniform distribution of some identical independent random variables over the interval [ 0.01; 1]Is shown in (a), that is, a_k∝∪(0.01，1.0)。

The adaptation of MM μ OSA to DWDM applications means that the data model is in the form:

wherein g is_xy(λ) is the optical response of the spectrometric sensor,

is an idealized spectrum of the so-called input light, and [. eta. ]_nIs a random error sum in the dataA sequence modeled by Amplified Spontaneous Emission (ASE) noise generated by a laser source. If the function g_sx(λ) is an approximation of the emission spectral shape of the laser, this is a suitable model for DWDM measurements.

The prior information about the emitted light of the laser can be used for the reconstruction of the idealized spectrum s (λ; I, a).

The continuous recalibration sub-routine allows the laser emission spectrum to be measured in time intervals of 1 second, so that the parameters P of the reconstruction sub-routine are continuously updated_R。

The selected projection operator transforms the idealized spectrum s (λ; I, a) into the data space:

the operator is determined by the following operation (operation):

<math> <mrow> <mi>x</mi> <mrow> <mo>(</mo> <mi>λ</mi> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mo>&Integral;</mo> <mrow> <mo>-</mo> <mo>∞</mo> </mrow> <mrow> <mo>+</mo> <mo>∞</mo> </mrow> </msubsup> <msub> <mi>g</mi> <mi>sx</mi> </msub> <mrow> <mo>(</mo> <mi>λ</mi> <mo>-</mo> <msup> <mi>λ</mi> <mo>′</mo> </msup> <mo>)</mo> </mrow> <mi>s</mi> <mrow> <mo>(</mo> <msup> <mi>λ</mi> <mo>′</mo> </msup> <mo>;</mo> <mi>I</mi> <mo>,</mo> <mi>a</mi> <mo>)</mo> </mrow> <mi>d</mi> <msup> <mi>λ</mi> <mo>′</mo> </msup> </mrow> </math>

the function g has been assumed_xy(λ) has the form of a Gauss function:

. Thus, the parameter vector P of the operator G_GContaining some g_xyDiscrete values of (λ) as shown in fig. 11 and a parameter σ equal to the spectral bandwidth of MM μ OSA_xy。

The selected reconstruction operator combines the data

Conversion into an estimate of s (lambda; I, a)

The reconstruction operator is determined by the following method:

● by applying to the dataFinding a discrete estimate of x (λ)

{{\hat{x}}_{n}};

● by being applied to

Computing an estimate of s (lambda; I, a) using a spline-based Kalman filter

Parameter vector P of operator R_R＝[P_R，1P_R，2...]^TCoefficients comprising the rational filter, and a function g_sxDiscrete values of (λ) and regularization parameters obtained with a spline-based Kalman filter, as described in the following paper: ben slim m, Morawski r.z, Barwicz a, "Kalman-filter-based algorithms of spectrometrological Data Correction-Part II: use of Splinesfor application of Spectra ", IEEE trans.& Meas.，Vol.46，No.3，June 1997，pp.685-689。

The following operations are done in the initial calibration:

● estimating the coefficients of the rational filter using an optimization algorithm;

● estimate the regularization parameters of the spline function based Kalman filter using an optimization algorithm.

The coefficients of the rational filter are updated in a continuous recalibration process based on the measured emission spectrum of the laser light.

The results of the adaptive reconstruction and interpretation of the telecommunication data obtained according to the present exemplary embodiment are shown in fig. 12.

The following errors are defined to assess the accuracy of the present exemplary method:

● Relative Root Mean Square Error (RRMSE):

● Maximum Absolute Error (MAE)

Δ_a＝max{|a_ex-a_est|}，Δ_a＝max{|I_ex-I_estAnd l. The estimation error of the position and height of the spectral peak is:

ε_l＝2.10^-3％，Δ_l＝0.05nm；ε_a＝1.3％，Δ_l＝0.5dBm；

4. applicability and scope of the invention

The proposed procedure AI-RC can be applied in various spectroscopic measuring instruments and systems, in particular in miniaturized integrated spectrometers for field use, such as in environmental detectors, spectroscopic analyzers, and optical performance monitors for telecommunications, etc. Its application aggressiveness in a given measurement scenario is based on the expected improvement in performance and resolution, some examples of which are as follows:

● the accuracy of the spectral analysis performed by a given spectral measurement system is improved as a result of the reduced error in the estimation of the instrument defect correction and measured spectral parameters;

●, because of their manufacturing differences, it is possible to automatically calibrate a particularly compact integrated spectral measuring device during manufacture;

● the miniaturization and integration of the associated instruments for spectroscopic measurements can be achieved as a result of the compensation of hardware imperfections by software and the replacement of certain functions by software;

● by replacing the high resolution spectral measuring device with a functionally equivalent but low resolution instrument, the cost of giving spectral analysis of the required accuracy can be reduced.

As will be apparent to those skilled in the art, a known disadvantage of the miniaturization of spectroscopic devices is that the dimensions being fabricated are small and light passing through such dimensioned devices often highlights even small defects in the manufacturing process, amplifying manufacturing errors. As such, calibration methods for correcting the above-described deficiencies of each device are always very advantageous in certain situations.

The exemplary embodiment of the present invention described in section 3 is not intended to limit the utility of AI-RC to absorption spectrophotometry and monitoring of optical telecommunication channels. Nor is it intended to be limited to the various algorithms that may be used to embody the operations that make up the program. On the contrary, the invention is intended to cover alternative algorithms and improvements. The present invention briefly describes some practical alternatives for a method of materializing the operation of the AI-RC program.

4.1. Alternative forms of projection and reconstruction operators

The following mathematical model of the spectroscopic measurement data can be used to define the operator G:

a) linear model of stability (stability):

<math> <mrow> <mi>y</mi> <mrow> <mo>(</mo> <mi>λ</mi> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mo>&Integral;</mo> <mrow> <mo>-</mo> <mo>∞</mo> </mrow> <mrow> <mo>+</mo> <mo>∞</mo> </mrow> </msubsup> <mi>g</mi> <mrow> <mo>(</mo> <mi>λ</mi> <mo>-</mo> <msup> <mi>λ</mi> <mo>′</mo> </msup> <mo>)</mo> </mrow> <mi>s</mi> <mrow> <mo>(</mo> <msup> <mi>λ</mi> <mo>′</mo> </msup> <mo>;</mo> <mi>I</mi> <mo>,</mo> <mi>a</mi> <mo>)</mo> </mrow> <mi>d</mi> <msup> <mi>λ</mi> <mo>′</mo> </msup> </mrow> </math>

b) unstable linear model:

<math> <mrow> <mi>y</mi> <mrow> <mo>(</mo> <mi>λ</mi> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mo>&Integral;</mo> <mrow> <mo>-</mo> <mo>∞</mo> </mrow> <mrow> <mo>+</mo> <mo>∞</mo> </mrow> </msubsup> <mi>g</mi> <mrow> <mo>(</mo> <mi>λ</mi> <mo>,</mo> <msup> <mi>λ</mi> <mo>′</mo> </msup> <mo>)</mo> </mrow> <mi>s</mi> <mrow> <mo>(</mo> <msup> <mi>λ</mi> <mo>′</mo> </msup> <mo>;</mo> <mi>I</mi> <mo>,</mo> <mi>a</mi> <mo>)</mo> </mrow> <mi>d</mi> <msup> <mi>λ</mi> <mo>′</mo> </msup> </mrow> </math>

c) non-linear models, such as:

<math> <mrow> <mi>y</mi> <mrow> <mo>(</mo> <mi>λ</mi> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mo>&Integral;</mo> <mrow> <mo>-</mo> <mo>∞</mo> </mrow> <mrow> <mo>+</mo> <mo>∞</mo> </mrow> </msubsup> <mi>g</mi> <mrow> <mo>(</mo> <mi>λ</mi> <mo>,</mo> <msup> <mi>λ</mi> <mo>′</mo> </msup> <mo>)</mo> </mrow> <msub> <mi>F</mi> <mi>s</mi> </msub> <mo>[</mo> <mi>s</mi> <mrow> <mo>(</mo> <msup> <mi>λ</mi> <mo>′</mo> </msup> <mo>;</mo> <mi>I</mi> <mo>,</mo> <mi>a</mi> <mo>)</mo> </mrow> <mo>]</mo> <mi>d</mi> <msup> <mi>λ</mi> <mo>′</mo> </msup> </mrow> </math>

<math> <mrow> <mi>y</mi> <mrow> <mo>(</mo> <mi>λ</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>F</mi> <mi>y</mi> </msub> <mo>[</mo> <msubsup> <mo>&Integral;</mo> <mrow> <mo>-</mo> <mo>∞</mo> </mrow> <mrow> <mo>+</mo> <mo>∞</mo> </mrow> </msubsup> <mi>g</mi> <mrow> <mo>(</mo> <mi>λ</mi> <mo>,</mo> <msup> <mi>λ</mi> <mo>′</mo> </msup> <mo>)</mo> </mrow> <msub> <mi>F</mi> <mi>s</mi> </msub> <mo>[</mo> <mi>s</mi> <mrow> <mo>(</mo> <msup> <mi>λ</mi> <mo>′</mo> </msup> <mo>;</mo> <mi>I</mi> <mo>,</mo> <mi>a</mi> <mo>)</mo> </mrow> <mo>]</mo> <mi>d</mi> <msup> <mi>λ</mi> <mo>′</mo> </msup> <mo>]</mo> </mrow> </math>

wherein g (λ) and g (λ, λ') are both instrumental functions of the spectroscopic measurement device; f_sAnd F_yIs a non-linear function.

The corresponding operator G may have the following form:

a) operator corresponding to the stable linear model:

<math> <mrow> <msub> <mover> <mi>y</mi> <mo>^</mo> </mover> <mi>n</mi> </msub> <mo>=</mo> <munder> <mi>Σ</mi> <mi>v</mi> </munder> <msub> <mi>P</mi> <mrow> <mi>G</mi> <mo>,</mo> <mi>n</mi> <mo>,</mo> <mi>v</mi> </mrow> </msub> <msubsup> <mo>&Integral;</mo> <msub> <mi>λ</mi> <mi>v</mi> </msub> <msub> <mi>λ</mi> <mrow> <mi>v</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </msubsup> <mi>s</mi> <mrow> <mo>(</mo> <msup> <mi>λ</mi> <mo>′</mo> </msup> <mo>;</mo> <mi>I</mi> <mo>,</mo> <mi>a</mi> <mo>)</mo> </mrow> <mi>d</mi> <msup> <mi>λ</mi> <mo>′</mo> </msup> </mrow> </math>

wherein

b) Operator corresponding to the unstable linear model:

<math> <mrow> <msub> <mover> <mi>y</mi> <mo>^</mo> </mover> <mi>n</mi> </msub> <mo>=</mo> <munder> <mi>Σ</mi> <mi>v</mi> </munder> <msub> <mi>P</mi> <mrow> <mi>Gn</mi> <mo>,</mo> <mi>v</mi> </mrow> </msub> <msubsup> <mo>&Integral;</mo> <msub> <mi>λ</mi> <mi>v</mi> </msub> <msub> <mi>λ</mi> <mrow> <mi>v</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </msubsup> <mi>s</mi> <mrow> <mo>(</mo> <msup> <mi>λ</mi> <mo>′</mo> </msup> <mo>;</mo> <mi>I</mi> <mo>,</mo> <mi>a</mi> <mo>)</mo> </mrow> <mi>d</mi> <msup> <mi>λ</mi> <mo>′</mo> </msup> </mrow> </math>

wherein

c) Operators corresponding to a typical non-linear model:

<math> <mrow> <msub> <mover> <mi>y</mi> <mo>^</mo> </mover> <mi>n</mi> </msub> <mo>=</mo> <munder> <mi>Σ</mi> <mi>v</mi> </munder> <msub> <mi>p</mi> <mrow> <mi>Gn</mi> <mo>,</mo> <mi>v</mi> </mrow> </msub> <msubsup> <mo>&Integral;</mo> <msub> <mi>λ</mi> <mi>v</mi> </msub> <msub> <mi>λ</mi> <mrow> <mi>v</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </msubsup> <msub> <mi>F</mi> <mi>s</mi> </msub> <mo>[</mo> <mi>s</mi> <mrow> <mo>(</mo> <msup> <mi>λ</mi> <mo>′</mo> </msup> <mo>;</mo> <mi>I</mi> <mo>,</mo> <mi>a</mi> <mo>)</mo> </mrow> <mo>]</mo> <mi>d</mi> <msup> <mi>λ</mi> <mo>′</mo> </msup> </mrow> </math>

<math> <mrow> <msub> <mover> <mi>y</mi> <mo>^</mo> </mover> <mi>n</mi> </msub> <mo>=</mo> <msub> <mi>F</mi> <mi>y</mi> </msub> <mo>[</mo> <munder> <mi>Σ</mi> <mi>v</mi> </munder> <msub> <mi>p</mi> <mrow> <mi>Gn</mi> <mo>,</mo> <mi>v</mi> </mrow> </msub> <msubsup> <mo>&Integral;</mo> <msub> <mi>λ</mi> <mi>v</mi> </msub> <msub> <mi>λ</mi> <mrow> <mi>v</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </msubsup> <msub> <mi>F</mi> <mi>s</mi> </msub> <mo>[</mo> <mi>s</mi> <mrow> <mo>(</mo> <msup> <mi>λ</mi> <mo>′</mo> </msup> <mo>;</mo> <mi>I</mi> <mo>,</mo> <mi>a</mi> <mo>)</mo> </mrow> <mo>]</mo> <mi>d</mi> <msup> <mi>λ</mi> <mo>′</mo> </msup> <mo>]</mo> </mrow> </math>

wherein

。

4.2. Alternative methods of signal reconstruction and interpretation:

the following method of signal reconstruction-deconvolution or generalized deconvolution-can be used to define the operator R:

a) a numerical differentiation based method of the original domain (original domain), which is defined in the following article by Morawski r.z., Sokolowski p: "application of Numerical Differentiation for measurement and Reconstruction", Proc. 7 th IMEKO-TC4 int. Symp. model electric & magnetic measurements (Prague, Sept.13-14, 1995), pp.230-234;

b) the iterative method of Jansson and Gold;

c) (ii) a method based on Tikhonov regularization-based spectral domain;

d) a method for cepstrum-domain based Tikhonov regularization, defined in the following papers by kallinowska a, Morawski r.z., Lubianka t: "Incorporation of the position compliance in a Cepstral Method of measurement and Reconstruction", Proc.XIII-th IMEKO World consistency, (Torino, Italy, Sept.5-9, 1994), pp.429-434;

e) a method of the original category which imposes a positive constraint on its solution based on Tikhonov regularization;

f) kalman filter-based methods that impose a positive constraint on their solution;

g) using a Kalman filter-based approach to strip approximation;

h) an adjoint operator (adjoint operator) method;

i) entropy-based variation methods;

j) a method based on a Volterra series;

k) rational filter-based approaches;

l) adaptive rational filter based methods.

In addition, many other methods developed in the fields of chemometrics, telecommunications, seismology, image processing, etc. can be applied for this purpose, the chemometric methods being described in the following papers: brown s.d., Bear jr.r.s., Blank t.b, "Chemometrics", anal.chem., vol.64, No.12, 1992, pp.22r-49R and Brown s.d., Sum s.t., Despagne f., "Chemometrics", Anal, chem.vol.68, No.12, 1995, pp.21r-61R; the method in telecommunications is described in the following paper: abreu e., Mitra s.k., marcesani r., "Non-minimum Phase Channel equalization Using Non-calusallfilters", IEEE trans.signal Processing, vol.45, No.1, jan.1997, pp.1-13; seismology methods are described in the following papers: methods in image processing are described in many articles, such as god houtt a.j., Seismic Migration, Elsevier 1985, such as gonsalaves r.a., Nisenson p., "HST ImageProcessing: an Overview of Algorithms for ImageRestoration ", Proc. SPIE, Vol.1567, 1991, pp.294-307; zerwaisis M.E., Kwon T.M, "On the Application of Robust functional in regulated Image retrieval", Proc IEEE int.Conf.Accoutics, Speech & Signal Process. -ICASSP' 93(Minneapolis MN, USA, April27-30, 1993), Vol.5, pp.289-292.

The following method is useful for determining the regularization parameters of the operator R:

a) the error principle of the measurement error variance of the prediction data, as described in the following paper: tikhonov a.n., Goncharsky a.v., Stepanov v.v., Yagola a a.g., Numerical Method for the Solution of Ill-postdublems, Kluwer 1995;

b) the L-curve method, as described in the following paper: hansen p.c., O' spare d.p.: "The Use of The L-curve in The regulated equation of The dispersed Ill-disposed publications", SIAMJ. Sci. Compout., Vol.14, No.6, 1993, pp.1487-1503;

c) method of attaching a calibration data set (method of additional set calibration data) as described in the following paper: szczeci ski L, Morawski R.Z, Barwicz A, "Numerical Correction of spectral data Using a nonlinear Operator of Measure and Reconstruction", Proc. IEEE Instrm. & Meas. technol. Conf. -IMTC95(Boston, MA, April24-26, 1995), pp.488-491.

4.3 calibration method

It is generally best to assume an isolated peak v_s(λ, l) has the following form:

a) dirac distribution for all values of l;

b) triangles whose width is constant or varies with l (a triangle whosewidth is constant or varying with l);

c) a rectangle whose width is constant or varies with respect to l;

d) a Gauss function shape, the width of which is constant or varies with respect to the l value;

e) lorenz function shape whose width is constant or varies with respect to l;

the following methods are useful in estimating the instrument function g (λ):

a) if an isolated peak v is considered_s(λ, l) has the form of a Dirac distribution δ (λ), then the data is directly aligned

A smooth approximation is applied to the image of the object,

b) relative to s (λ; i is^cal，a^cal) For dataThe result of the deconvolution is,

c) deconvolution and smoothing approximations are then used.

The following method can be used to determine other parameters of the operator R:

a) directly transforming the parameters of the operator G;

b) in another deviation norm (norm of discrepcy)

Applying some constraint to make any norm of solution | P_RII, minimizing;

c) another norm | P in the solution_RAny norm of the deviation with some constraint imposed on it

And (4) minimizing.

4.4. Method for estimating spectral peak parameters

The following method is useful for estimating the size a of those spectral peaks, giving an estimate  of the position I:

<math> <mrow> <mover> <mi>a</mi> <mo>^</mo> </mover> <mo>=</mo> <mi>a</mi> <msub> <mi>rg</mi> <mi>a</mi> </msub> <mi>inf</mi> <mo>{</mo> <msub> <mrow> <mo>|</mo> <mo>|</mo> <mo>{</mo> <msub> <mover> <mi>y</mi> <mo>~</mo> </mover> <mi>n</mi> </msub> <mo>}</mo> <mo>-</mo> <mi>G</mi> <mo>[</mo> <mi>s</mi> <mrow> <mo>(</mo> <mi>λ</mi> <mo>;</mo> <mover> <mi>I</mi> <mo>^</mo> </mover> <mo>,</mo> <mi>a</mi> <mo>)</mo> </mrow> <mo>;</mo> <msub> <mi>P</mi> <mi>G</mi> </msub> <mo>]</mo> <mo>|</mo> <mo>|</mo> </mrow> <mi>q</mi> </msub> <mo>|</mo> <mi>a</mi> <mo>&Element;</mo> <mi>A</mi> <mo>}</mo> </mrow> </math>

or

<math> <mrow> <mover> <mi>a</mi> <mo>^</mo> </mover> <mo>=</mo> <msub> <mi>arg</mi> <mi>a</mi> </msub> <mi>inf</mi> <mo>{</mo> <msub> <mrow> <mo>|</mo> <mo>|</mo> <mover> <mi>s</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mi>λ</mi> <mo>)</mo> </mrow> <mo>-</mo> <mi>s</mi> <mrow> <mo>(</mo> <mi>λ</mi> <mo>;</mo> <mover> <mi>I</mi> <mo>^</mo> </mover> <mo>,</mo> <mi>a</mi> <mo>)</mo> </mrow> <mo>|</mo> <mo>|</mo> </mrow> <mi>q</mi> </msub> <mo>|</mo> <mi>a</mi> <mo>&Element;</mo> <mi>A</mi> <mo>}</mo> </mrow> </math>

Here, a is a reasonable set of solutions; the options are: q 2, A * R^k；q＝∞，A*R^k；q＝2，A*R₊ ^k；q＝∞，A*R₊ ^k. Some examples of algorithmic solutions are given in the following works: morawski R.Z., Mie Kina A., Barwicz A., "CombinedUse of Tikhonov depletion and Current fixing for SpeetrogramInterprediction", Instrum.science& Technology，Vol.24，No.3，August 1996，pp.155-167；Morawski R.Z.，Mie Kina A.，Barwicz A.，“The Use of Decovolution and IterativeOptimization for Speetrogram Interpretation”，IEEE Trans.Instrum.&Meas., vol.47, No 5, oct.1997. A particularly effective solution to the above optimization problem based on an unstable Kalman filter or an adaptive LMS algorithm is given in the following paper: ben slim m., Morawski r.z., Barwicz a, "Kalman-filter-based Algorithms of specrophotometric DataCorrection-Part II: use of Splines for application of spectra ", IEEE trans.& Meas.，Vol.46，No.3，June1997，pp.685-689。

Optionally, the method of estimating the size a is used interchangeably with the following method to iteratively calibrate estimates of spectral peak size and position:

<math> <mrow> <mover> <mi>l</mi> <mo>^</mo> </mover> <mo>=</mo> <msub> <mi>arg</mi> <mi>l</mi> </msub> <mi>inf</mi> <mo>{</mo> <msub> <mrow> <mo>|</mo> <mo>|</mo> <mo>{</mo> <msub> <mover> <mi>y</mi> <mo>~</mo> </mover> <mi>n</mi> </msub> <mo>}</mo> <mo>-</mo> <mi>G</mi> <mo>[</mo> <mi>s</mi> <mrow> <mo>(</mo> <mi>λ</mi> <mo>;</mo> <mi>I</mi> <mo>,</mo> <mover> <mi>a</mi> <mo>^</mo> </mover> <mo>)</mo> </mrow> <mo>;</mo> <msub> <mi>p</mi> <mi>G</mi> </msub> <mo>]</mo> <mo>|</mo> <mo>|</mo> </mrow> <mi>q</mi> </msub> <mo>|</mo> <mi>l</mi> <mo>&Element;</mo> <mi>L</mi> <mo>}</mo> </mrow> </math>

or

<math> <mrow> <mover> <mi>l</mi> <mo>^</mo> </mover> <mo>=</mo> <msub> <mi>arg</mi> <mi>l</mi> </msub> <mi>inf</mi> <mo>{</mo> <msub> <mrow> <mo>|</mo> <mo>|</mo> <mover> <mi>s</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mi>λ</mi> <mo>)</mo> </mrow> <mo>-</mo> <mi>s</mi> <mrow> <mo>(</mo> <mi>λ</mi> <mo>;</mo> <mi>I</mi> <mo>,</mo> <mover> <mi>a</mi> <mo>^</mo> </mover> <mo>)</mo> </mrow> <mo>|</mo> <mo>|</mo> </mrow> <mi>q</mi> </msub> <mo>|</mo> <mi>l</mi> <mo>&Element;</mo> <mi>L</mi> <mo>}</mo> </mrow> </math>

Wherein L is a reasonable set of solutions; the options are: q 2 and L * R^k(ii) a q ═ infinity and L * R^k(ii) a q 2, and L * R₊ ^kQ ═ infinity and L * R₊ ^k。

4.5 preprocessing of spectrometric data

The following methods are useful for normalization of the data:

a) linear or non-linear transformation of the lambda-axis with the aim of attenuating the effects of instability in the data;

b) linear or non-linear transformation of the y-axis with the aim of attenuating non-linear effects in the data;

c) linear or non-linear transformations of the λ -and y-axes with the aim of attenuating instabilities and non-linear effects in the data;

the following method is useful for smoothing data:

a) linear, FIR-type or IIR-type filtering;

b) median filtering;

c) taking smooth approximation by a cubic spline function;

d) deconvolution is performed with respect to identity operators.

The standard method of baseline calibration, which is useful for the present invention, is described in the following works: branch e.g., Grasselli j., Infrared and Raman Spectroscopy, Marcel deacer 1976, and ASTM 1987 (American Society for testing and Materials): annual Book of ASTM Standards 1987.

Numerous other embodiments may be devised without departing from the spirit and scope of the present invention.

Claims

1. A method for adaptive interpretation of spectrometric data combined with recalibration for a spectrometric apparatus comprising a number of sensor elements, comprising the steps of:

a) initially calibrating a spectral measuring device that provides spectral measurement data;

b) in the absence of physical adjustment of individual sensor elements in isolation, the device is automatically recalibrated at intervals, as follows;

● provide light to the device from a reference light source

● obtains auxiliary reference data 'relating to detected light from the reference light source'

● calculating an updated calibration result based on the auxiliary reference data;

c) detection of spectra { x with a spectral measuring device_nIn order to provide a spectrum (x) representative of the spectrum_nSpectroscopic measurement data of

d) Based on the spectral measurement data

And updated calibration results, adaptively determined with the spectrum { x }_nCorrelated idealized spectrum s_nEstimated value of }

e) Based on the estimated value

Adaptively estimating the constituent spectra { x }_nThe positions l of some peaks of₁，l₂,., and size a₁，a₂，....。

2. The method of claim 1, wherein: the recalibration step (b) comprises updating the previous calibration results in the absence of physical alterations and adjustments to the sensor elements.

3. The method of claim 1, wherein: step (a) further comprises the steps of:

a1) selecting the idealized spectrum s_nPeak morphology in;

a2) the form of the operator R is chosen to reconstruct the idealized spectrum:

in which P is_RFor a vector of parameters, the selected form is related to the selected morphology of the spectral peak;

a3) according to the parameter library { P_R ⁽ⁱ⁾J, some of which are chosen to use the parameter P_RAdapt to the data

The rules of selected features F1, F2.. the parameters of the parameter library form part of the calibration data, which are determined at the initial calibration step and updated on recalibration;

a4) selecting the reference optical signal for the initial calibration step: { x_n ^cal(j) And associated s_n ^cal(j) J, where J is 1.· J;

a5) obtaining a representation { x_n ^cal(j) Data of the feature

J, where J is 1.·, J;

a6) for data

Carrying out pretreatment;

a7) from three sets of data:，{x_n ^cal(j) and { s }_n ^cal(j) } to determine the parameter vector P_R ^(j)J, where J is 1.·, J;

a8) parameter P for control adaptation_RApproximate the relationship between features F1, F2.

4. A method according to claim 3, characterized by: the step (a6) includes the steps of: priori information is obtained relating to a pre-estimated value of a change in error in the calibration data.

5. The method of claim 4, wherein: the step (a6) includes the steps of:

the elimination of the outlier is performed,

a subtraction of the baseline is performed,

the smoothing of the data is performed such that,

the data was normalized.

6. A method according to claim 3, characterized by: the step (a1) includes the steps of:

a method of idealising a spectrum showing peak morphology is selected.

7. The method of claim 1, wherein: the step (b) comprises the steps of:

b1) selecting a signal of reference light for recalibration: { x_n ^recal(j) And associated s_n ^recal(j) J, where J is 1.· J;

b2) obtaining a representation { x_n ^recal(j) Data of } in the same manner as described aboveWhere J is 1.. ang., J;

b3) for the obtained data

Carrying out pretreatment;

b4) according to the three groups:

，{x_n ^recal(j) and { s }, and_n ^recal(j) }, updating the parameter vector P_R ^(j)Where J is 1.. ang., J;

b5) updating a control-adaptive parameter vector P_RAnd the approximation of the relationship between features F1, F2.

8. The method of claim 7, wherein: the step (b3) includes the steps of:

priori information is obtained relating to a pre-estimated value of error variance in the obtained data.

9. The method of claim 8, wherein: the step (b3) includes the steps of:

the elimination of the outlier is performed,

a subtraction of the baseline is performed,

the smoothing of the data is performed such that,

the data was normalized.

10. The method of claim 1, wherein: the step (d) comprises the steps of:

d1) to pair

Carrying out pretreatment;

d2) by having a parameter P_ROperator R of (2), based on the dataCalculating and studying spectra { x }_nCorrelated idealized spectrum s_nEstimate of P, based on a library of parameters determined in an initial calibration and updated in successive recalibration processes, said parameters P_RAt each successive stage of data processing is adapted to the data characteristics F1, F2.

11. The method of claim 10, wherein: the step (d1) includes the steps of:

priori information related to accurate estimation of spectral peak parameters is acquired.

12. The method of claim 11, wherein: the step of acquiring the Priori information includes the steps of:

priori information is obtained relating to a pre-estimated value of error variance in the spectral measurement data.

13. The method of claim 12, wherein: the step (d1) includes the steps of:

the elimination of the outlier is performed,

a subtraction of the baseline is performed,

the smoothing of the data is performed such that,

the data was normalized.

14. The method of claim 1, wherein: the step (e) comprises the steps of:

e1) for the estimated value obtained in step (c)The pre-treatment is carried out, and the pretreatment,

e2) calculating at the first spectrum { x_nEstimate of the position and size of the internal spectral peak.

15. The method of claim 14, wherein: the estimated position and size are related to the position and size within the first spectrum, which is idealized from the obtained spectrum, the updated calibration data, and the operators derived therefrom.

16. The method of claim 15, wherein: the step (e1) includes the steps of:

priori information is obtained relating to the number of spectral peaks in the spectral measurement data and estimates of the widths of these spectral peaks.

17. The method of claim 15, wherein: the step (e1) includes:

the elimination of the outlier is performed,

a subtraction of the baseline is performed,

the smoothing of the data is performed such that,

the data was normalized.

18. A spectral measuring device, comprising:

a sensor element for detecting a spectrum x together with the spectroscopic assembly_nTo provide a spectrum s representing the spectrum_nSpectroscopic measurement data of

Means for initially calibrating the spectral measuring device in accordance with the provided reference light to provide an initial calibration result,

means for automatically recalibrating the spectral measuring device in the absence of physical adjustment of the sensing element in response to the provision of reference light, an

A processor for measuring data based on the spectrumAnd updated calibration results to determine the first spectrum { x }_nCorrelated idealized spectrum s_nEstimated value of }

And for using in dependence on the estimate

To estimate the spectrum s in the idealized spectrum_nPosition of spectral peak within } l₁，l₂,., and size a₁，a₂，...。

19. A spectral measuring device, comprising:

a sensor element for detecting a spectrum x together with the spectroscopic assembly_nTo provide a spectrum x representing the spectrum_nSpectroscopic measurement data of

(ii) a And

the method is characterized in that:

means for automatically recalibrating the spectral measuring device in the absence of physical adjustment of the sensing element in response to the provided reference light,

wherein the determination of the parameters used to reconstruct the idealized spectrum from the data relating to the light provided to the device is performed during calibration of the spectroscopic measurement device.