2018
Anal. Chem. 1983, 55,2018-2021
Stray Radiation from Holographic Gratings Wilbur Kaye Beckman Instruments, Inc., P.O. Box C-19600, Irvine, California 92713
Measurements of stray radlation in a spectrophotometer equipped with a holographic grating have been made by using a convolution test. The stray radiation has been found to vary with wavelength and polarization of the incident radiation because of plasmon scattering at the grating. This plasmon scattering causes an enhancement in scatter by factors up to 4 at wavelengths In the vicinity of the Wood anomaly for the grating. When plasmon scattering exists the convolution test is best conducted by using a number of slit functions spanning the interval of primary radiation.
Considerable progress has been made in recent years concerning the diffraction of radiation from gratings, and this understanding has been applied to the construction of more efficient monochromators (1).Development of a satisfactory theory of scattering of light from gratings has advanced more slowly, but the treatment of Sharpe and Irish is impressive (2). Part of the difficulty in understanding gratings can be assigned to the extenuating experimental problems. The fraction of incident radiation scattered at modern gratings is very low. Measurement of this scattered radiation requires instrumentation of very high S I N and wide dynamic range. Nevertheless the continued effort to develop spectrophotometers capable of measuring ever higher absorbances provides the impetus for further study. Stray radiation directly impacts absorbance measurements and most of this stray radiation arises from scattering a t the grating. One of the stumbling blocks in the understanding of stray radiation can probably be attributed to definition of the term. The author has found it advantageous to classify the radiation in a spectrophotometer into two categories, primary and stray. Primary radiation is that (detected) having wavelengths within a specified wavelength interval, L units above and below the center of the nominal pass band of the spectrophotometer, and stray radiation is that (detected) having wavelengths outside this interval. The interval, L , called the “limit”, has to be larger than the HBW of the instrument by an increment that accommodates experimental realities. With this definition it is possible to measure the stray radiation by performing a convolution of the slit function with the single power spectrum (sometimes called the detected radiant power (DRP) spectrum or relative instrument response function) (3). This convolution operation is relatively simple when the slit function varies little over the wavelength interval of radiation incident on the grating. A new finding, reported here, is that the slit function may vary significantly with wavelength in the region of the Wood anomaly. At certain grating angles, expressed as the reading X of the monochromator wavelength dial, certain wavelengths X of radiation are scattered from the grating with unexpected intensity. The enhancement of scatter appears to arise from surface plasmon scattering first observed by Teng and Stern ( 4 ) and more recently described by Hutley (5). Because of this enhancement of scatter it is desirable to use a multiplicity of slit functions when performing the convolution test if any of the detected radiation incident on the gratings is of wavelength near the Wood anomaly. Convolutions with
multiple slit functions are still manageable when studying holographic gratings; however, grating ghosts usually seen when studying ruled gratings impose complications that are addressed in a separate paper (6).
THEORY The convolution method assumes that the DRP emerging from the exit slit of a monochromator set to a wavelength dial reading X is equal to the sum of the slit functions for all properly weighted increments of essentially monochromatic radiation incident on the grating. Assuming that the distribution of radiation incident on the grating is given by the single beam power spectrum, the proper weighting of slit functions is obtained by multiplying the elit function by the single beam power spectrum. The method categorizes the detected signal as either primary or stray radiation by means of a parameter called the limit, L. Choice of this limit is arbitrary but, in practical applications, is determined by the half-band-width (HBW) of any sample absorption band under study and by the band width of radiation used in measuring the slit function. The equation for that portion of the detected signal attributable to stray radiation is
S(X,L)= -LJA
K[
P(X - nA)F(nA) +
*=-m
m
P(X - nA)F(nA)] (1) n=LJA
where P is the single beam power spectrum, F is the slit function, and A is the wavelength interval of each increment. The total number of terms in this summation is not infinite but only extends over the interval of significant single-beam power. The term K is evaluated at a X value where the blocking filter is opaque and, hence, where the calculated stray radiation must equal the observed signal. Derivation of this equation is given elsewhere (3). Surface plasmon scattering arises from a coupling of the incident radiation field with the field this radiation sets up in the conducting surface on the grating. This coupling can occur even when the surface plasmon is traveling obliquely to the grooves on the grating, but only for components of the incident wave polarized perpendicular to the grooves on the grating (S plane polarization). The equation sin 6 = [(el(u))/(l
+ C ~ ( W ) ) ] ’ -/ ~ (mX sin @ ) / d
(2)
has been given to describe the direction at which the plasmon scattering is observed (5). 0 is the angle between the incident beam and the grating normal while 4 is the angle between the scattered ray and the grating grooves in the plane of the grating. m is an integer and d is the groove spacing. q(u)=
n2
-
122
(3)
where n and k are the real and imaginary parts of the refractive index for the metal coating on the grating. Equation 2 should be considered only a first approximation to the reality of surface plasmon scattering.
EXPERIMENTAL SECTION Instrumentation. Spectra shown here were obtained with a DU-8 spectrophotometer manufactured by Beckman Instruments, Inc., operated in the same manner described earlier ( 3 ) .
0003-2700/83/0355-2018$01.50/00 1983 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 55, NO. 13, NOVEMBER 1983
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Figure 2. Slit function for 546 nm radiation polarized in the S and1 P planes.
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Figure 1. Single beam power spectrum for a 1200 groove/mm holographic grating. However, the source was a tungsten-halogen lamp and monochromaticity of the illuminating beam was determined by pairs of narrow-band interference filters. A t normal incidence these filters transmitted radiation of 546, 568, 589,632,656,694,and 853 nm with HBWs of 3 nm. The single filters had transmittances of about 0.01% at wavelengths 6 nm from the band centers. The filter pairs were spaced about 12 cm apart to avoid optical feedback. The wavelengths of the band centers could be 'lowered as much as 15 nm by tilting the filters. Tilted filters did exhibit side bands and the error thereby introduced was minimized by extrapolation. In all cases the light scattered by the grating was considerably greater than the light transmitted by the filter pairs at wavelengths of 10 nm or more from the band centers. A Polaroid type HNP'EI filter was used to polarize the source radiation. This filter had a very high extinctiion ratio for radiation of wavelengths between 320 and 700 nm. The beam was also strongly polarized by the interference filters when tilted. In the experiments reported here the filters were tilted about an axis parallel to the grooves on the grating and hence polarized the beam in the "S" plane. Use of tilted interferenlce filters with the tungsten source not only allowed selection of many wavelengthg but also minimized the dependence of slit function on slit width so long as the slit width was significantly less than the HBW of the filter.
RESULTS AND DISCUSSION Effect of Polarization. The most dramatic effects of polarizing the beam are seen a t wavelengths near the Wood anomaly as illustrated in Figure 1. In this case the blocking filter was removed from1 the instrument and the DRP was determined by the source emission, detector sensitivity, and grating efficiency (first order). When the incident radiation was polarized in a plane perpendicular to the grooves on the grating (S plane), grating efficiency varied considerably over a relatively short wavelength interval. This is attributed t o the Wood anomaly (7). As a consequence the beam emerging from the exit slit of a monochromator is always partially polarized and the degree of polarization varies with wavelength. While the variation in degree of polarization with wavelength for first order diffracted light is well-known, the variation in polarization of the stray radiation is not so well-
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Figure 3. Slit function ifor 632-nm radiation polarized in the S plane. known. The effect 11sbest seen in the slit function. Slit Function. The slit function of a monochromator can be obtained by scanning wavelength while illuminating tlhe entrance slit with monochromatic radiation. It can be considered to be proportional to the transmittance function of the monochromator for monochromatic radiation. On a linear scale this slit function usually has a triangular shape and the half-band-width (HEtW) corresponds to the resolution of tlhe instrument. Actuallythe slit function is never strictly triangular and some radiation can be detected at all orientations of the grating. This can be seen in Figure 2 where polarized 546 nm radiation was incident on the slit and the ordinate was greatly expandeld. The solid (noisy) curve was obtained with the E vector perpendicular to the grooves on the grating (S plane). The dashed curve was obtained with the E vector parallel (P plane). The wavelength drive circuit introduces a very small dark current offset detectable at high gain and necessitates checking zero while scanning. Such a check is seen at = 880 nm. The zero- and first-order signals at = 0 and 546 nin, respectively, are shown only for S plane polarization. Tlhe DRP for first-order radiation is 2.2 times that for P plane polarization. The zero order signal is 1.3 times lower for S than for P plane polarization. The DRP a t a grating angle corresponding to X =I 300 nm is independent of polarization and amounts to about 8 X lo4 of the first-order P plane signd. Of most significance, a distinct shoulder can be seen for S plane polarization in Figure 2 a t = 460 and 630 nm. When radiation of longer wavelength is incident on the grating, these bands are resolved as seen in Figure 3 and are detectable only for the S component of polarization. The DRP a t X = 465 nm is about 4 times greater for S than for P plane polarizaticn. The ratio is higher than that (2.4 times) for the first-order diffracted beam at 7, = 632 nm. After the study of slit functions for radiation of many wavelengths, it was possible to describe the location of the maximum of this scattering enhancement by the graph in Figure 4. The displacement, IX - XI for the maximum scalt-
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Figure 6. Pattern of surface plasmon scattering when 632-nm radiation is incident normally on a 1200 groove/mm grating.
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Flgure 5. System for the observation of surface plasmon scatter.
tering enhancement is seen to increase linearly with IX - 5821. Plasmon Scattering. Hutley has described a method of viewing plasmon scattering for a grating (5). An even simpler system involves illuminating a grating with laser radiation and observing the radiation diffracted and scattered from the grating onto a sheet of paper as shown in Figure 5. The incident laser radiation passes through a hole in the paper. The image seen on the grating side of the paper will be similar to that formed on the inside of the exit slit of a monochromator. When the plane of the grating surface is normal to the laser beam, the zero order passes back through the hole in the paper. Radiation diffracted into the +1and -1 orders scatters intensely from the paper and may be absorbed with small pieces of black glass. Above a general background one can then easily distinguish a series of arcs as illustrated in Figure 6 when light of 632 nm falls on a 1200 groove/mm grating. These arcs are seen only for laser light polarized in the S plane. When the grating is rotated about an axis parallel to the grooves, the pattern of arcs moves at a slower rate than the diffracted orders and the situation seen in Figure 7 occurs when the first order passes back through the hole in the paper. This corresponds to the condition prevailing in the plane of the exit slit of a Littrow monochromator when the dial setting X equals
Figure 7. Pattern of surface plasmon scattering when the first-order diffracted beam returns parallel to the Incident radiation.
the wavelength of light entering the entrance slit. Figure 6 prevails when X = 0. It should be apparent that there are two grating orientations with X greater and smaller than 632 nm where the plasmon arcs will fall on the exit slit and any detector beyond the exit slit will "see" the increase in radiation. This is exactly the situation occurring in Figure 3. It has not so far been possible to visualize the plasmon arcs while illuminating the grating with filtered radiation from a tungsten lamp, but it appears likely that the separation between plasmon arcs decreases as wavelength approaches 582 nm for the 1200 groove/mm grating. Similarly it would be predicted from Figure 4 that the arcs would disappear when the radiation had a wavelength less than 410 nm. From Figure 6 one can see that the exit slit intercepts only a small portion of the plasmon arcs. Furthermore the plasmon arc is significantly wider than the slit used for Figure 3. Consequently the total radiation in the arcs will be much greater than that detected in Figure 3. On the other hand essentially all of the fnst-order radiation will exit the slit. After integration of the potential area of the arcs it is found that only about 0.03% of the arc area can pass through the exit slit of the DU-8 instrument used here. The intensity of scatter at X = 465 in Figure 3 is about 4 x IO4 that of the first-order signal. If the intensity of radiation in the arcs were constant, it can be seen that the integrated signal in the plasmon arcs would be about 1% of that in the first order. Stray Radiation with Polychromatic Light. As the band width of radiation falling on the grating increases, the width of the plasmon arcs also increases. Ultimately it may become difficult to identify the plasmon radiation from the shoulder of the primary radiation. However, the convolution test reveals the plasmon component. This is illustrated in Figure 8. The solid lines are the experimental single-beam power spectra. They were determined largely by a special
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Figure 9. Ratio of stray radiation “spectrum” calculated by use of a single slit function to that calculated by use of multiple slit functions. 400
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Figure 8. Stray radiation “spectrum”calculated by using a inultipllcity of slit functions.
blocking filter placed in the beam. This filter consisted of Hoya type 0-54 and CM-500 glass and was selected to pass light only in the region of the Wood anomaly. Light was polarized in the S plane. Gain of the instrument was increased 4000 times at dial settings below 520 nm where the blocking filter is essentially opaque. The dashed lines and the discrete points below T( == 540 nm were calculated by use of eq 1 with incirements of A = 5 nm. Slit functions appropriate to each increment of wavelength were used. The calculated stray radiation was normalized to the experimental curve at r; = 460 nm and was expanded 4000 times. The discontinuity just below 460 nm is a zeiro check. The normalization factor K was 1.59. Clearly this use of multiple slit functions should yield the most accuicate estimation of stray radiation, and experimental evidence of this is provided by the close fit of calculated to observed data in the 400-500 nm interval. Note that three calculated values of stray radiation are plotted at T; = 520 nm. This is a consequence of there being significant primary radiation within 20 nm of this grating orientation. The three plotted points correspond to calculations made with the three indicated values of L. Calculations of S(x, 10) and S(x, 15) were also made. They show no difference from Figure 8 below 500 nm and show an expected increase at longer wavelengths. The maximum stray light for L = 10 nm is 3.6 times higher than that for L = 20 nm. How much error results from the use of a single d i t ffinction? The computations of eq 1 were repeated by using the single slit function measured with 589 nm S plane radiation. The ratio of stray radiation calculated by using a single slit function to that using multiple slit functions is graphed in Figure 9. In both cases the normalization factor K was calculated at 460 nm, but for the single slit function data K = 3.74. The graph shows that the K value for the slit function data will depend on the normalization wavelength while that for the multiple slit function data does not. The error using the single slit function calculation will depend on the blocking filter, A worse-case situation will occur when the normalization wavelength corresponds to the plasmon scattering maximum from radiation a t the maximum DRP, Had a blocking filter been chlosen whose DRP maximum occurred a t 630 nm with a HBW of 50 nm or less, the DRP aipectiwm
would have looked much like Figure 3. Only by using multiple slit functions would the calculations faithfully reproduce the plasmon scattering maximum at wavelengths where the blocking filter was opaque. The normalization step by which the K value of eq 1 is calculated compensates for much of the error in the convolution test caused by the choice of slit function. However, nothing has been said about the X value at which this normalization is performed. It does not appear that the stray radiation calculated by using the convolution test is very sensitive to the choice of X so long as the blocking filter is effectively opaque at this wavelength and multiple slit functions are used. A different situgtion exists when estimating stray radiation by either the conventional ASTM (8) or blocking filter (3) tests. Both of thesmemethods use sharp cutoff test materials and estimate stray radiation from the magnitude of the detected signal at r; vadues where the test materials are essentially opaque. If plasmoa scattered light exits the slit at this X the calculated stray radiation will read high. If the plasmon scattered light falls at a of significant primary radiation and not at the test A, thle stray radiation will be low. If the blocking filter has a narrow HBW and transmits in the vicinity of the Wood anomaly, the plasmon scattering may be clearly resolved as in Figure 3. Without a knowledge of plasmon scattering one might erroneously conclude that the test material was fluorescent or that some undesirable reflection existed within the monochromator. The data discussed here were taken with a 1200 groove/mm holographic grating in a Littrow monochromator. Were a grating of different groove spacing or a monochromatclr of different mounting, e.g., Ebert, to be used, one would ex:pect the surface plasmon scattering maximum to appear e1sew:here than that given by Figure 4.
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LITERATURE CITED (1) (2) (3) (4) (5)
(6) (7)
(8)
Loewen, E. G.; hlevlere, M.; Maystre, D. Appl. Opt. 1977, 16, 2711. Sharpe, M. R.; Irish, D. Opt. Acta 1978, 25, 861. Kaye, W. Anal. Ishem. 1981, 53, 2201. Teng, Y. Y.; Stern, E. A. Phys. Rev. Lett. 1967, 19, 511. Hutley, M. C. “Diffraction Gratings”; Academic Press: New York. 1982. Kaye, W. Anal. (Chert. 1983, 55, 2022. Stewart, J. E.; Gallaway. W. S.Appl. Opt. 1962, 7 , 421. “Standard Method of Estimating SRE”; ASTM Designation E-387-72; American Society for Testing Materials: Philadelphia, PA.
RECEIVED for review May 16, 1983. Accepted August 8,1983.
