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Citation: Salim, S. G. R., Fox, N. P., Hartree, W. S., Woolliams, E. R., Sun, T. & Grattan, K. T. V. (2011). Stray light correction for diode-array-based spectrometers using a monochromator. Applied Optics, 50(26), pp. 5130-5138. doi: 10.1364/AO.50.005130

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Stray light correction for diode-array-basedspectrometers using a monochromator

Saber G. R. Salim,1,2,3,* Nigel P. Fox,2 William S. Hartree,2 Emma R. Woolliams,2

Tong Sun,3 and Kenneth T. V. Grattan3

1National Institute of Standards (NIS), Tersa Street, El-Haram, P.O. Box 136, Giza 12211, Egypt2National Physical Laboratory (NPL), Hampton Road, Teddington, Middlesex, TW11 0LW, UK

3City University London, Northampton Square, London, EC1V 0HB, UK

*Corresponding author: saber.salim@nis.sci.eg

Photodiode-array-based spectrometers are increasingly being used in a wide variety of applications. However, the signal measured by this type of instrument often is not what is anticipated by the user and is often subject to contamination from stray light. This paper describes an efficient and low-cost stray light correction approach based on a relatively simple system using a monochromator-based source. The paper further discusses the limitations of using a monochromator instead of a laser, as used by previous researchers, and its impact on the quality of the stray light correction. The reliability and robustness of the stray light correction matrix generated have been studied and are also reported.

1. Introduction

A photodiode-array-based spectrometer can be de-fined as a dispersive instrument with multiple opti-cal sensors that enables simultaneous acquisition ofthe radiant flux over a particular spectral range [1].These instruments are in general characterized bytheir small size, light weight, and low cost. In addi-tion, they have the key advantage of capturing aspectrally resolved signal over a wide spectral rangein a very short time compared to many mechanicalscanning spectrometers. This has led to their wide-spread use in applications where signals are low, un-stable, or short lived. Diode array spectrometers arebecoming the preferred tool for many applicationsusing optical radiation, for example, in remote sens-ing, spectroscopy, astrophysics, analytical chemistry,health, and process control [2–5].

Although such spectrometers have many ad-vantages, they almost always suffer from straylight—arising from situations where the measuredspectrally resolved signal is contaminated with ra-diation of a nominally different spectral content. Awell-designed spectrometer, fittedwith ahigh-qualitydiffraction medium (usually a grating), will minimizestray light, but it rarelywill do so adequately. Furtherimprovement can be obtained by using “cut-on” filters(usually glasses with a spectrally sharp transition be-tween high absorption and high transmittance, e.g.,RG 665 glass from Schott) in front of the array detec-tor to remove higher order diffraction effects. How-ever, even in the best spectrometers, the stray lightvalue measured at any pixel, obtained from a mono-chromatic source of a different wavelength, is of theorder of 10−5 of the true in-band (IB) monochromaticsignal. While small for a monochromatic source, thisvalue can be a serious problem when a broadbandsource is being measured, as each “wavelength”emitted by the source produces stray light at a levelof 10−5 at each pixel, results in a cumulative effect,

whichhasa significant impact on the final signalmea-sured. This issue can be an even greater problem forany part of the spectrum where the desired signal isrelatively weak, e.g., the blue for an incandescentlamp as compared to the red, for example.

The responsivity of a diode array spectrometer isusually obtained by calibration against a referencestandard source, such as a tungsten lamp of knownspectral distribution. It is subsequently used to detectradiation from sources or surfaces with differentspectral distributions, such as oceans, sky, and landsurfaces and sources such as lasers or LEDs. Becauseof the spectral mismatch between the calibrationsourceand the sourceunder test, the stray light signalis not canceled out by a simple substitution process.This limits the accuracy and reliability of spectralmeasurements carried out using an array spec-trometer. It is thus essential that the stray lightperformance of such instruments is assessed prop-erly for each application, particularly for thoserequiring high accuracy and where necessary andpossible, corrections for the presence of stray light aremade.

2. Sources of Stray Light insidean Array Spectrometer

Ideally, each pixel in an array spectrometer shoulddetect only the radiation with a spectral contentcharacterized by those wavelengths directed to it bythe dispersing element, without sensing any contri-bution from light at any other wavelengths. In prac-tice, there is always some response due to otherwavelengths (i.e., what is termed “stray light”) thatideally should not be present but is. The majorsources of stray light inside diode array spectro-meters can be summarized as follows:

i. Scattered light from the internal wallsand input optics of the spectrometer. Light thatdeviates from the desired optical path and light fromnegative, zero and higher orders can be reflected ontothe array detector from the internal walls or othercomponents of the spectrometer.

ii. Dispersive element, usually a diffractiongrating.Diffraction grating limitations are more ap-parent in photodiode array spectrometers than inmechanical scanning spectrometers: higher orderdiffraction signals “pollute” the desired first-orderdiffraction, and ruling imperfections in the gratinggrooves and coatings may lead to further scatteringeffects [6]. In addition, “cut-on” filters are used infront of the array elements to eliminate higher orderdiffraction signals, but these filters themselves be-come sources of stray light.

iii. Interreflections. Some light is always re-flected by each optical detector element onto otherparts of the spectrometer. If cut-on filters are used,some of this reflected light will be rereflected backonto the sensor or its neighboring pixels. This istermed “near-field stray light” and appears as a“hump” near the profile of a monochromatic light

source. This near-field signal can be quite significant,as observed by Zong et al. [7].

iv. Light coupling. Design constraints of thespectrometer, particularly related to the way thatlight is coupled into it, may also be a source of straylight. This may occur, for instance, when using a fiberwith a larger numerical aperture (NA) than that spe-cified by the design increases stray light levels.

3. Existing Stray Light Correction Methods

Several approaches have been suggested to evaluateand correct for the spectral effects of stray lightin diode array spectrometers. One such approach,proposed by Brown et al. in 2003 [1], depends oncharacterizing the slit scattering function (SSF) (pro-posed by Kostkowski [8]). The SSF is commonly usedfor stray light evaluation in mechanical scanningspectrometers, where the monochromator is held ata particular wavelength setting then illuminated bya series of monochromatic wavelengths.

Another more comprehensive (and relatively sim-ple approach) has been proposed by Zong et al. [7].The method uses a spectrally tunable laser sourceto measure the full spectrometer response for differ-ent monochromatic input wavelengths. At eachwavelength (λj), the spectrometer has a spectral linespread function (LSF) denoted by f LSF, which repre-sents the response of each pixel to this wavelength.Because the incident light in such a case is mono-chromatic, any response at pixels outside the IBregion, as detected by the spectrometer, can be con-sidered as stray light. This stray light signal can beevaluated by dividing the response at each pixel i bythe integration of the IB signal after normalizing thevalue of f LSF.

The resultant function is called the spectral straylight distribution function (di;j), and this can be ex-pressed as [7]

di;j ¼f LSF;i;jP

i∈IBf LSF;i;j

; i∉IB; ð1Þ

where di;j is the spectral stray light signal at pixel idue to a monochromatic light that shows its maxi-mum at pixel j. An n × n stray light distributionmatrix (D) can be formed by populating the matrixwith the individual elements, di;j.

When light from a broadband source illuminatesthe photodiode array, the measured signal (Ymeas)can be expressed as the sum of the signal for no straylight (YIB) plus the contribution of the stray light tothis signal:

Ymeas ¼ YIB þD · YIB ¼ ½1þD�YIB ¼ AYIB; ð2Þwhere A is called the square coefficient matrix. Insuch a case, the correction obtained by Zong et al.[7] is given by

YIB ¼ A−1Ymeas ¼ CYmeas; ð3Þ

where C is called the stray light correction matrix,which is the inverse of A.

In practice, the stray light distribution matrix (D)can be obtained from knowledge of a reasonable sub-set of the elements, di;j measured at different wave-lengths across the spectral range of the spectrometer.The remainder of the n number of columns can beinterpolated and, with care, extrapolated.

In the work carried out by Zong et al. [7], a tunablelaser was used to determine the spectrometerresponse to a set of wavelengths across its range ofoperation to obtain the inputs for the matrix D.

The work carried out and reported in this paperhas aimed to demonstrate how this approach couldbe further simplified through the use of monochro-mator-generated radiation.

4. Monochromator-Based Correction

Unlike spectrally tunable lasers, monochromatorsare widely available at relatively low cost and areeasy to use. They are readily accessible, not only tonational metrology institutes but also to commercialorganizations. A monochromator-based approachhas previously been implemented, as presented byLenhard et al. [9], but this paper explores this con-cept in significantly more detail. While monochro-mators have a number of operational advantages,they also suffer from some issues that may limit theoverall performance achievable, e.g., the sourcebandwidth, the output radiation levels, and the pre-sence of inherent stray light. There is an interrela-tionship between these factors; for example, outputlevels can be increased by using larger bandwidthsbut this, of course, compromises spectral resolution.This work reviews these limitations and their impacton the correction obtained.

A. System Bandpass Function

1. Calculating the System Response Function

When a laser source is used, the overall systembandpass function will be essentially that of the spec-trometer. For a monochromator-based method, thesystem bandpass function is given by a combinationof the monochromator and spectrometer bandpassfunctions.

This interaction between the diode array spectro-meter and monochromator was studied using a sim-ple model that allowed an estimation of the shape ofthe overall system bandwidth and the signal level.The spectrometer bandpass function was taken to bethat measured using an He–Ne laser at 632:8nm,and the monochromator bandpass function was as-sumed to be a triangular function of 1nm FWHM.The bandpass functions of the spectrometer andmonochromator were normalized to unity at theirmaxima, as shown in Fig. 1.

Each point on the monochromator bandpass func-tion was assumed to result in the same spectrometerbandpass profile as if it were a laser, i.e., being

equivalent to the output of the He–Ne laser, as shownin Fig. 2.

The spectrometer signal at a particular pixel isthus the sum of the pixel responses to each pointon the monochromator bandpass function. The dark-est (black) line in Fig. 3 shows the combination of themonochromator and the spectrometer bandpasses,as calculated by the model. The calculated resultantsystem bandpass (∼1:6nm FWHM) is slightly widerthan the spectrometer bandpass function obtainedusing the laser (∼1:2nm FWHM) and the monochro-mator bandpass profile (∼1nm FWHM).

It should be noted that this approach can becreated by convolving the monochromator spectrom-eter bandpass function xðnÞ and the spectrometerbandpass function, as described elsewhere in the lit-erature [10]. The convolution YðnÞ can simply bewritten as

YðnÞ ¼ xðnÞ � yðnÞ ¼Xn

i¼−n

xðiÞyðn − iÞ; ð4Þ

where n is the pixel number and i is an integer in thiscase. This equation is numerically intensive to eval-uate; therefore, it can be converted into a multiplica-tion by using a FFT such as

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Fig. 1. Spectrometer bandpass and themonochromator bandpassfunctions—the X axis is replaced by the pixel order inside thearray detector rather than the wavelength.

Fig. 2. Response of the spectrometer to every point on the mono-chromator bandpass function.

Y ¼ IFFTðFFTðxÞFFTðyÞÞ: ð5ÞAlthough this approach is straightforward, it may

be necessary to apply windows (e.g., Hanning) to thefunctions, which may affect the profile of the band-width in the final result. In addition, it may be re-quired to remesh the functions so they are on thesame grid.

The applicability of the model was confirmed ex-perimentally by measuring the bandpass functionof the instrument using the system shown in Fig. 4.The measured bandpass profile was found to be veryclose to that calculated by the model (the dark grayline shown in Fig. 3).

Even with wider monochromator bandpass values(of 2 and 3nm—these are wider than the spectro-meter bandpass), the system bandpass was foundto be only slightly larger than the monochromatorbandpass. However, the best results were obtainedexperimentally with the slit width of the monochro-mator set to be as narrow as possible, to make thesystem bandwidth and spectrometer bandwidth veryclose to each other in value—although there will be acompromise in this choice when the signal levelsare small.

2. Bandpass Profile and Stray Light Calculations

The chosen width of the “IB” region affects the resul-tant stray light correction matrix, as the spectro-meter response at each pixel element is divided bythe integration over the IB region. The width of

the IB region increases at higher wavelengths dueto the increased bandwidth of the spectrometer, alsothe level of the near-field stray light has been foundto vary across the spectrometer spectral range.Therefore, it is seen as important to take these con-siderations into account when defining the IB region,and this was done.

B. Stray Light Signal inside the Monochromator

Unlike a laser, monochromators will have their ownstray light. Therefore, the stray light correctionshould be carried out using a double grating mono-chromator in which the associated internal straylight is typically of the order of ∼10−6. Ideally, the re-sidual stray light should be completely preventedfrom entering the spectrometer, but this is not easilyachieved in practice. However, the effect of this smalllevel of monochromator-based stray light is thoughtto be negligible in the operation of the system.

5. Experiment and Setup

The experimental system used in this work, shown inFig. 4 and based largely on the NPL spectral respon-sivity facility, was set up to conduct the stray lightcorrection. An argon arc lamp, which has a relativelyhigh spectral emission (especially in the UV region),was used. The light emitted from the lamp was fo-cused onto the entrance slit of a double monochroma-tor using a convex mirror.

The monochromator output light was directed byconvex and plane mirrors to the lens attached to theSMA connection of the spectrometer fiber. This lensis used to define the field of view of the spectrometer.The f number of the beam could be adjusted using afield stop located beyond the exit slit of the mono-chromator. During the measurements carried out,care was taken to ensure that the light overfilled thelens aperture to mimic normal operation. The spec-trometer fiber lens was aligned to maximize thecollection of light; this occurred when the spot (repre-senting the optical beam) on the plane mirror waslocated in the field of view of the fiber lens.

Higher order diffraction was suppressed duringthe spectral scan of the monochromator by the useof cut-on filters inside the monochromator facility,operating at wavelengths of 390 and 670nm. Thisin turn ensured a further reduction of the stray lightinside the monochromator.

Below a wavelength of 650nm, gratings with ablaze of 500nm were used, while for longer wave-lengths, gratings with a blaze of 700nm wereemployed in this work. The lamp current was opti-mized to ensure that a reasonable signal level wasobtained over all the spectral regions studied.

The spectrometer used for the tests carried outis a commercial instrument that employs a high-sensitivity miniphotodiode array manufactured byHamamatsu (type C10083CAH), and the array de-tector is a 2048 pixel element back-thinned siliconphotodiode array. The spectrometer covers the spec-tral range from 208 to 1078nm; as this also covers

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Fig. 3. Convolution of the spectrometer and the monochromatorbandpass functions: model and experimental results.

Argon arc lamp

Doublemonochromator

Convex mirror

Mirror

Field stop

Spectrometer fiber head

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Shutter

Light tight enclosure

Fig. 4. Monochromator-based stray light correction system.

most of the silicon detector responsivity range, errorsdue to stray light from wavelengths outside thisrange were considered negligible. The analog-to-digital converter used with the spectrometer has16 bit resolution, which means that one single countis 1:52 × 10−5 of the maximum number of counts(65,536). To detect stray light values less than thislevel, the spectrometer output signal was sampled1000 times, ensuring sufficient resolution in thestray light measurement (i.e., a signal level couldbe obtained to sufficient significant figures) to eval-uate the actual low-level stray light present.

To study the impact of the monochromator band-width on the efficiency of the stray light correctionmatrix, the column vector di;j was evaluated by themeasurements at 555nm, for four different mono-chromator bandwidths (1, 2, 3, and 4nm), and theresults obtained are shown in Fig. 5.

For the bulk of the spectrum, it can be seen thatthe results obtained are nearly identical. However,the use of narrower bandwidths is required to deter-mine the stray light levels at the pixels immediatelyadjacent to the IB region. This means that to obtain ameasurable signal, priority should be given to eitherincreasing the source signal or using a higher in-tegration time, rather than simply using a widermonochromator bandwidth. The monochromator slitwidth was therefore adjusted to give a 1nm band-width, and the lamp power increased to ensure a rea-sonable signal-to-noise ratio was obtained. The samebandwidth was used over the entire wavelength do-main to ensure consistent results for the values givenby di;j.

The nonlinearity performance of the spectrometerhas been found to be affected by using different inte-gration times and different source intensities [11].The impact of these two factors on the values ofthe spectral stray light distribution function hasbeen studied. The effect of using different integrationtimes was studied at a wavelength of 850nm, whereintegration times of 10, 20, and 30ms were used totune the spectrometer signal level from a maximumof 20,000 counts to nearly 60,000 counts, while keep-ing a fixed source intensity. No noticeable differencesin the resultant values of di;j were observed, other

than obtaining improved noise characteristics for theuse of higher integration times. The effect of usingdifferent source intensities was studied at a wave-length of 550nm, while keeping a fixed integrationtime. The results of this effect are shown in Fig. 6.The measured stray light was observed to increaseslightly when low signal levels were used, but therewas no noticeable change between the stray lightlevel observed at signal levels of 40,000 and 60,000counts. This can be explained in terms of the relativeresponse of each pixel, which is slightly higher at lo-wer signal levels. The effect is generally small, butto ensure consistency, all subsequent analysis wasdone with signal levels greater than 20,000 counts.

6. Results

A. Spectral Stray Light Distribution Function

The spectrometer signal wasmeasured at 5nm inter-vals over the whole spectral range. At each measuredwavelength, a corresponding dark signal was also re-corded. The dark-corrected spectrometer signal wasnormalized to the maximum level to obtain the valueof f LSF. Although all the spectral LSFs were mea-sured at high integration times, some pixels gave ne-gative values as a result of noise in the dark and lightsignals. However, the number of such pixels was, ingeneral, small, as were the values of the (negative)numbers they gave. The values of f LSF have been cal-culated as a result of repeated measurements at awavelength of 550nm, following which the results ob-tained were compared. It was noticed that when theexperiment was repeated, these negative valueswere not repeatable for these specific pixels, therebyconfirming that these results were simply due tonoise. Ideally, noise with both signs (negative andpositive) should be removed from the “real” signal;however, it is not possible to distinguish noise witha positive sign from the stray light signal. Therefore,it was decided in the analysis to replace any negativevalues obtained with a zero, as they did not representa real stray light signal. Further justification forthis was that, in addition, leaving the negative val-ues may result in “undercorrecting” the stray light

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Fig. 5. Spectral stray light distribution function for differentmonochromator bandwidths.

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signal. It is important to note that a “rolling average”signal to reduce noise should be avoided, as thiswas found to result in poorer correction than theapproach suggested.

The IB region was determined manually by care-fully selecting the pixels defining the “wings” beforeintegration. The spectrometer signal at each pixelwas then divided by the integral of the IB signalto obtain the values of di;j required.

The values of f LSF obtained showed no signal forinput wavelengths below 270nm despite a signifi-cant output from the monochromator (as measuredby a reference photodiode). This lack of a spectro-meter response was attributed to the very poor trans-mittance of the lens in this region. As a consequence,zero values for f LSF were used in the spectral rangebelow 270nm.

With input wavelengths from 270 to 340nm, therewas some noticeable second-order diffraction light,as shown by di;j and illustrated by the black line inFig. 7. This second-order diffraction was not visiblefor longer wavelengths. The stray light levels werealso higher for wavelengths corresponding to pixelslocated at both ends of the spectrometer detectorarray than for those pixels in the middle.

By comparison to Fig. 7, Fig. 8 shows an increasedIB width at wavelengths around 500 and 700nm dueto an increase in the near-field stray light signal. Afiner scanning of the input wavelength, at 1nm inter-vals, was used to examine thoroughly the stray lightlevels in these regions. Figure 9 shows the values ob-tained for f LSF for inputs at wavelengths of around507.6 and 709:5nm (corresponding to pixel numbers753 and 1225), which represent the observed centerof this increased IB width.

According to the manufacturer’s literature, thereare three cut-on filters, which are used to blockthe higher order diffraction signals (these are typesWG305, GG475, and RG665). The boundaries be-tween the filters occur at pixels that correspond towavelengths of 507.6 and 709:5nm. This is likelyto result in an increase in the scattered light inthe region of these pixels and hence the broadeningin the stray light profile. The presence of these filtersalso explains the reduced signal level in the vicinity

of these wavelengths when the spectrometer is ex-posed to light from a broadband source.

Because of this, the spectral ranges around 507and 709nm were measured at input spectral inter-vals of 1nm so as to show the exact spectral distribu-tion of the stray light around those pixels.

B. Stray Light Correction Matrix

The stray light correction algorithm used is requiredto ensure that it not only provides a good estimate ofstray light but also that it does not alter any othercharacteristic of the spectrometer under test. Forexample, a poor correction matrix may lead to a de-crease in the apparent signal-to-noise level of thespectrometer. To test the reliability of the stray lightcorrection matrix, measurements of two stray lightsensitive sources were analyzed, while modelingwas also performed to understand the sensitivityto noise.

1. Performance of the Stray Light CorrectionMatrix

Having calculated di;j at the pixels where measure-ments were made, values for di;j in other regionswere interpolated using a MATLAB routine withinthe stray light correction software [12]. To deliveran accurate near-field correction, di;j was interpo-lated along the matrix diagonals (parallel to thematrix main diagonal).

The stray light distribution matrix is shown inFig. 10. The figure further shows an increased near-field stray light signal in the IR region. The second-order diffraction stray light is also shown in thefigure at the shorter wavelengths.

The effectiveness of the stray light correctionmatrix to achieve a suitable correction for the straylight was tested using two sources: a low argonpressure lamp and a tungsten halogen lamp, withthe output filtered with a 630nm cut-on filter. Ineach case, the measured signal was normalized tothe maximum before the stray light correction wasapplied.

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Fig. 7. Spectral stray light distribution function (di;j) at differentinput wavelengths.

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Fig. 8. Spectral stray light distribution function (di;j) at 507.6 and709:5nm input wavelengths.

The cut-on filter signals before and after correctionwas applied are shown in Fig. 11 for the filtered lampand Fig. 12 for the spectral lines of the argon lamp.Figure 11 shows a signal level <10−6 below the filtercut-on wavelength and a reduced signal level in theIR region where stray light also would be expected.Figure 12 shows the use of the correction has re-sulted in a nearly ideal shape of the spectral profileof the selected argon lines. In addition, the stray lightin the far field has also been reduced by nearly 1order of magnitude.

Having obtained these high-quality results, thereliability of the correction matrix when using asmaller number of input data points was evaluated.In this example, the resolution of the scanning ofthe input wavelength was reduced to 20nm inter-vals, contrasting with the 5nm interval previouslyused. For the highly sensitive regions at wavelengthsaround 507 and 709nm, data taken every 3nm(contrasting with the previous 1nm) were used.The new stray light correction matrix showed iden-tical results to those obtained previously with thewhole set of measured points. Thus, relatively few

characterization wavelengths are required for thedetermination of an accurate stray light correctionmatrix; however, where there are anomalies, e.g.,where cut-on filters may overlap, it is clear that amore detailed spectral evaluation is required.

2. Matrix Sensitivity Coefficient

For a linear algebraic system, such as that repre-sented by Eq. (2), the sensitivity of the solution (YIB)to changes in the measured signal given by the spec-trometer (Ymeas) and the square coefficient matrix (A)can be studied using the condition number of thesquare coefficient matrix A [13]. The condition num-ber is defined as the product of the norm of A and thenorm of A−1. This number is always greater than orequal to 1. If it is close to 1, this means that the ma-trix inverse can be calculated with high accuracy;however, if it is much larger, this means that the ma-trix inverse is “ill-conditioned” and cannot be calcu-lated accurately. A large condition number will meanthe correction is more sensitive to measurementerrors in the determination of the stray light cor-rection matrix, and less able to reproduce small

Fig. 10. 3D stray light distribution matrix obtained by using di-agonal interpolation.

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Fig. 11. Cut-on filter signal before and after stray light correc-tion.

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variations in the spectrum being recovered. A condi-tion number equal to infinity means that the matrixis noninvertible.

For the correction of the spectrometer used in thiswork, the condition number of the square coefficientnumber was found to be 1.86, which is somewhathigher than the value 1.07 obtained by Zong et al.[7]. This is likely mainly to be due to the fact that thisstray light correction matrix was zero for inputwavelengths below 270nm (due to the lens transmit-tance), and, in addition, the signal also had relativelyhigh stray light signals at longer wavelengths.

As the condition number was somewhat higher, itwas considered necessary to check the sensitivity ofYIB to variations in Ymeas. A spectral structure of per-iodically oscillating amplitude of �0:5% of the valueof Ymeas was deliberately added to Ymeas for a tung-sten lamp signal, and YIB was calculated before andafter adding this periodic oscillation. The differencebetween the two output spectra showed the sameperiodic spectral structure with a corresponding os-cillating amplitude of �0:56% at 400nm increasinggradually to�0:72% at 1078nm. In addition, randomnoise of relative amplitude within �0:5% was addedto Ymeas, and YIB was recalculated before and afteradding this random noise. The difference betweenthe two output spectra was found to be similar to thevalues observed when adding the periodic oscillationto Ymeas. These tests show that the stray light correc-tion matrix causes only minor distortions to smallchanges in the spectrum being measured, and thecondition number for this spectrometer is acceptable.

7. Summary

This paper has shown that one of themajor sources ofuncertainty that limits the performance of the diode-array-based spectrometers—stray light—can be ac-curately corrected with a relatively fast procedureusing cheap and readily available monochromators,with results comparable to those obtained usingtunable lasers. The work reported in this paper hasdescribed the sensitivity of the stray light character-ization method to both the measurement system and

subsequent mathematical evaluation processes. Italso has shown that the number of measurementpoints needed for the correction can be reduced signif-icantly without impacting on the overall performanceof the system.

The application of these procedures could be usedto make it possible for low-cost spectrometers of thisnature to move from being useful spectral monitoringdevices to high-performance optical spectroradiom-eters capable of transforming optical radiation mea-surement in a wide variety of applications thatcurrently are limited by the achievable accuracy orby the lack of flexibility arising due to large immova-ble instrumentation.

The authors would like to acknowledge the contri-bution of Ian Smith of the NPL Scientific ComputingTeam for his help in writing the MATLAB code fordiagonal interpolation and Andrew Levick for hisvaluable comments. One of the authors (S. Salim)gratefully acknowledges the award of a fellowshipfrom the Cultural Affairs & Scientific Missions Sec-tor, Egypt. This work was supported by the NationalMeasurement Office of the UK Department “Busi-ness, Innovations, and Skills (BIS).”

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Fig. 12. Performance of the stray light correction matrix at the 407.2, 706.7, and 1025:4nm argon lines.

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