Selectively modulated interferometric dispersive spectrometer for

Selectively-Modulated Interferometric Dispersive Spectrometer for Ultraviolet-Visible Atomic and Molecular Spectrometry J. J. Fitzgerald, 1.L. Chester, and J. D. Winefordner' Deparfment of Chemistry, University of Florida, Gainesville, Fla. 326 11

A novel selectively-modulated interferometric dispersive spectrometer (SEMIDS) for UV-Visible atomic and moiecuiar spectrometry has been constructed and evaluated. SEMIDS consists of a Micheison interferometer In which the stationary mirror has been replaced with a rotating grating. The oscillating mirror modulates only those wavelengths which are diffracted by the grating in a direction perpendicuiar to the mirror-detector optical axis. SEMIDS is shown to have excellent stability, linear response, an increasing signal-to-noise ratio with decreasing anaiyte concentration (in atomic emission flame spectrometry), and a near theoretical resolution for any aperture. Some initial studies involving measurement of flame emission (air/CpH2 flame) are presented.

Basic interferometric techniques have two potential performance advantages Over more conventional dispersive monochromators: the Fellgett, or. multiplex, advantage; and the Jacquinot, or throughput, advantage. However, the potential signal-to-noise improvement from the multiplex advantage is, in practice, realized only where detector noise predominates, typically in the IR spectral region. The Jacquinot advantage, because it does not directly concern noise, persists in all spectral regions. The theory of the Jacquinot advantage can be derived from purely physical arguments involving the second law of thermodynamics or from purely geometrical considerations using the Helmholtz-Lagrange Invariant in two planes. Simply stated, these arguments require that in a lossless optical system, the brightness of an object equals the brightness of the image; therefore, the flux throughput and the brightness can be considered a t any point in such a system ( I ) . This applies to any series of lossless optical elements and can be expressed in terms of Btendue, E :

where the subscript, i, refers to the flux increment d@,in W, between the source and the first optical element and the subscript, f , refers t o the same quantity between the last optical element and the detector; B refers to the source radiance, in W m-2 sr-l. The solid angle of collection for each optical element Q is in sr and the area S of each device is in m2. Jacquinot noted that for interferometers the term dSdQ was a constant, and therefore it was possible to have a single optical system with both high resolution and large E (2,3). While these advantages of high optical throughput and high spectral resolution have been known for some time, a number of severe restrictions have precluded widespread use of interferometric techniques in UV-Visible atomic emission spectrometry. In this spectral region, optical toll

Author t o whom reprint requests should be sent.

2330

erances must be kept within small fractions of the wavelengths of interest; such tolerances require extremely precise optics and correspondingly precise mechanical tolerances on all parts of the interferometer. In addition, the interferogram must be processed mathematically to obtain usable power density spectra which requires access to a computer or, more generally, the dedicated use of a minicomputer or hard-wired Fourier transform spectrum analyzer. These combined considerations necessitate a practical interferometer being both complex and expensive. This paper describes a spectrometer which uses interferometric optics to retain high Btendue but which uses several techniques developed by Connes ( 4 ) with SISAM (spectrometric interfbrential B selection par l'amplitude de modulation) and by Dohi and Suzuki ( 5 )to eliminate many of the previous difficulties in visible interferometry. The instrument described here is a selectively-modulated interferometric dispersive spectrometer (SEMIDS) and has been used here to investigate emission in an air-acetylene flame. THEORETICAL CONSIDERATIONS Operating Principle of SEMIDS. The operational principle of SEMIDS differs from a conventional interferometer in two major aspects. In conventional Fourier transform spectroscopy (FTS), the unmodified output represents the sum of a number of cosine waves. The period and amplitude of each of these cosine functions is determined by the wavelengths of the input radiation. SEMIDS, however, optically-limits the number of wavelengths that can interfere with each other a t any one time, and the output contains only the cosine functions of the selected wavelengths. Because of the simpler output configuration, simpler modulation-demodulation techniques provide a measure of the radiation intensity in any spectral interval, and mathematical transformation is not required. A simple schematic diagram of the optical system is provided in Figure 1. The configuration is the same as that of a Michelson interferometer with the fixed reflecting component (mirror) replaced with a rotating diffraction grating, G. The aperture, H , and the lens, L1, are the components of a conventional Fizeau collimator. The input collimated beam is split a t point C by the beamsplitter, BS, one beam striking the mirror, M, and the other beam is incident on the grating a t an angle 0 to the incident optical axis. The reflected and the diffracted wavefronts are then recombined by BS, and the interference pattern is focussed on the detector by the lens, Lp. The interference pattern is a series of alternating bright and dark concentric circular rings. The distribution of the bright and dark rings on any observation plane is determined by the phase difference or, equivalently, the path difference between the two arms of the interferometer a t any point on the observation plane. Instrumental Function. The complete derivation of the SEMIDS instrumental function is given by Dohi and Suzuki ( 5 ) and will be discussed only in a general way. The effects of substituting a diffraction grating for a fixed mirror in the Michelson interferometer can be explained by means

ANALYTICAL CHEMISTRY, VOL. 47, NO. 14, DECEMBER 1975

so

.-

X

-H

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‘R

w M SOP

I

Figure 2. Schematic diagram of wavefront 2 , and diffracted wavefront & (note that axis CO, in Figure 1 is folded at point C to coincide with axis CO, and the virtual image of the source, So’, as formed by the grating and the virtual image of the source, SO, as formed by the mirror are shown in Figure 2)

ID

Ornil

\

‘d

So, = virtual image of source formed by mirror, So, = virtual image of source formed by grating, 0 = 0, or 0, (see Figure 1 caption), X = observation plane (grating on mirror piane). Z1 = wavefront falling on mirror, Zp = wavefront falling on grating, ZR = resultant wavefront towards detector

Figure 1. Simplifiedschematic diagram of optical system BS = beam splitter, C = vertex of two axes, D = detector, G = grating, H = aperture, Ls = source collimating lens, Ld = detector focusing lens, M = mirror, 0, = centroid of grating reflecting surface, 0, = centroid of mirror reflecting surface, B = angle of grating with respect to optical axis, CO,

of Figure 2. The schematic in Figure 2 is derived from the diagram in Figure 1 by rotating the axis CO, to coincide with the axis defined by CO, (the subscripts relating to the grating, g, and the mirror, m). The diffraction grating and mirror are treated as transparent optical elements with the appropriate transformation properties. The equivalent grating plane defined by OX is chosen as the observation plane for convenience. The stipulation that the input radiation contain equiphasic waves simplifies the treatment and is physically realized in the present system. The complex amplitude (5) of the wavefront in each arm of the spectrometer expressed along the observation plane is a function of the spectral amplitude distribution of the source, a ( u ) , the wavenumber, u, in cm-l, the grating rotation angle, 0, the displacement along the observation plane, x , in cm, as well as the spectral amplitude reflection coefficient of the mirror r ( u ) , and the analogous “mth” order spectral diffraction coefficient of the grating G, b ( o ) . The intensity distribution, Z(x), of the fringes along the plane OX can be obtained by superimposing the complex amplitudes of the wavefronts in each arm and integrating over the spectral range. The total energy transmitted by the interferometer can be obtained by integrating Z(x) over the effective width of the flux. Assuming the grating to be the field stop and the width of the flux to be 2W, then the integration limits will be - W/cos 8 to Wlcos 8, and the total intensity transmitted, Z, is given by

I =

1

W/COS

- W / C O 8S

6

Z(r)dx

(2)

Performing the integration, the instrumental function can be expressed as

[

(-)I]

2r(u)b(u)sinc2 ( 2 u ~ i n B - ~ ) W du (3) 6 cos8 where 6 is the distance between the grating grooves and m is the diffraction order. By inspection of Equation 3, it can be seen that the third term in the bracket changes with the phase difference of the interfering waves, i.e., as the phase (or path difference due to grating rotation) of a given wavenumber, u , at point C (in Figure 1) varies with grating angle, 8, the intensity varies with the function, fo, defined by

Because the sinc function is defined (sin z ) / z , it can be shown that f 8 drops rapidly as the value of 2 (T sin 8 differs from m/& Therefore, it is possible to obtain the spectrum a 2 ( o ) b ( c ) r ( uas ) a function of 6, the grating angle. The expression for f 8 may be used to estimate the theoretical resolving power, Ro, because for a given wavenumber; o, in a given spectral order, m,there is a unique 8 which gives maximum signal and a wide range of 8’s which give minimum signals. The Rayleigh criterion that two spectral lines are completely resolved when the maximum of one line falls on the minimum of the other has little theoretical foundation but may be used as a performance estimate (6). This provides

where N is the total number of grating lines illuminated and m is the spectral order. Equation 5 is, of course, the theoretical resolving power of the grating; therefore, the resolving power of the spectrometer will depend on the number of illuminated grooves and, hence, the size of the grating. In order to calculate the solid angle of collection, Q, it is necessary to consider that the aperture, H, is not an ideal point source but has a finite area. As a result, some off-axis radiation will also reach the collimating lens, L1, and pass through the system, The effect of this off-axis radiation is to diminish the fraction f o given in Equation 4. To determine the maximum acceptable aperture for a given collimator configuration, it is necessary to include the off-axis flux contribution in Equation 3 and to rederive the subsequent expressions. A more thorough discussion of this approach is given by Dohi and Suzuki (5). Path Length Considerations. The interferometer action requires only that there be an optical path difference in the two arms and that this difference be controllable. With a Michelson interferometer, there are additional considerations. First, the field of a conventional Michelson is normally limited by the restriction that

R = 8F2/h2

(6)

where R is the resolving power, F is the focal length of the collimator and h is the diameter of the source. This condition results from the fact that the two rays derived from the marginal ray have a different path difference in the two arms than the two rays obtained from the axial ray. The in-


* 2331

tensity at the detector due to a monochromatic ray from the edge of the field stop will be modulated a t a different rate from that due to the same monochromatic ray from the center of the field. Larger fields can be obtained by placing a compensating plate of the same material and dimensions as the beamsplitter in one arm. This field compensating device causes rays from all parts of the field to have the same optical path difference in both arms. In field compensated interferometers, the field is generally limited by the spherical aberration of the optics and can be expressed as

R = -4n2F4 h4

(7)

where n is the refractive index of the compensating plate. The compensator serves another function even when field size is not of primary importance. Consider the equation for zero path difference in two arms of the interferometer labelled 1 and 2 at a particular wavelength 1

Xix= l nlidli = X

1 j=1

nzjdzj

(8)

where n is the refractive index and d the geometrical path length in each segment of the arm. When this equation is fulfilled, the entire focal plane has uniform intensity, has essentially one fringe, and represents the most efficient operation of the device. As the path difference becomes progressively greater than zero, more circular fringes of smaller dimensions appear on the focal plane. As the index of refraction is a function of wavelength, there is no position of zero path difference for all wavelengths in an uncompensated interferometer. The problem is that the ray from one arm passes through the beamsplitter once while the other ray passes through the beamsplitter three times, and since the refractive index is a function of wavelength so is the path difference. SEMIDS was designed as an uncompensated interferometer for two reasons. First, the instrument collimator operates well within field limiting conditions. Second, as the rays from the beamsplitter to the grating are a t an angle 8, there is obviously an irreducible geometrical path difference from one side of the grating to the other. The implications of this design are several. With the grating in zero order, it is necessary to use a bright “white” source to obtain very low contrast fringes. However, with the grating rotated so that the first-order reflection of monochromatic light interferes, the difficulties encountered are not the same as when an optical flat is rotated the same way. Since the “reflector” is a grating, all the diffracted coaxial rays are equiphasic, each parallel ray differing only by integral A’s across the grating. A comparison of fringes obtained with a monochromatic line source in zero and first order shows no change in number or dimension. The fringe contrast is worse in the first order primarily because of the reduced reflection coefficient, b (o),of the grating. The derivations of the equations of the modulation system in the next section are performed as if zero path difference were realizable in the system. The conclusions are representative of the functioning system. Effect of Mirror Modulation. The use of the grating provides that only radiation with a wavelength that fulfills the grating equation will interfere with the reflected radiation. By assuming monochromatic interference, the theory of the detection system may be described. Consider Figure 1 with a different emphasis. Given incident monochromatic radiation with amplitude A , it will be split a t the beamsplitter BS to two beams-one reflected and one transmitted with amplitudes ( A / f i ) exp (i&) and (A/.\/2) exp (i&), respectively, where 41 and 42 are the reflection and 2332

*

transmission phase changes. After passing along the arms of the interferometer, the two beams return to the beamsplitter where the amplitudes before recombination are

( A / v % exp (i&

+ Paidla)

(9)

( A / f i )exp (i&

+ 2nid20)

(10)

and

where d l and d2 are the paths of the interferometer arms. Each beam will now undergo the complementary phase change, the reflected beam will now be transmitted and vice versa, so that the resultant amplitude will be ( A / 2 ) exp

+ @dl[exp

[~(I$I

(2aidlcr) + exp (2aidzo)I ( 1 1 )

and this multiplied by its complex conjugate will give the resultant transmitted intensity I ( A ) ,

+

[(A) = ( A 2 / 2 ) [ 1 cos (2xoA)I

(12)

where A is the path difference Id1 - d21. Thus, the transmitted intensity varies sinusoidally with A and depends on the amplitude of the monochromatic radiation. Figure 3a shows the simplified modulation scheme. By applying a linearly variable voltage (triangular wave) V to a piezoelectric assembly, the mirror is displaced linearly and the path difference A varies with the same frequency as the applied voltage. If the spectrometer is aligned with the grating a t a fixed 8, the mirror displacement from zero being an integral multiple of V4o,and if the initial phase of the fringe and triangular voltage are properly matched, then the photomultiplier current will be a pure sinusoidal wave of the same frequency as the applied triangular wave. Integrating the signal, SO,will then provide an estimate of the source intensity. Figure 3b reflects the actual modulation system. The system undergoes minor thermal changes which result in a phase drift of the fringes. This corresponds to a slow change (=2 min) of the central spot a t rest position from a bright fringe to a dark fringe. When this occurs, the distortion of the waveform resembles that on the -a side of the SOplot but appears on both sides of the waveform. The assymmetrical distortion shown in Figure 3b results from grating rotation. As was noted above, it is impossible to obtain zero path difference with this device and a small nonzero difference remains. This irreducible difference will change as the wavelength changes. Using elementary Fourier theory, any periodic function may be expressed as a series of sines and cosines. Expressing I ( A ) , the intensity function as a function of path difference, A, gives a0

I(A) = 2

+ x a , COS (2::A) n=l

+

,f P,

n= 1

sin

(y)

(13)

Because the intensity function is symmetric, the summation of the cosine values is sufficient. The term a0 and the path difference A0 refer to the “equilibrium path difference”, i.e., the small optical path difference between the arms which remains when the system is oscillating a t equilibrium. It is impossible to keep A0 a constant as the grating is rotated which results in a signal drift as the term a~ changes and a superimposed modulation from the cosine term. Fortunately, the solution to these low frequency distortions of So is simply to modulate the phase inversion and A0 at a different frequency than the spectral line modulation. In practice, such modulation is achieved by biasing the applied triangular wave with a sine wave voltage applied at low frequencies. This permits the spectrum to be obtained with purely analog electronic techniques, selective amplification, filter-


Ib)

(0)

Flgure 3. Simplifiedmodulation scheme (a)IlluSbation 01 effect Of mcdulation Of mirror upon the modulatedlight Sigml. So. the optical path difference.A. Note that V is the ac voltage applied to the mirror. (b) influence 01 zero path differen- upon the Optical path difference. A, the mdulated light signal. So, and the resultant signal; $,

ing, and rectification, instead of digital techniques. In Figu r e 4, a picture of an oscilloscope t r a c e is given showing the applied voltage V and the r e s u l t a n t signal S, obtained with sodium emission at 589.6 nm in an air-acetylene flame.

EXPERIMENTAL Instrumental Design. Because the spectrometer was designed to operate in the UV-Visible spectral region where commerciallyavailable dispersive monochromators have heen widely used, i t is inevitable that comparisons with respect to performance should he made. Therefore, any design feature of the spectrometer that required either a special environment or complex operating proeedures was considered to he a severe disadvantage for such B eamparison. Therefore, in the design concept, simplicity and reliability are emphasized. Furthermore, the spectrometer was designed t o he flexible enough to permit investigation of other interferometric techniques in flame spectrometry. This required that the meehanical design be somewhat larger and more complex than actually required for the simpler SEMIDS spectrometer. All the components of the optical system rested on a single aluminum plate, -1.3 m by -1.3 m and 2.5 cm thick. Because this plate was not used to define an optical plane, i t was not necessary to use a more rigid or thermally-stable material than aluminum. The surface of the plate wae divided by aluminum tracks which extended from the middle of each side through the plate center t o the middle of the opposite side. On two adjacent sides, the tracks terminated at perpendicular plates of 2.5-cm thick aluminum which acted as supports for the entrance and exit apertures and for the photomultiplier tube housing. The principal advantage of the massive base and support plates was that they acted as massive heat sinks. In practice, i t was found that, provided the room temperature had no sharp gradients (+l*C), the thermal drift caused by plate expansion or contraction was negligihle. The flexibility of the plate required that i t he well supported to prevent warping. However, i t wae also found that most support materials, whether rigid or semi-rigid, transmitted ambient vibrations through the underlying table to the base plate. This sensitivity to vibration is predictahle in interferometers and, unless isolation is achieved, the signal-to-noise levels are generally unacceptable. An inexpensive dual-support system was devised which not only efficiently damped ambient vibrations hut which also provided quick damping of perturbations t o the plate itself. Basically, the plate was supported a t eight points. At points located approximately 30 cm from the plate center underneath the track lines, the plate rested on four stacks of four No. 13 rubber stoppers. Each stack of rubber stoppers was topped by two layers of Isomode ruhber fabric (Isomode is a composition fabric and rubber mat manufactured by M. B. Electronics Co., 782 Whalley Ave., New Haven, Conn.; it was designed t o isolate vibrations, particularly in heavy load bearing applications). The second set of four supports eonsist-

..

Figure 4. Oscilloscopic trace of voltage and resultant signal vs. time waveforms for atomic emission at 589.0 nm. 100 ppm of Na introduced into an airlCnHPflame ed of four air-filled vinyl halls positioned in the center of each quadrant of the plate. The laboratory where the spectrometer was located was not ideally equipped t o analyze vibrations and so a description of the techniques used t o deterine vibrational levels is given here. For ambient vibrations, the spectrometer was aligned using a He-Ne laser, and the output signal was monitored on a n oscilloscope. When no vibration was observed, the signal resembled the wave packets in Figure 4. Any vibration caused extreme distortion of the signal and persisted until the source of vibration was removed. The vibrations were investigated with the described support system and found to he undetectable in all cases including striking the support table, slamming doors, and operating machinery such as teletypes and air conditioners in close proximity. Perturbations t o the base plate were also investigated using B simple weighted pendulum to apply B 1 N impact to the edge of the plate. In all cases, i t was found that the subsequent oscillations damped below detectable limits in less than l see and that the optical alignment was not changed. Each optical component was mounted on a translation stage constructed of %-in. thick aluminum plates. The bottom plate was grooved to slide along the base plate tracks and had tracks fitted an the top surface a t right angles t o the grooves. The upper section of the stage was machined to fit these tracks, and hoth pieces were equipped with set screws to permit them to be locked in position. In Figure 5, a more complete description of the layout of the


2333

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Figure 5. Detailed schematic diagram of optical system spectrometer is provided than given in Figure 1. The lens holders and the beam splitter holder were all mounted in machined-fittings that allowed the height of each fixture to be adjusted by turning a screw while maintaining the optical elements orientation. The lens holders and the beam splitter supports were machined from brass in designs described by James and Sternberg (7). The grating was fixed in an angular orientation device (No. 10.203, Lansing Research Corporation, Ithaca, N.Y.) which used two micrometer screws to adjust the grating in three planes. This device rested on a rotating grating table constructed with a spring-loaded rotating thimble supported by two opposing thrust bearings. This rotation device was constructed with minimum play in the bearings and allowed the grating to be precisely repositioned by the stepping motor during repetitive scans. The stepping motor (Model HDM-15, Responsyn Motor, USM Corporation, Goar System Division, Wakefield, Mass.) was coupled through a micrometer screw directly to the grating table edge and was capable of driving the grating through two spectral orders. In the present spectrometer configuration, the motor was controlled through the keyboard of a PDP-11/20 mini-computer. The mirror and piezoelectric assembly were supported by another angular orientation device (No. 10.503 Lansing Research Corp.). The entrance and exit apertures were iris diaphragms allowing a minimum aperture diameter of 0.5 mm and a maximum of 13.6 mm. The collimating and focusing lenses were ground and polished (by ESCO Products, Oak Ridge, N.J.) from Suprasil-fused quartz. The bi-convex lenses have a 3-in. diameter and an 8-in. focal length (the mirror and the beam splitter were supplied by Dell Optics, North Bergen, N.J.). The mirror was polished from a %-in. thick fused quartz blank, 2-in. diameter. The aluminized surface was protected by an Alflex-A coating (Dell Optics) and is flat to within ]/IO A. In Figure 6, the spectral characteristics of the beam splitter are given. The substrate for the splitter was a 3-in. diameter blank of fused silica approximately '14 in. thick. The reflected and transmitted intensities are approximately equal and have approximately a 40% transmission and 40% reflection. The grating was obtained from the Jarrell-Ash Division, Fisher Scientific Company, Waltham, Mass. The blank size was 40 mm on each edge and 10 mm thick. The entire surface was ruled with 590 grooves/mm blazed at 3.9O to give a blaze wavelength of 240.0 nm. The oscillation of the mirror was achieved with three Clevite PZT unimorphs (Vernitron Piezoelectric Division, Bedford, Ohio) mounted in a triangular arrangement. A unimorph is a small wafer, 1-in. diameter, of PZT5B ceramic mounted on a brass plate of 1.350-in. diameter. The major advantage of using circumferentially-mounted unimorphs is the relatively large displacement (0.01 mm/V) a t low voltages. The mirror was simply glued with a vinyl adhesive to the ceramic section of the unimorphs. Each crystal was not matched, so it was necessary to provide an individual voltage control to each transducer. In Figure 7, the electronic circuit used to drive the mirror is shown. Because the crystals are primarily capacitors, it was necessary to use transistors to isolate each device and provide voltage control because a voltage divider network formed a complex series of parallel RC filters. With the circuit given in Figure 7, it was possible to apply a dc offset voltage to each unimorph unit and to oscillate the driving voltage around this offset level. This prevented any spurious signal nodes from form-

2334

Figure 6. Spectral characteristics (transmission spectrum) of beam splitter over 200-500 nm range

ing when the mirror strikes the back of the unimorph support. Adjustment of the circuit was performed in three stages: first, the spectrometer was aligned to form circular fringes with no voltage; second, with a dc voltage applied, the trim resistors on each transistor were adjusted until the fringe pattern was restored to the same configuration as the first step; and, third, a low-frequency oscillating voltage was applied to check the alignment. If the first two stages had been correktly performed, then the fringe pattern in the third stage remained constant. The oscillations blurred the contrast somewhat but did not shift the fringes. This alignment has proved to give stable results over a two-month time span and has shown no indications of circuit or unimorph fatigue a t the correct voltage drive levels. The radiation was converted to an electrical signal with an RCA 1P28A photomultiplier tube (power supplied with a PAR model 280 high voltage power supply mounted in an Ortec model 401A bin (Princeton Applied Research, Princeton, N.J., and Ortec, Inc., Oak Ridge, Tenn.). The signal was amplified with a current-tovoltage module constructed around an operational amplifier (model 405, Analog Devices, Inc., Cambridge, Mass.) which provided a variable gain from lo4 to lo8 VA-l. The amplified signal was processed by a frequency selective amplifier (PAR Model 210) which provided a switch to select the Q and a gain of 10 and had a frequency response range of 100 kHz. The filtered-output signal from the selective amplifier was further amplified by a wide-band amplifier (PAR, Model 211) and then introduced into a multiplier unit (PAR, Model 230). The multiplier unit was used to square the input signal, filter it (variable time constant from 1 msec to 30 sec), and amplify the resultant signal voltage by a factor of 100. The final stage of the signal conditioning was to take the square root of the signal with a multiplier/divider module (Model 426A, Analog Devices, Norwood, Mass.). The combined effect of the multiplier unit (PAR 230) and the square root module (Analog Devices Unit) was to square the signal, filter it (equivalent to mathematical averaging), and again to take the square root of the voltage. The signal presented at the output was then the rms area of the voltage curve output of the photomultiplier. The output voltage was displayed on a recorder and showed the source spectral distribution during a scan of the source intensity over a given spectral interval. (See Figure 8.) Operational Procedure. The basic alignment of the system was similar to the treatment described by Bell (8).A helium-neonlaser was used to define the optical path. Proceeding in a stepwise fashion, the first optical element aligned was the grating. With the laser aligned to pass radiation through the entrance aperture to the geometric center of the grating, the angular orientation micrometers were adjusted so that the zero-order reflected laser light passes back out the entrance aperture. The beam splitter was then placed in the approximate center of the plate and adjusted so that the angular orientation of the incoming laser light to the grating was not modified, and so the reflected light from the grating was directed to the exit aperture. Because the collimator overfilled the grating field stop, it was not necessary to readjust the grating so that the laser ray from the beam splitter was geometrically centered.


r

-24V 20K 0 $22 4 -

ov

1

IO K

-=

-

IOK

1

Same as above f o r Unimorph 2

Same as above f o r Unimorph 3

Figure 7. Electronic circuit used to drive unimorphs ROOT M E A N S Q U A R E M O D U L E

PHOTOMULTI PLlER

w RECORDER

Figure 8. Block diagram of electronic circuit for photocurrent detection

At this point, it was important to ensure that the grating grooves were exactly perpendicular to the optical plane defined by the incoming and reflected laser beams. If this was not done, then as the grating was rotated during a scan, the alignment of the spectrometer would change and the fringe contrast would decrease. The most convenient method of monitoring the grooves was to check that the laser image from the first four diffraction orders of the grating could be superimposed by simply rotating the grating. With this accomplished, the mirror could now be mounted using the translation stages to center the laser beam reflected from the beam splitter and using the angular orientation micrometers to superimpose the reflected mirror image on the grating image a t the exit slit. The next step was to adjust the mirror and grating to zero path difference (see earlier discussion of path difference); this step was necessary because, even though fringes were formed by any two parallel reflectors, the number, contrast, and size of the fringes was strictly a function of the absolute path difference between the two reflecting elements. Theoretically for collimated monochromatic light, a t zero path difference, tho entire illuminated area of the field stop is equal to one fringe whether the area is 1 cm2 or 1 m2. In practice, adjustment to precisely zero order was extremely tedious and was not generally necessary. With SEMIDS, the optical path difference was adjusted until there were no more than 3 circular fringes in the illuminated target. This gave a central fringe “spot” slightly larger than 1cm. After the path length was adjusted, then the lenses were aligned. The collimating lens was positioned with its focus directly on the aperture so that the laser beam passed directly through the center of the lens and was not deflected in any direction. The focusing lens was placed so that the focus was slightly in front of the aperture. This allowed the photomultiplier to be illuminated primarily by the central fringe and gave good depth of modulation. At this point, it was necessary t o construct an “aiming target” in front of the focusing lens. With all the optical components aligned for maximum performance, an upright Plexiglas alignment target was slid into position, and the laser spot was marked. By resetting the target, it was possible to grossly alter the system configuration and to quickly realign it without moving the lens or the baffles to observe the exit aperture.

After the above alignment procedure, the baffles were mounted. The light baffles consisted of a box containing parallel plates in front of the photomultiplier tube and a 3-in. diameter polyvinyl chloride tube from that box to the focusing lens. These baffles minimized uncollimated room light effects on the photomultiplier. The two other tube baffles, also polyvinyl chloride tubing, served another purpose. Because the spectrometer was situated in the fan flow of an air conditioning unit, the varying density of the turbulent air flow adversely affected the fringes. Without the baffles in place, the heat from a hand placed beneath the optical path would make the fringes waver like viewing a parking lot on a hot day. With the baffles in place, these effects were not observed. After adjusting the applied voltage to each unimorph and performing the optical alignment, the final required procedural step was to choose the working frequency and to adjust the selective amplifier accordingly. Investigation showed that the unimorph assembly had essentially flat frequency response over the frequency range of 1 Hz to 2 kHz. The choice of 210 Hz for the applied triangular wave was therefore arbitrary. The low frequency sine wave which was superimposed on the triangular wave was chosen to be a multiple of the triangular voltage frequency and was approximately 15 Hz. This combination was readily synchronized with the oscilloscope trace as shown in Figure 4. The peak-to-peak voltage of each waveform was chosen a t 30 V because, with a 70-V dc offset, this combination gave displacement over one interference fringe in each half cycle. The selective amplifier was tuned to twice the frequency of the triangular wave. Because the mirror was actually displaced over two fringes per cycle, it was possible to monitor the signal a t both 210 and 420 Hz. The higher frequency seemed to yield a more stable signal, was less susceptible to low frequency noises like thermal drift, and was therefore the frequency used for all measurement. Provided the basic alignment had been made, the operating system required little attention. No position encoding had been designed in the motor shaft or grating table, so day-to-day operation required that the grating be rotated so that the laser image spot would strike the target center. This provided a wavelength reference for motor position and could be used to calculate the number of steps from a given wavelength to another. To scan from 500.0 to


2335

NuI*bii of Fringes

Figure 9. Variation of fringe number with applied voltage (V rms) (1 fringe = 316.6 nm) 200.0 nm required a grating angle change of 5.8’ and approximately 8500 steps. It is difficult to give the time necessary for the alignment procedure because the experience of the operator is, of course, a major factor. Nevertheless, the times are given to provide a “ball park” figure for the complexity of operation. To proceed from a bare base plate to an operational SEMIDS takes approximately 4 hr. Alignment of the grating and centering the fringes on the target required approximately 30 sec.

RESULTS A N D DISCUSSION M i r r o r Displacement. The most stringent requirement of the operating system is that the mirror displacement follow the applied waveforms and be both linear and reproducible. Because the unimorphs were being employed in a novel mode to displace the 54-g mirror, it was necessary to investigate their performance. The grating was aligned in zero order, and the circular fringes from a diffused He-Ne laser were focused on the detector. The output of the photomultiplier was the input to the I-V amplifier, and the resultant voltage displayed on one channel of a dual trace oscilloscope. The applied triangular waveform a t 210 Hz was displayed on the other channel. The amplified photomultiplier signal had a sinusoidal waveform. By varying the applied voltage of the triangular waveform and visually counting the wave cycles of the photomultiplier output on the oscilloscope, it was possible to obtain a measure of the mirror displacement as a function of applied voltage (see Figure 9). The voltage was measured with a digital voltmeter (DVM), and the displacement was limited to six fringes by the op-amp circuit voltage. I t can be seen from the graph that over the range of 7-42 V rms, the unimorph assembly was linear. I t should be noted that since the waveform measured was triangular and not sinusoidal, the DVM output was not true rms voltage but only an estimate. However, this does not affect the conclusion that the unimorphs are displaced in a linear manner. Stability a n d Reproducibility. Because the optics are basically interferometric and therefore sensitive to small changes in orientation, the stability and reproducibility of SEMIDS were suspect and extensively investigated. Using radiation sources, including diffuse laser beam, Hg penlamp, and hollow cathode tubes, the variation of system parameters with time and operating conditions was examined. 2336

A measure of stability was obtained by aligning the spectrometer on the wavelength of the diffuse laser beam (633 nm) and monitoring the photomultiplier signal with a strip chart recorder for periods ranging from 1 to 3 hr. The possible sources of instability were ambient vibrations, thermal drift in the support devices, electronic drift in the detection system, and source intensity variation. No attempt was made to compensate for possible source variation. Normal personnel traffic in and out of the SEMIDS room was continued, and no extraordinary measures were taken to protect the system. The results were impressive. The worst variation over a 3-hr period was slightly more than 1%of the signal level. Over shorter time lengths, the variation averaged slightly less than 1%of the signal level. The precision of SEMIDS was investigated in a number of ways. A mixture of 10 wg/ml Li and 10 pg/ml Na was aspirated into a laminar flow chamber-burner. Argon was used to separate the air-acetylene flame in order to minimize flame background. Repetitive scans of the flame emission were performed from 633.3 to 550.0 nm. The scanning was always from high to low wavelengths, and the spectrum was recorded each time on an x/y recorder with a variable time base used for the x axis. The scanning speed was not varied and the peak heights a t 610.3 nm (Li) and a t 588.99 and 589.59 nm were used for measurement. Twenty-five spectra were obtained. For the collected spectra, the average peak height a t each wavelength and the standard deviation a t each wavelength were obtained. The ratio of the standard deviation divided by the average peak height was used as an estimate of the reproducibility. The results a t each wavelength were averaged. The worst case for an individual spectrum gave 1.4% deviation from the average, but the percent relative standard deviation for 30 repetitive scans was 0.8%. The next investigation involved the possibility that slop or misalignment of the grating rotation mechanism might adversely affect the system when driving from different directions. The procedure described above was repeated for 30 spectra with each spectrum alternating in scanning direction. The estimate of reproducibility was obtained with the above techniques. The worst case for directional precision was 1.95% but the average was 1.3%. The final case investigated was the effect of scanning speed on reproducibility. Twenty spectra were obtained; four each a t 10, 30, 60, 90, and 120 sec scanning time over the wavelength range 633.3 to 550.0 nm. This time, however, the time constant, T , of the detection system was modified to allow a t least 5 T a t each spectral interval. Peak heights were measured and the percent relative standard deviation was found to be 2.7% with the worst case of 3.6%. These estimates of reproducibility seem to be satisfactory and indicate sufficient reliability for quantitative analysis. T a r g e t Sensitivity. The procedure for aligning the grating and the mirror is given in the Operational Procedure section. I t is not difficult to align the undiffused laser image on the target center and then to center the fringes. However, it is conceivable that the target itself may be improperly positioned. If the laser image is aligned 2 mm above, below, left, or right of the target center, then the peak signal is found to be 38%, 30%, 81%,and 78%, respectively, of the signal for the centered image. Thus, slight misalignment or misorientation of the optical axis does not cause a catastrophic failure of the system. The high and low positions give more attenuation because the grating scans left to right or vice versa and therefore is more tolerant of deviations in this plane. Misalignment did not affect the overall reproducibility of the system. The primary difficulty was peak height attenuation, and the resultant decrease in the measured signal-to-noise ratio. Time Constant a n d Scan Speed. A large number of


1

/

I

,'

I

i

Figure 10. Resolution of Na-resonance doublet by SEMIDS system

I I

(steps on peaks result from stepping interval on grating drive). Conditions: 10 wg/ml Na sprayed into air/CpHp flame

spectra were obtained of the Ne emission lines of a Hg hollow cathode lamp in the spectral region from 626.6 t o 585.2 nm a t various combinations of scanning speed and time constants. I t was found that both signal level and the half width of the measured spectral lines were a function of the measurement time constant, T. In addition, because the time constant was used to average the signal for the rms circuit, the noise level was also a function of T. For example, in two spectra obtained with the same scanning speed, changing T from 1 sec to 300 msec increased the signal level slightly less than 50% while the noise increased 200%. This phenomenon was observed a t all scan speeds. Below a certain T, the detector circuits provide insufficient averaging capacity, and S/N deteriorates. Conversely, a t every scan speed, if T were above a certain value, the peak width increased and the peak height decreased. This results, of course, because the electronic measurement system cannot respond to the changing photomultiplier signal fast enough to preserve linearity. In practice, these observations did not prove to be limiting because it was possible to pick a T a t least five times faster than the time each spectral interval was observed a t all scan speeds; T was generally decreased until the unfiltered noise became a problem. Resolving Power,'Resolution. As noted in the Theory section, the theoretical resolving power of SEMIDS should be the same as the resolving power of the grating. In the present system, the grating has 590 grooves/mm and is 40 mm wide; approxima1:ely 30 mm is imaged on the detector. Therefore, in the first order, the resolving power should be 17700. In Figure 10, the resolved Na doublet spectrum (under highest resolution) obtained with SEMIDS is shown. The steplike formations on the peak sides are caused by the motor motion. The bandwidth of the peaks in Figure 10 is approximately 0.039 nm. If we use this bandwidth a t 588.99 nm and solve for the resolving power, we obtain 15063, approximately 85% of the theoretically possible resolving power. Theoretical considt?rations following the Dohi and Suzuki ( 5 ) paper indicate that, for the particular configuration of SEMIDS, the depth of modulation and, hence, the signal should decrease with an aperture of 6.4 mm or larger. In Figure 11,the effect of various size apertures on peak signal intensity is shown. With apertures above 4 mm with the current entrance optics configuration, the peak signal remains constant. However, a much more interesting observation is that a t all apertures, t h e resolution is constant. This is, of course, not the case in conventional grating spectrometers. Therefore, in the latter case, the inherent adANALYTICAL CHEMISTRY, VOL. 47, NO. 14, DECEMBER 1975

2337

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0 '

,

485 2

6074

666 E

wAVELENGTn,nm

Figure 12. Spectrum of copper hollow cathode lamp emission from -626.6 to -585.2 nm

Figure 14. Flame emission spectra of the Na doublet and of Cr in the 425-429 nm region

588.99

and 589.59 nm

Conditions: Na, 1.0 @g/ml: Cr, 10 pglmi; air/C2H* flame; scan speed, 50 A/sec for Na; 70 A/sec for Cr

Conditions were: photomultiplier voltage = 500 V: current-to-voltage gain = lo6; selective amplifier settings: 420 Hz, 0 = 100, gain = X10; amplifier gain = X100: multiplier = 10 V input, 7 = 1 sec; recorder 25 seclcm x-axis, 0.5 Vlcm y-axis: time for spectrum = 30 sec

150. 140-

130.

120110. IO0

1009 0.

BO.

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, 50 10

20

30

40

50

60

70

80

90

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CONCENTRATION. p v / m l

I

Figure 15. Analytical calibration curves for Sr and Cu in flame (air/ C2H2)atomic emission spectrometry

0

Figure 13. Spectrum of copper hollow cathode lamp emission from to -585.2 nm

-626.6

Conditions were: same as Figure 12 except for recorder x-axis = 10 seclcm and time for spectrum = 10 sec

of the Sr determination was 2.5 chart u n i t d l pg/ml while for Cu the sensitivity was somewhat lower, 1.5 chart u n i t d l pg/ml. Analytical calibration curves have been obtained for Na, Li, Sr, Cu, Ag, Mn, Ba, Ca, and Cr.

SUMMARY SEMIDS has been demonstrated to be analytically useful for emission spectrometry in the UV-Visible region. Linear response and good stability have been established. Investigation of S/N behavior indicates that low background radiation sources enhance performance and resolving power near the theoretical limit has been essentially attained. The combination of high resolution and high collection solid angle makes SEMIDS a sensitive scanning spectrometer capable of rapid scans with excellent resolution and 2338

sensitivity. The S/N disadvantage from bright sources becomes an advantage with faint signals, e.g., SEMIDS should be very useful for fluorescence work. The major disadvantage encountered was a frequency shift in the modulation frequency over long wavelength scans. The problem arises because the mirror displacement necessary to drive over four fringes a t 600 nm will drive over eight fringes at 300 nm. At wavelengths somewhere between 300 and 600 nm, an odd number of fringes are passing over the detector surface and the signal maximum shifts away from the frequency of the selective amplifier. Work is currently under way to correct the problem and allow long scans. Because the unimorphs are linear with voltage, it is possible to vary the applied waveform voltage with the grating rotation and therefore maintain a fixed number of fringe displacements rather than a fixed distance displacement. Investigations are also proceeding with SEMIDS in atomic fluorescence spectroscopy, especially in sequentially-slewed (9) multielement atomic fluorescence spectrometry.

LITERATURE CITED (1) F. A. Jenkins and H. E. White, "Fundamentals of Optics", 3rd ed., McGraw-Hill. New York. 1957, p 111. (2) P. Jacquinot and J. C. Dufour, J. Rech. CNRS, 6 , 91 (1948).


(3) (4) (5) (6)

P. Jacquinot, Rep. Progr. Pbys., 23, 267 (1960). P. Connes, Rev. Opt., 38, 157 (1959). T. Dohi and T. Suzuki, Appl. Opt., I O , 1359 (1971). F. A . Jenkins and H. E. White, Fundamentals of Optics", 3rd ed., McGraw-Hill, New York, 1957, p 300. (7) J. F. James and R. S. Sternberg, "The Design of Optical Spectrometers", Chapman & Hill Ltd., London, 1969, p 189.

(8) R . J. Bell, "Introductory Fourier Transform Spectroscopy", Academic Press, New York, 1972, p 287. (9) D. J. Johnson, F. W. Plankey, and J. D. Winefordner, Can. J. Spectrosc., 19, 151 (1974).

for review June 2 y lg7'. Accepted August l 2 ~ 1975. This work supported by AF-AFOSR-74-2574.

Errors in Absorbance Measurements in Infrared Fourier Transform Spectrometry because of Limited Instrument Resolution Robert J. Anderson' and Peter R. Griffiths* Department of Chemistry, Ohio University, Athens, Ohio 4570 1

Calculations have been performed of the errors introduced in the measurement of peak absorbances by Infrared Fourler transform spectrometry as a result of the flnlte spectral resolutlon of the Instrument. A Lorentzian line shape and either triangular or no apodization has been assumed. A simple expression Is presented for the minlmum error expected in the former case. For comparison with conventlonal Infrared spectrometers, similar calculations were made assuming a triangular slit function. Except for large peak absorbances, comparable errors are calculated for trlangular apodization and a triangular slit function. Errors wlthout apodization are much smaller and become large only when resolution is numerically greater than line width. Spectra of the 2231 cm-' band of benzonltrile in CCI4 solutions have been measured and confirm the results of the calculations.

The measurement of an absorption or emission spectrum with a spectrometer of finite resolution distorts the spectrum to a greater or lesser extent depending on the resolution of the instrument. The differences between true and apparent intensities which are caused by the finite spectral resolution of an instrument will be termed resolution errors in this work. They arise because the intensity experimentally observed at any wavelength is actually the intensity of the spectrum averaged over the spectral bandpass of the spectrometer. Such errors have been of particular importance in infrared spectrometry where comparatively weak sources and insensitive detectors have often necessitated use of rather large spectral bandpasses. A number of authors have discussed the effects of limited resolution on spec1ra obtained with conventional grating and prism spectrometers. Dennison ( I ) , Ramsay ( 2 ) , and others (3-5), have calculated the distortion of single absorption lines by various spectrometer slit functions. Either Lorentzian (1-4) or Gaussian ( 4 , 5 ) line shapes and triangular (1-3, 5 ) , Gaussian (1, 3, 4 ) , or Lorentzian ( 4 ) (or, more accurately, Cauchy) slit functions were assumed. Experimental investigations of resolution errors found with liquid samples and conventional spectrometers have been reported by Ramsey ( 2 ) and others (6-9). A general rule of thumb (2, 7, 8,101 appears to have emerged from this work which states that for conventional spectrometers the full On sabbatical leave from Department of Chemistry, Ithaca College, Ithaca, N.Y. 14850. Author to whom reprint requests should be sent.

width a t half height ( F W H H )of the absorption band (plotted on a linear absorbance scale) should be greater than five times the spectral slit width of the instrument to maintain acceptable distortion. The reader is referred to the literature cited for further details. A review of theoretical and experimental work on shapes and intensities of infrared absorption bands has been published by Seshadri and Jones (11). The review by Nielson et al. (3) treats absorption by gases. Despite the increasing use of infrared Fourier transform spectrometry (FT-IR), no systematic study has been published concerning resolution errors as they occur in FT-IR. We here report the results of theoretical and experimental investigations of such errors. Calculations of resolution errors for single absorption lines measured by FT-IR using either unapodized or triangularly apodized interferograms have been performed. The results are compared with similar calculations for a conventional spectrometer with a triangular slit function. Experimental FT-IR spectra of liquid samples have been measured and the observed resolution errors are compared with those calculated. Finally, some additional practical considerations regarding the choice of an apodization function are discussed.

THEORETICAL CALCULATIONS Theory. The resolution of a spectrometer is quantitatively described by its instrument function or instrument line shape (ILS) (11, 1 2 ) , u(v,vi), which describes the response of the instrument to radiation of frequency u when the instrument measures a t a frequency ui. For conventional spectrometers this is commonly called the spectral slit function, but for FT-IR we prefer the generalized terminology. The ILS would be observed experimentally by measuring the spectrum of an infinitely narrow emission line. The ILS functions considered in this work depend only on the difference between u and vi and can be written u(v - vi). If the intensity of radiation of frequency u incident on the spectrometer is given by Z ( v ) , the apparent intensity recorded by the spectrometer a t frequency vi is given by the convolution of Z ( u ) with the ILS function

For absorption measurements, the intensity of radiation incident on the sample, Z,,(u), which is transmitted to the detector is I ( u ) = I,(u) exp ( - k ( v ) l ) where k ( u ) is the absorption coefficient and 1 is the optical depth. If Z,(v) is taken


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Selectively modulated interferometric dispersive spectrometer for

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