Complete Theoretical Treatment of the Transmittance RatioUltraviolet/Visible Spectrophotometric Stray Radiant EnergyTest Method

PADDY FLEMINGInstitute of Technology, Sligo, Ireland

This paper develops the theoretical basis behind the transmittance ratio

test method for determining the relative stray radiant energy level in a

double-beam dispersive spectrophotometer so as to allow for the non-

transparency of a test solution towards the stray radiant energy for all

sample beam-to-reference beam cuvette path length ratios. Non-trans-

parency is defined as the transmittance of the reference beam solution,

whose monochromatic absorbance is unity, towards stray radiant energy.

The proposed method has the same concentration absorbing sample

placed in the beams of the scanning spectrophotometer, the sample-beam

cuvette being a known factor longer than the reference-beam cuvette.

While scanning towards shorter wavelengths, an apparent differential

absorbance Mielenz peak is recorded. An exact formula is derived in this

paper relating the relative stray radiant energy level to the Mielenz peak

absorbance, to the known cuvette path length ratio, to the observed

monochromatic absorbance of the test sample at the Mielenz peak

wavelength, and to the sample transmittance towards the stray radiant

energy. Sample transmittance towards stray radiant energy cannot be

determined experimentally. However, the derived formula only allows the

other experimental quantities to tie in together for a single numerically

calculated value for the sample-transmittance towards stray radiant

energy. The formulae are tedious to derive and cumbersome to handle,

but their application is facilitated greatly by a Microsoft Office Excel 2007

spreadsheet. The test method was applied to an ultraviolet–visible (UV/

VIS) scanning spectrophotometer at nine wavelengths in the range 713 .

k (nm) .; 649 for a sample beam-to-reference beam cuvette path length

ratio of 10 mm/5 mm and using blue food dye (E123) as the test material.

Sample transparency to stray radiant energy fluctuated in wavelength

between 0.819 and 0.948, while the relative stray radiant energy level

fluctuated between 1.283 3 10�3 and 2.516 3 10�3. The investigation was

repeated at 665.6 nm for all fifteen sample beam-to-reference beam

cuvette path length ratios, which it was possible to establish using

combinations of quartz-glass cuvettes with path lengths of 100, 50, 20, 10,

5, 2, and 1 mm. The sample transparency to stray radiant energy at 665.6

nm was 0.95 6 0.5, while the relative stray radiant energy was (1.5 6 0.33)

3 10�3.

Index Headings: Ultraviolet–visible spectrophotometer; UV/VIS spectro-

photometer; Stray radiant energy; Stray radiant energy sample trans-

mittance; Transmittance ratio; Cuvette path length ratio.

INTRODUCTION

Many modern dispersive spectrophotometers with theassistance of double monochromation specify a relative strayradiant energy (SRE) level of ,10�6. The ultraviolet–visible–near-infrared (UV/VIS/NIR) Shimadzu UV3600, whose absor-bance range is from�6 AU toþ6 AU, claims to have a relativeSRE level of 5 3 10�7 (0.00005%) at 340 nm when usingNaNO2 as the test solution. This relative SRE level means thatthe observed absorbance deviates by ,1% from the mono-chromatic absorbance until a value of 5.4 absorbance units is

reached. The routine testing and verification of such a low SRElevel challenges existing sample-based test methods to theirlimits. SRE, being composed of wavelengths outside thenarrow band transmitted by the slit-width setting of themonochromator, contributes to the overall photo-signal in acomplicated way owing to the sensitivity of the detector beingwavelength dependent. Optical designers may be interested inthe spectral composition of the SRE emanating as monochro-matic stray light with the intention of tracing its origins so thatoptical components and monochromator design might beimproved so as to minimize the SRE, but analytical scientistshave to live with the total instrument and are more interested inthe lumped effect of all SRE emanating as instrumental straylight. Slavin1 defined relative SRE (s) to be ‘‘the ratio of thesignal (S) produced by the detector for radiation of allwavelengths outside the monochromator spectral slit width tothe total signal (I0) at a particular wavelength setting’’, i.e., s¼S/I0. The absolute amount of SRE present is less relevant thanthe ratio defined by Slavin in determining the effect onabsorbance readings.

Knowles2 identified two fundamental criteria that must befulfilled so as to ensure a good transmittance measurement:

(1) only monochromatic wavelengths reach the detector and(2) absorption of the said monochromatic wavelengths is

solely due to the solute.

Factors that might hinder the fulfillment of criterion (2), beingmultiplicative, are minimized or compensated for by running a‘‘cuvette-blank baseline’’ and need not concern this paper.Stray radiant energy, being additive, is not compensated for byrunning a cuvette-blank baseline and is the principal factoraffecting the fulfillment of criterion (1). SRE arises fromradiation being scattered by imperfections in optical compo-nents and from overlapping diffraction orders in grating-basedinstruments. The definition, origin, effect, determination, etc.,of SRE were reviewed by Fleming3 and Burgess.4

The E 387-04 ‘‘Standard Test Method for Estimating StrayRadiant Power Ratio (SRPR) of Dispersive Spectrophotome-ters by the Opaque Filter Method’’5 betrays, through the use ofthe word ‘‘estimating’’, the approach heretofore to determiningSRE in spectrophotometry. The reasoning proffered is that‘‘SRP test filters always absorb some of the SRP, etc.,’’ so that‘‘this test method underestimates the true SRPR’’. The SRE andSRP terms are synonyms. Fleming and O’Dea6 addressed thisquandary via the direct transmittance spectrometry sample-based test method so that the SRE could be determined ratherthan estimated. Fleming7 generalized the Mielenz et al.8 SREsample-based test method to include the attenuating effect ofthe test sample on SRE but did not furnish a means of applyingthe same. This paper remedies that defect by incorporating the

Received 4 April 2009; accepted 25 June 2009.E-mail: fleming.paddy@itsligo.ie.

1128 Volume 63, Number 10, 2009 APPLIED SPECTROSCOPY0003-7028/09/6310-1128$2.00/0

� 2009 Society for Applied Spectroscopy

transmittance of the test sample towards SRE (i.e., t) into twoseparate exact expressions relating the observed differentialabsorbance of the Mielenz peak (i.e., DAmax) and the relativeSRE level (i.e., s) to A, the separately observed monochromaticabsorbance of the test sample at the Mielenz peak’swavelength, to t, and to a, the sample beam-to-reference beamcuvette path length ratio.

EXPERIMENTAL QUANTITIES

The relative SRE level in a spectrophotometer may bedetermined via the transmittance ratio spectrophotometricmethod of Mielenz et al.8 and Fleming.9 Cuvette path lengthratios of a¼ 10, 5, 4, 2.5, and 2 are used throughout this papervia appropriate combinations of 100 mm, 50 mm, 20 mm, 10mm, 5 mm, 2 mm, and 1 mm quartz-glass cuvettes. Thetransmittance ratio (r) of a sample beam solution whose cellpath length is a times greater than the cell path length of thereference beam solution is given by Fleming:7

r ¼ Tak þ s0taAk

Tk þ s0tAk¼ 10�aAk þ s0taAk

10�Ak þ s0tAkð1Þ

where Tk is the monochromatic transmittance of the referencebeam solution at the set wavelength, s ¼ s0/(1 þ s0) is therelative SRE level, and t is the transmittance of the referencebeam solution of monochromatic absorbance Ak (¼�log10Tk)¼1 to SRE. It may be assumed that s ¼ s0 for all practicalpurposes when s � 1.

If spectrophotometers are operated in the absorbance modethen transmittance ratio becomes differential absorbance andthe measurements may be made either as per Neal10,11 at afixed wavelength and the gradual increase in the differentialabsorbance is achieved through the simultaneous pro-rataincrease in the sample-beam and reference-beam concentrationin a pair of matched quartz glass cuvettes, or as per theproposal of Mielenz et al.8 by the gradual increase in thedifferential absorbance via wavelength scanning through theleading/trailing slope of an absorbing test sample placed in apair of quartz glass cuvettes whose sample beam-to-referencebeam path length ratio is greater than unity. The stated methodsare opposite sides of the same coin. The differential absorbancefor both methods will not increase indefinitely but will peak ata value determined by a, s, and t.

The transmittance ratio function defined in Eq. 1 will have aminimum, rmin¼ q, at a certain monochromatic transmittance,1 . (Tk ¼ s). This ensues because the value for r approachesunity for the extreme monochromatic transmittance values ofTk ¼ 1 and Tk ¼ 0 and providing the sample is transparent toSRE, i.e., t¼ 1. Equation 1 has a transmittance ratio minimum,q, for a¼ 2 and t¼ 1:7 q¼asa�1¼ 2s, and this yields s¼ [(a�1)/(1 – q)](q/a)a/(a�1) ¼ q2/(4 – 4q).

However, the caveat must be stated that the t value, whichwas assumed to be unity when deriving the above equations, islikely to differ from unity.

Applying Eq. 1 to Neal’s method and plotting Fig. 1 for s0¼10�3, a¼ 2, and t¼ 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, and1 reveals that DA (¼�log10r) approaches zero as the extremevalue of Ak (¼�log10Tk) ¼ 0 is approached; DA will have amaximum value of DAmax (¼ �log10q) at some intermediatevalue of Ak, denoted by A (¼�log10s), which depends on s, a(¼2), and t. Further increases to Ak will result in DA decreasingto a minimum value of DAmin . 0 (¼ 0 when t ¼ 1) before

increasing asymptotically with increasing Ak. The linearasymptotes are represented by the equation DA ¼ (�log10t)Ak.When t¼ 0.1, the test sample has the same absorptivity towardsSRE as it has towards monochromatic radiation and the twosources of detected radiation become indistinguishable. Equa-tion 1, as may be seen in Fig. 1, does not yield a DAmax value ora DAmin value for t , 0.4 and a¼ 2 irrespective of the relativeSRE level and, therefore, only t values of 0.4 and greater willbe considered hereafter. The cut-off t value, below whichDAmax is not manifest, for a values . 2 and s¼ 10�3 are pairedas follows a, . t; 2.5, . 0.5; 4, . 0.65; 5, . 0.7; 10, . 0.85.DAmin, although as real as DAmax and containing informationabout the system, will not be considered herein. DifferentiatingEq. 1 with respect to Tk, setting it equal to zero at Tk¼ s andrearranging the terms, gives the quadratic expression

ða� 1Þsa � s�ð1þ a log10taÞtaA � ðaþ log10tÞtAsa�1

�

� s2ða� 1Þðlog10tÞtaþ1s�1 ¼ 0 ð2Þ

If s ¼ 10�A is substituted in Eq. 2 then, with furthersimplification, it becomes

ða� 1Þ � s ð1þ a log10tÞð10tÞaA � ðaþ log10tÞð10tÞAh i

� s2ða� 1Þlog10tð10tÞaþ1 ¼ 0 ð3Þ

Equation 3, being a quadratic in the form as2þ bsþ c¼ 0, maybe solved for s as follows:

s ¼

ðaþ log10tÞð10tÞA � ð1þ a log10tÞð10tÞaAh i

6

�ð1þ a log10tÞð10tÞaA � ðaþ log10tÞð10tÞAh i2

þ 4ða� 1Þ2log10tð10tÞðaþ1ÞA�0:5

!

4 2ða� 1Þlog10tð10tÞðaþ1ÞAh i

ð4Þ

Equation 4, for a ¼ 2, reduces to

s ¼

ð2þ log10tÞð10tÞA � ð1þ 2 log10tÞð10tÞ2Ah i

6

�ð1þ 2 log10tÞð10tÞ2A � ð2þ log10tÞð10tÞAh i2

þ 4 log10tð10tÞ3A

�0:5!

4 2 log10tð10tÞ3Ah i

ð5Þ

Equation 4 does not allow s to be determined in terms of�log10s¼ A even when t is known because A is not observeddirectly in the transmittance ratio spectral scan. The s and tvalues, being fixed at a given wavelength and for a given testsample, require two A values to satisfy Eq. 4 because the 6signs contained therein correspond to DAmax and DAmin,respectively. The þ solution is the more relevant solution andis used in this paper. Substituting Eq. 4 for s into Eq. 1 at rmin¼q for all a and simplifying further gives Eq. 6:

APPLIED SPECTROSCOPY 1129

DAmax ¼ �log10q

¼ �log10

(

tða�1ÞA�

2ða� 1Þlog10tð10tÞA

þðaþ log10tÞð10tÞA

�ð1þ a log10tÞð10tÞaA

6

�hð1þ a log10tÞð10tÞaA

�ðaþ log10tÞð10tÞAi2

þ4ða� 1Þ2log10tð10tÞðaþ1ÞA�

0:5�

4

�2ða� 1Þlog10tð10tÞaA

þðaþ log10tÞð10tÞA

�ð1þ a log10tÞð10tÞaA

6hð1þ a log10tÞð10tÞaA

n

�ðaþ log10tÞð10tÞAi2

þ4ða� 1Þ2log10tð10tÞðaþ1ÞAo

0:5�)

ð6Þ

Eq. 6, for a ¼ 2, reduces to

DAmax ¼ �log10q

¼ �log10

(

tA

�2log10tð10tÞA

þð2þ log10tÞð10tÞA

�ð1þ 2log10tÞð10tÞ2A

6nhð1þ 2 log10tÞð10tÞ2A

�ð2þ log10tÞð10tÞAi2

þ4log10tð10tÞ3Ao0:5

�

4

�2log10tð10tÞ2A

þð2þ log10tÞð10tÞA

�ð1þ 2 log10tÞð10tÞ2A

6nð1þ 2 log10tÞð10tÞ2Ah

�ð2þ log10tÞð10tÞAi2

þ4 log10tð10tÞ3Ao0:5

�)

ð7Þ

The monochromatic absorbance, A (¼ �log10s), of the testsample in the reference beam at the Mielenz peak wavelength,which will be on the leading or trailing slope of a broadabsorbance peak, has to be determined independently of thetransmittance ratio scan. If the experimental values for A and aare inserted into Eq. 6 in the form of a Microsoft Excel 2007spreadsheet, then a unique t value may be readily found tosatisfy the experimental value for DAmax in Eq. 6, therebyallowing Eq. 4 to be solved for s. If it is established

FIG. 2. Nine experimental differential absorbance (DA) versus wavelength(nm) scans obtained using a Shimadzu 160A spectrophotometer for everdecreasing concentrations of Orleans blue food dye (E123) as test material in apair of quartz-glass cuvettes of dimensions 10 mm (sample beam) and 5 mm(reference beam).

FIG. 1. Equation 1 simulated differential absorbance (DA) versus monochro-matic reference beam absorbance (Ak) for a¼ 2, s0¼ 10�3, and t¼ 0.1, 0.2, 0.3,0.4, 0.5, 0.6, 0.7, 0.8, 0.9, and 1.

1130 Volume 63, Number 10, 2009

experimentally that A ¼ 2.369 and DAmax ¼ 2, then Eq. 7 issolved for t¼ 0.75, and inserting t¼ 0.75 into Eq. 5 gives s¼9.75 3 10�5. The resulting value for s will always be greaterthan or at best equal to that calculated via s¼ q2/[4(1� q)] fora ¼ 2 and t¼ 1.

EXPERIMENTAL MATERIALS AND RESULTS

The Mielenz et al.8 transmittance ratio SRE test method wasapplied to a Shimadzu 160A spectrophotometer to give ninedistinct Mielenz peaks in the wavelength range 713 . k (nm). 649 using ever decreasing concentrations of Orleans bluefood dye (E123) as test material in a pair of quartz-glasscuvettes of dimensions 10 mm (sample beam) and 5 mm(reference beam) (Fig. 2). The spectrophotometer was used inthe absorbance mode throughout so that differential absorbancespectra, i.e., DA versus k (nm), were recorded rather thantransmittance ratio spectra. The spectrophotometer had been

base-lined using H2O as the blank. The Mielenz peak, being onthe lead-in edge of the absorbance peak, is blue-shifted fordecreased concentration of the E123 food dye. The absorbanc-es (A1

0 , 0.34) at the Mielenz peak wavelength of eachdilution were determined in a 1 mm quartz-glass cuvette andhence the corresponding reference absorbances in an x mmcuvette may be calculated via A0¼ xA1

0. Hence, an s value maybe calculated via Eqs. 6 and 5. However, A0 is not themonochromatic reference absorbance (A) to be used in Eqs. 5and 6 because A1

0 , A1 due to the small influence that SREexerts at low absorbances. If A1

0 , 0.2, s , 0.01, and t¼1 thenA1¼ A1

0 is a good approximation, etc., or A1 may be calculatedfrom A1

0 and the first estimate of s mentioned above as follows:10�A1 þ stA1 ¼ 10�A 0

1 ð1þ sÞ. An improved s value may nowbe recalculated and iterate the process until the calculated svalue settles down.

Table I records spectrophotometric parameter values basedon the nine Mielenz peaks in Fig. 2, i.e., kM (nm), A, DAmax, t,and s. UV/VIS spectrophotometry being a quantitative method,it is not worthwhile to calculate an average value of eachparameter over the range of wavelengths involved herein aseach wavelength is a stand-alone entity. The transmittance ofthe test sample to SRE and the relative SRE level fluctuateirregularly up and down as wavelength decreases. Thissuggests that the spectral composition of the SRE has a will-o’-the-wisp quality. However, this paper is not so much aboutthe performance of an individual spectrophotometer or a testmaterial as it is about highlighting a method for determiningrather than estimating SRE.

The above exercise was repeated with the Orleans Blue(E123) food dye as a test sample at a single wavelength, i.e.,665.6 nm, for the 15 possible Hellma cuvette combinationratios, i.e., 10 (100/10, 50/5, 20/2, 10/1), 5 (100/20, 50/10, 10/2, 5/1), 4 (20/5), 2.5 (50/20, 5/2), and 2 (100/50, 20/10, 10/5,2/1), using the seven cuvette sizes available. Each cuvette pathlength is specified to within 60.02 mm. The remaining cuvettepath length combinations were not entertained because a ratiosgreater than 10 give DAmax readings exceeding the 2.5 AU fsdof the Shimadzu 160A at the particular wavelength selected.

Figure 3 displays five such Mielenz differential absorbancespectra for a ¼ 10, 5, 4, 2.5, and 2. Table II contains thespectrophotometric parameter values based on thirteen of thefifteen Mielenz peaks recorded. Two Mielenz peaks were justoff-scale, i.e., for the cuvette combinations of 100/10 and 50/5.The average relative SRE level and standard deviation at 665.6nm is (1.5 6 0.33) 3 10�3 and the corresponding average SRE

TABLE I. The relative stray radiant energy levels, determined at nine distinct wavelengths in the range 713 .; k (nm) . 649, are recorded in the finalcolumn for a fixed cuvette path length ratio of a = 10 mm/5 mm = 2.

Mielenz peakwavelength

[k (nm)]

Cuvette path lengthratio (a), 10 (mm)/

5 (mm)Reference

absorbance (A)Mielenz peak

absorbance (DAmax)SRE

transmittance (t)Relative SRE level

[s (310�3]

712 2 1.573 1.236 0.850 1.510704.5 2 1.508 1.196 0.947 1.283696.0 2 1.507 1.182 0.893 1.646688.5 2 1.505 1.167 0.847 1.208684.0 2 1.489 1.159 0.875 1.947674.5 2 1.495 1.148 0.819 2.516665.5 2 1.443 1.131 0.948 1.732656.5 2 1.464 1.134 0.876 2.171650.0 2 1.445 1.123 0.905 2.171

FIG. 3. Five experimental differential absorbance (DA) versus wavelength(nm) scans obtained using a Shimadzu 160A spectrophotometer for varioussample beam-to-reference beam cuvette path length ratios, i.e., a ¼ 20 mm/2mm (uppermost curve), 10 mm/2 mm, 20 mm/5 mm, 5 mm/2 mm, and 2 mm/1mm (lowest curve), and Orleans blue food dye (E123) as test material.

APPLIED SPECTROSCOPY 1131

transmittance and standard deviation of Orleans Blue (E123),whose monochromatic absorbance is unity at 665.6 nm, is 0.956 0.05. The large error in determining both parameters may bedue to the uncertainty in knowing the true cell path lengths ofthe wide range of quartz-glass cuvettes employed. Theexperimental reference beam absorbances A at DAmax for agiven a, recorded in column four of Table II, should be equal toone another within the experimental error, although the cuvettepath lengths and test sample concentrations involved varywidely, e.g., the a ¼ 10/1 combination’s reference sampleconcentration should be a factor of ten greater than the a¼100/10 combination’s reference beam sample concentration,thereby giving equal reference beam absorbances at the testwavelength. However, the experimental DAmax values, record-ed in column five of Table II, vary widely within the same aand this, although it is also contrary to expectations, mayexplain the variation in the corresponding A values.

CONCLUSION

The idea of estimating a central spectrophotometricspecification parameter such as the relative SRE level ratherthan determining same is anathema to instrumentalists. Thispaper offers a belated remedy to the situation prevailingheretofore, which obliged instrument manufacturers to specify‘‘ultra low stray light level of 0.00005% max (340 nm)’’.12 Theauthor contends that ‘‘max’’ should be ‘‘min’’ so as to makeallowance for absorbance of the SRE by the test material,NaNO2(Aq). The author recommends the method outlinedabove to instrument manufacturers and standards laboratorieswhere good quality ancillary services are available. Althoughthe proposed method is far from being complicated, it doesrequire some technical application and therefore, it wouldbenefit analysts greatly if the relative SRE level in aspectrophotometer was specified ab initio across a wide rangeof wavelengths while indicating the nature of the test materialemployed at each wavelength. The instrument’s specificationsheet should also indicate wavelengths at which anomalouschanges to the SRE may occur, e.g., at filter changeoverwavelengths. The author is of the subjective opinion that theSRE performance of a modern spectrophotometer, i.e., post-1990, does not deteriorate with time or with the lamp-hours

operated by the radiation source. The decrease in source outputwith use affects monochromatic and stray intensities equally,thereby leaving relative intensities unchanged. The optics of aninstrument, being sealed, should not deteriorate with time.Therefore, if SRE is specified at the manufactured stage then itshould hold for the instrument’s lifespan.

Heretofore, the transmittance ratio spectrometry SRE testmethod, when applied to determine the relative SRE level at asingle wavelength, was pursued only to beyond the sampleconcentration value where the differential absorbance experi-ences a ‘‘downturn’’. If the concentration had been followedfurther, then an ‘‘upturn’’ would have become apparent for testsamples that absorb SRE (Fig. 1). The more absorbing the testsample is to SRE, then the lower the concentration at which the‘‘upturn’’ becomes manifest. The non-transparency of a testsample to SRE in transmittance ratio spectrometry is analogousto the ‘‘drifting baseline’’ phenomenon commonly met in otherinstrumental methodologies, e.g., high-performance liquidchromatography (HPLC). The true peak height in differentialspectrophotometry for this SRE test method as in HPLC, i.e.,DAmax, must be measured to the asymptote baseline and not tothe abscissa baseline; otherwise DA0

max will be overestimatedand hence the relative SRE level will be underestimated. Theslope of the asymptote baseline yields further useful informa-tion on the transparency of the test sample to SRE. Thisphenomenon is partly manifest in analogous work byFleming13 on the determination of the relative backgroundemission from hollow cathode lamps employed in atomicabsorption spectrophotometers.

ACKNOWLEDGMENTS

The author is grateful for the critical and constructive comments of thereviewers. The formulae herein are tedious to derive and cumbersome to handlebut their application is facilitated greatly by a Microsoft Office Excel 2007spreadsheet.

1. W. Slavin, Anal. Chem. 35, 561 (1963).2. A. Knowles, ‘‘Absorption Spectrometry’’, in Standards and Best Practice

in Absorption Spectrometry, C. Burgess and T. Frost, Eds. (BlackwellScience, Oxford, 1999), Chap. 10, p. 145.

3. P. Fleming, ‘‘Stray Light’’, in Standards and Best Practice in AbsorptionSpectrometry, C. Burgess and T. Frost, Eds. (Blackwell Science, Oxford,1999), Chap. 6, p. 81.

TABLE II. The relative stray radiant energy levels, determined at the fixed wavelength 656.6 nm, are recorded in the final column for the various cuvettepath length ratios of a¼ 2, 2.5, 4, 5, and 10.

Mielenz peakwavelength

[k (nm)]

Cuvette path lengthratio (a), S (mm)/

R (mm)Reference

absorbance (A)Mielenz peak

absorbance (DAmax)SRE

transmittance (t)Relative SRE level

[s (310�3]

656.6 100/10 ¼ 10 0.337 .2.5 N/A N/A656.6 50/5 ¼ 10 0.345 .2.5 N/A N/A656.6 20/2 ¼ 10 0.393 2.469 0.965 1.445656.6 10/1 ¼ 10 0.382 2.415 0.987 1.525656.6 100/20 ¼ 5 0.760 2.291 0.940 0.933656.6 50/10 ¼ 5 0.735 2.203 0.955 1.121656.6 10/2 ¼ 5 0.694 2.060 0.978 1.555656.6 5/1 ¼ 5 0.697 2.030 0.932 2.002656.6 20/5 ¼ 4 0.846 1.928 0.985 1.356656.6 50/20 ¼ 2.5 1.300 1.518 0.900 1.412656.6 5/2 ¼ 2.5 1.204 1.404 0.985 1.626656.6 100/50 ¼ 2 1.600 1.274 0.890 1.093656.6 20/10 ¼ 2 1.502 1.164 0.843 2.125656.6 10/5 ¼ 2 1.433 1.130 0.990 1.529656.6 2/1 ¼ 2 1.420 1.118 0.995 1.564

1132 Volume 63, Number 10, 2009

4. C. Burgess, ‘‘Recommended Procedures for Standardization’’, in Standardsand Best Practice in Absorption Spectrometry, C. Burgess and T. Frost,Eds. (Blackwell Science, Oxford, 1999), Chap. 9, p. 130.

5. E 387-04, Standard Test Method for Estimating Stray Radiant Power Ratioof Dispersive Spectrophotometers by the Opaque Filter Method (AmericanNational Standards Institute, Silversprings, MD, 2004).

6. P. Fleming and J. O’Dea, Analyst 116, 195 (1991).7. P. Fleming, Analyst 116, 909 (1991).

8. K. D. Mielenz, V. R. Weidner, and R. W. Burke, Appl. Opt. 21, 3354

(1982).

9. P. Fleming, Analyst 115, 375 (1990).

10. W. T. L. Neal, Photoelec. Spectrom. Group Bull. 9, 204 (1956).

11. W. T. L. Neal, Analyst 79, 403 (1954).

12. UV-3600 Handbook, Shimadzu website.

13. P. Fleming, Appl. Spectrosc. 46, 1400 (1992).

APPLIED SPECTROSCOPY 1133