GB2475368A

GB2475368A - Compensation of high spectral orders in diffraction grating-based optical spectrometers

Info

Publication number: GB2475368A
Application number: GB1015359A
Authority: GB
Inventors: Bernd Nawracala
Original assignee: Agilent Technologies Inc
Current assignee: Agilent Technologies Inc
Priority date: 2009-11-09
Filing date: 2010-09-15
Publication date: 2011-05-18
Also published as: GB201015359D0

Abstract

Direct compensation of higher order spectral contributions in a grating-based optical spectrometer is provided thus avoiding filter devices such as sorting filters. A light source 200 emits a beam 210 through a sample fluid in flow cell 220. The light beam 210 passes slit 250 and is diffracted by grating 260. The diffracted partial beams 270 hit photo detector 280 e.g. a photo detector array (PDA) at different angles dependent on the wavelength of the partial beam. A photo current intensity is measured, and spectral intensity contributions of higher orders are subtracted from the measured photo current intensity. A correction term for each wavelength, corresponding to a respective position in the spectrometer, may be derived from calibration measurements of the spectrometer using filter 290. The system has particular application in high performance liquid chromatography (HPLC) systems.

Description

COMPENSATION OF HIGH SPECTRAL ORDERS IN DIFFRACTION

GRATING BASED OPTICAL SPECTROMETERS

BACKGROUND ART

[0001] The present invention relates to compensation of high spectral orders in diffraction grating based optical spectrometers, in particular in a high performance liquid chromatography application.

[0002] Optical spectrometers are widely used for measuring spectra and calculating optical parameters such as absorbance of samples under test. A subclass of optical spectrometer comprises diffraction gratings as dispersive elements.

[0003] According to grating theory the first order of diffracted light of wavelength A and those of orders k> 1 of wavelength A/k will diffract to the same angle, if such wavelengths are present in the spectrum of the light source. Therefore the light e.g. emerging from a monochromator exit slit or hitting a photo detector array (PDA) of a spectrograph in general will contain wavelengths other than desired (typically only the first order) due to the overlap of orders. The unwanted orders must be blocked in order to accurately measure the light intensity at wavelength A and avoid severe non-linearity.

[0004] "Order-sorting" filters are most commonly used for this purpose. These are essentially long-wave pass optical filters (LWP) that transmit longer wavelengths while blocking the shorter wavelengths. Such order-sorting filters are available both as absorbance and interference type.

[0005] Order sorting filters of absorbance or interference type implementing an optical LWP filter are commonly located in front of the spectrometer or PDA of a monochromator or spectrograph, respectively in order to block light of unwanted higher orders. Examples of such order sorting filters are described in US 2009/0168182 Al, titled "Optical device and optical filter", or in US 5139335 A, titled "Holographic grating imaging spectrometer".

[0006] An interference type filter comprises a substrate partly coated with a stack of thin films thereon, resulting in an edge between coated and uncoated area. This edge disturbs light transmission of incident light causing an intensity "dip" in the recorded spectrum degrading signal-to-noise ratio and optical resolution at corresponding spectral position. Also, especially with interference type filters, which are preferred due to their spectral performance, comprise thin film coatings which are susceptible to humidity causing changes of filter transmission and signal drift in consequence.

[0007] Drawbacks of this approach result from the fact, that a physical filter constitutes an additional optical element which not only reduces transmittance and increases optical aberrations but also degrades optical signal to noise due to the fact that they increase stray and scattered light levels.

[0008] Optical spectrometers are often used as detector in high performance liquid chromatography (HPLC). In HPLC, a liquid has to be provided usually at a very controlled flow rate (e. g. in the range of microliters to milliliters per minute) and at high pressure (typically 20-1 00 MPa, 200-1000 bar, and beyond up to currently 200 MPa, 2000 bar) at which compressibility of the liquid becomes noticeable. For liquid separation in an HPLC system, a mobile phase comprising a sample fluid with compounds to be separated is driven through a stationary phase (such as a chromatographic column), thus separating different compounds of the sample fluid which may then be identified.

[0009] The mobile phase, for example, a solvent, is pumped under high pressure typically through a column of packing medium, and the sample (e.g. a chemical or biological mixture) to be analyzed is injected into the column. As the sample passes through the column with the liquid, the different compounds, each one having a different affinity for the packing medium, move through the column at different speeds.

Those compounds having greater affinity for the packing medium move more slowly through the column than those having less affinity, and this speed differential results in the compounds being separated from one another as they pass through the column.

[0010] The mobile phase with the separated compounds exits the column and passes through a detector, which identifies the molecules, for example by spectrophotometric absorbance measurements. A two-dimensional plot of the detector measurements against elution time or volume, known as a chromatogram, may be made, and from the chromatogram the compounds may be identified. For each compound, the chromatogram displays a separate curve or "peak". Effective separation of the compounds by the column is advantageous because it provides for measurements yielding well defined peaks having sharp maxima inflection points and narrow base widths, allowing excellent resolution and reliable identification of the mixture constituents. Broad peaks, caused by poor column performance, are undesirable as they may allow minor components of the mixture to be masked by major components and go unidentified.

DISCLOSURE

[0011] It is an object of the invention to provide an improved compensation of high spectral orders in diffraction grating based optical spectrometers, in particular for HPLC applications. The object is solved by the independent claim(s). Further embodiments are shown by the dependent claim(s).

[0012] According to the present invention, a signal output is derived from an optical spectrometer comprising a diffraction grating, by measuring a photo current intensity, and subtracting spectral intensity contributions of higher orders from the measured photo current intensity.

[0013] Embodiments of the invention thus provide a direct compensation of higher order spectral contributions and allow avoiding filter devices such as the aforedescribed order sorting filters, which in spectrograph type spectrometer have to be mounted in direct proximity of the detector e.g. a photodiode array detector (PDA).

Fixing of the filter and stability of the latter is no simple task, which can be avoided with embodiments of the present invention. Further, such filter in monochromator layouts have to be moved into and out off the optical beam requiring sophisticated mechanical means to achieve desired speed, accuracy and repeatability, which can also be avoided with embodiments of the present invention.

[0014] Filter omission improves spectrograph resolution due to avoidance of optical aberration caused by the filter and improved linearity due to avoidance of scattered light from filter substrate and -especially for interference type filters -reduced stray light originating from back reflection of filter coating. Omission of a filter also relaxes constrains regarding spatial location of optical spectrum relative to the PDA detector as boundary conditions set by the mechanical position of the filter are avoided.

[0015] In an embodiment, the photo current intensity is measured at a position in the spectrometer corresponding to an expected wavelength diffracted by the grating.

[0016] Measuring the photo current intensity can be done at a plurality of positions in the spectrometer, each corresponding to an expected wavelength diffracted by the grating.

[0017] Subtracting spectral intensity contributions of higher orders from the measured photo current intensity may comprise subtracting spectral intensity contributions of orders greater than one from the measured photo current intensity.

[0018] The spectral intensity contributions of higher orders to be subtracted can be derived by summing the spectral intensity contribution of each higher order. The spectral intensity contribution of each higher order may be determined by the spectral intensity contribution of the first order corrected by a correction term. A plurality of correction terms, each for a different wavelength corresponding to a respective position in the spectrometer, may be used.The correction term for each wavelength may represent a response ratio of an intensity at this wavelength to an intensity at first order. The correction term for each wavelength may be derived from calibration measurements of the spectrometer, each calibration measurement being executed with a different filter having a substantially known wavelength transmission characteristic.

[0019] The signal output 11(A) for a wavelength A can be derived from the measured photo current intensity y(A) by the formula 11(A)= y(A)-Rk(A/k)Il(A/k) k=km () wherein k is the diffraction order, and Rk is a response ratio of an intensity at the wavelength A to an intensity at first order derived from previous calibration of the spectrometer, and 11(A/k) is the measured photo current intensity at A/k.

[0020] Subtracting of the spectral intensity contributions of higher orders from the measured photo current intensity is preferably done by mathematically subtracting a value of the spectral intensity contributions of higher orders from a value of the measured photo current intensity.

[0021] An embodiment comprises a data processing unit for deriving a signal output from an optical spectrometer comprising a diffraction grating. The data processing unit comprises means for receiving a measured photo current intensity, and means for subtracting spectral intensity contributions of higher orders from the measured photo current intensity.

[0022] An embodiment comprises a fluid separation system for separating compounds of a sample fluid in a mobile phase. The fluid separation system comprises a mobile phase drive, preferably a pumping system, adapted to drive the mobile phase through the fluid separation system, a separation unit, preferably a chromatographic column, adapted for separating compounds of the sample fluid in the mobile phase, a detector adapted to detect separated compounds of the sample fluid, and a data processing unit as aforementioned adapted to process data received from the fluid separation system.

[0023] The fluid separation system of the preceding claim may further comprising one or more of a sample injector adapted to introduce the sample fluid into the mobile phase, a collection unit adapted to collect separated compounds of the sample fluid, and a degassing apparatus for degassing the mobile phase.

[0024] Embodiments of the present invention might be embodied based on most conventionally available HPLC systems, such as the Agilent 1290 Series Infinity system, Agilent 1200 Series Rapid Resolution LC system, or the Agilent 1100 HPLC series (all provided by the applicant Agilent Technologies -see www.açilent.corn -which shall be incorporated herein by reference).

[0025] Embodiments of the invention can be partly or entirely embodied or supported by one or more suitable software programs, which can be stored on or otherwise provided by any kind of data carrier, and which might be executed in or by any suitable data processing unit. Software programs or routines can be preferably applied in or by the control unit.

BRIEF DESCRIPTION OF DRAWINGS

[0026] Other objects and many of the attendant advantages of embodiments of the present invention will be readily appreciated and become better understood by reference to the following more detailed description of embodiments in connection with the accompanied drawing(s). Features that are substantially or functionally equal or similar will be referred to by the same reference sign(s).

[0027] Figure 1 shows a liquid separation system 10, in accordance with embodiments of the present invention, e.g. used in high performance liquid chromatography (HPLC).

[0028] Fig. 2 schematically illustrates a typical embodiment of the detector 50.

[0029] Fig. 3 shows an instrument profile before (-) and after (---) compensation of high orders.

[0030] Fig. 4 shows a typical curve shape of response Ratios R2 (-) and R3 (---) determined during instrument calibration process.

[0031] Fig. 5 depicts a transmission spectrum of a sample, without(---) and with (- ) high order compensation.

[0032] Referring now in greater detail to the drawings, Fig. I depicts a general schernaticofa liquid separation system 10. Apump2O receives a mobile phase from a solvent supply 25, typically via a degasser 27, which degases and thus reduces the amount of dissolved gases in the mobile phase. The pump 20 -as a mobile phase drive -drives the mobile phase through a separating device 30 (such as a chromatographic column) comprising a stationary phase. A sampling unit 40 can be provided between the pump 20 and the separating device 30 in order to subject or add (often referred to as sample introduction) a sample fluid into the mobile phase. The stationary phase of the separating device 30 is adapted for separating compounds of the sample liquid. A detector 50 is provided for detecting separated compounds of the sample fluid. A fractionating unit 60 can be provided for outputting separated compounds of sample fluid.

[0033] While the mobile phase can be comprised of one solvent only, it may also be mixed from plural solvents. Such mixing might be a low pressure mixing and provided upstream of the pump 20, so that the pump 20 already receives and pumps the mixed solvents as the mobile phase. Alternatively, the pump 20 might be comprised of plural individual pumping units, with plural of the pumping units each receiving and pumping a different solvent or mixture, so that the mixing of the mobile phase (as received by the separating device 30) occurs at high pressure und downstream of the pump 20 (or as part thereof). The composition (mixture) of the mobile phase may be kept constant over time, the so called isocratic mode, or varied over time, the so called gradient mode.

[0034] A data processing unit 70, which can be a conventional PC or workstation, might be coupled (as indicated by the dotted arrows) to one or more of the devices in the liquid separation system lOin order to receive information and/or control operation.

For example, the data processing unit 70 might control operation of the pump 20 (e.g. setting control parameters) and receive therefrom information regarding the actual working conditions (such as output pressure, flow rate, etc. at an outlet of the pump).

The data processing unit 70 might also control operation of the solvent supply 25 (e.g. setting the solvent/s or solvent mixture to be supplied) and/or the degasser 27 (e.g. setting control parameters such as vacuum level) and might receive therefrom information regarding the actual working conditions (such as solvent composition supplied over time, flow rate, vacuum level, etc.). The data processing unit 70 might further control operation of the sampling unit 40 (e.g. controlling sample injection or synchronization sample injection with operating conditions of the pump 20). The separating device 30 might also be controlled by the data processing unit 70 (e.g. selecting a specific flow path or column, setting operation temperature, etc.), and send -in return -information (e.g. operating conditions) to the data processing unit 70.

Accordingly, the detector 50 might be controlled by the data processing unit 70 (e.g. with respect to spectral or wavelength settings, setting time constants, start/stop data acquisition), and send information (e.g. about the detected sample compounds) to the data processing unit 70. The data processing unit 70 might also control operation of the fractionating unit 60 (e.g. in conjunction with data received from the detector 50) and provides data back.

[0035] Fig. 2 schematically illustrates a typical embodiment of the detector 50. A light source 200 emits a light beam 210 through the sample fluid to detect, which might be conducted through a flow cell 220. Optical elements 230 and 240 might be used for directing the light beam before and after the passing the flow cell 220. After passing a slit 250, the light beam 210 is diffracted by a grating 260, and the diffracted partial beams 270 hit a photo detector 280 (e.g. a PDA) in different angles dependent on the wavelength of such partial beam. Further shown in Fig. 2 is a filter 290, which may be used for calibration as discussed in detail later.

[0036] Modeling the detector response Ik(Xo) of an optical spectrometer, such as the detector 50 shown in Fig. 2, at wavelength setting Xo and diffraction order k results in integral Equation (1): max (t0,k) 1k(AO) = $T(A)L(A)Ek(2)r(A)S(2O,k2)d2 (1) min (2u0,k) where T(X) is sample transmittance, L(X) intensity of the light source, Ek(X) is the grating efficiency of diffraction order k, r(?)the detector responsivity and S(Xo, X) is the normalized slit function at wavelength setting X. [0037] The integration range in Equation (1) is given by 20,k)=)0/k-SBW 1k max(Ao)2o31c (2) where SBW is spectral bandwidth of the spectrometer.

[0038] As all terms in Equation (1) are continuous with values greater than zero inside integration range, thus according Mean Value Theorem of integration Equation (1) can be factorized resulting in kR)) = T(2l)xk(Ao) (3) where the partial response of order k and without sample (i.e. T = 1) is given by 2max (o,k) Xk(A) = (4) min (O") [0039] In Equation (3) for X1 the relation Xmin(Xo, k) «= Xi «= Xmax(Xo, k) holds and as T(X) is a slowly varying function within optical band pass, it is well approximated by Xi = X01k in the following.

[0040] As the total detector response y(X) of all diffraction orders present is the linear superposition of all fractional responses Ik(X) contributing, it finally results in: kinax () y)= T(/k)xk)+n(2) (5) [0041] Summation in Equation (5) runs over all orders k = 1 up to kmax(Xo) which is the index of maximum diffraction order present at wavelength X0 and n(X) is an additive perturbation term due to noise.

[0042] Maximum diffraction order kmaxtO be considered for X is given by:

A

kmax(A)=floor( ) (6) blow [0043] In Equation (6) the floor(x) operator yields greatest integer value x while XO is minimum value of lamp spectrum i.e. smallest wavelength entering the spectrometer.

[0044] Introduction of response ratios Rk(X) for k = 2... kmax(X) -to be established during individual calibration of the spectrometer 50 and eventually stored e.g. in instruments non-volatile memory for later use -according Rk(A)=xk(kA)/xl(A) (7) allows for compensation of high orders by recursive spectral decomposition I1()=y()-Rk(/k)Il(A/k) (8) k=km (A) as values of 11(X/k) in Equation (8) can be obtained from uncorrected total response y(XIk) which is undisturbed by higher orders, if for the maximum wavelength, Ahj9h, to be corrected, Ah9h < 6 * A10 holds and if decomposition proceeds from kkmax... k2.

Otherwise the correction needs iterations between orders in order to correct y(2Jk) before further usage.

[0045] Determination of response ratios Rk(X) according Equation (7) for the calibration requires knowledge of xk(?) which is possible utilizing different well known inverse-problem methods. As an example a spectrometer of spectral range 185.. .640 nm is considered together with a light source of lower wavelength limit XO =185nm and maximum wavelength Ahjgh = 640nm <6 * = 111 Onm, therefore the correction is possible. According to Equation (6) we need to deal with diffraction up to 3rd order.

[0046] Calibration of compensation model using M > kmax intensity spectra measured using M-1 optical filters 290 (see Fig. 2) of known transmission Tm(X), m = 2.. .M and one so-called Blank spectrum without filter for every wavelength X results in an over-determined system of M sets of calibration scans ym(2) together with related variance cm(2)2 and may be written according to Equation (5) in matrix form 1 1 1 n1(2u) y2) T2(A) T2(2u/2) T2(A/3) x1(2) n2(2) (8) * x2) + x) YM('2) TM) TM/2) TM/3) [0047] Using parameter estimation terminology the total response vector or observable y represents the measurement of Tx subject to random effects n so that y=Tx+n (9) [0048] The estimated values of x will not, in general, be identical to the "true" for -10-two reasons: a) measurement uncertainties, and b) modelization imperfections. For this reason, it is generally not possible to solve inverse problems properly without consideration of both.

[0049] Estimation methods differ in whether or not including a priori information on model (i.e. design matrix T) and parameter x. A priori information shall mean information that is obtained independently of the results of measurements. A priori knowledge regarding model imperfection, for example, is introduced by uncertainties Tm(2) of respective Tm(A)'s for error propagation purpose.

[0050] Introduction of a priori knowledge allows for application of Maximum a posteriori Likelihood (MAP) methods for estimation of x with the drawback of being non-linear requiring e.g. Monte-Carlo methods for solution.

[0051] It shall be assumed perfect knowledge of design matrix T and no reliable prior knowledge of the value and statistics of x. Measurement of y also is subject to uncertainties which are managed using mean values of several measurements of y together with respective variances by the covariance matrix Cy of which. Given this information, x of Equation (9) is estimated with maximum likelihood by Linear Gauss-Markov problem r -1 mm -(v-Tx) C (v-Tx) y * X (10) the well known solution of which is given by = (TTC T)'TTC y -V (11) while uncertainty of x is C = (TTC T)' X (12) [0052] Determination of x now allows for calculation of Rk according Equation (7) which in turn using recursion of Equation (8) enables order compensation and recovery of pure first order intensity spectrum.

[0053] Example intensity spectra are depicted in Fig. 3, while Fig. 4 shows typical Response Ratios of example detailed above. Fig. 5 presents an exemplary sample spectrum before and after order compensation. -12-

Claims

CLAIMS1. An method of deriving a signal output from an optical spectrometer (50) comprising a diffraction grating (260), comprising measuring a photo current intensity, and subtracting spectral intensity contributions of higher orders from the measured photo current intensity.
2. The method of the preceding claim, comprising measuring the photo current intensity at a position in the spectrometer corresponding to an expected wavelength diffracted by the grating.
3. The method of any of the preceding claims, comprising measuring the photo current intensity at a plurality of positions in the spectrometer, each corresponding to an expected wavelength diffracted by the grating.
4. The method of any of the preceding claims, wherein subtracting spectral intensity contributions of higher orders from the measured photo current intensity comprises subtracting spectral intensity contributions of orders greater than one from the measured photo current intensity.
5. The method of any of the preceding claims, wherein the spectral intensity contributions of higher orders to be subtracted are derived by summing the spectral intensity contribution of each higher order.
6. The method of the preceding claim, wherein the spectral intensity contribution of each higher order is determined by the spectral intensity contribution of the first order corrected by a correction term.
7. The method of the preceding claim, comprising -13-a plurality of correction terms, each for a different wavelength corresponding to a respective position in the spectrometer.
8. The method of the preceding claim, wherein the correction term for each wavelength represents a response ratio of intensity of order k to intensity at first order at this wavelength.
9. The method of claim 7 or 8, wherein the correction term for each wavelength has been derived from calibration measurements of the spectrometer, each calibration measurement being executed with a different filter having a substantially known wavelength transmission characteristic.
10. The method of any of the preceding claims, wherein the signal output 11(A) for a wavelength A is derived from the measured photo current intensity y(A) by the formula 11(A) = y(A)-Rk(A/k)Il(A/k) k=km (k) wherein k is the diffraction order, and Rk is a response ratio of an intensity at the wavelength A to an intensity at first order derived from previous calibration of the spectrometer, and 11(A/k) is the measured photo current intensity at A/k.
11. The method of any of the preceding claims, wherein subtracting of the spectral intensity contributions of higher orders from the measured photo current intensity comprises mathematically subtracting a value of the spectral intensity contributions of higher orders from a value of the measured photo current intensity.
12. A software program or product, preferably stored on a data carrier, for controlling or executing the method of claim 1 or any of the above claims, when run on a data processing system such as a computer. -14-
13. A data processing unit (70) for deriving a signal output from an optical spectrometer (50) comprising a diffraction grating (260), the data processing unit (70) comprising means for receiving a measured photo current intensity, and means for subtracting spectral intensity contributions of higher orders from the measured photo current intensity.
14. A fluid separation system (10) for separating compounds of a sample fluid in a mobile phase, the fluid separation system (10) comprising: a mobile phase drive (20), preferably a pumping system, adapted to drive the mobile phase through the fluid separation system (10), a separation unit (30), preferably a chromatographic column, adapted for separating compounds of the sample fluid in the mobile phase, a detector (50) adapted to detect separated compounds of the sample fluid, and a data processing unit (70) according to claim 13 adapted to process data received from the fluid separation system (10).
15. The fluid separation system (10) of the preceding claim, further comprising at least one of: a sample injector (40) adapted to introduce the sample fluid into the mobile phase; a collection unit (60) adapted to collect separated compounds of the sample fluid; a degassing apparatus (27) for degassing the mobile phase. -15-