Two-mirror wave-front-dividing interferometer forinfrared synchrotron radiation

K. D. M1ller, D. P. Siddons, C. J. Hirschmugl, D. Scardino, P. Petrone,

D. Carlson, and G. P. Williams

We describe what is to our knowledge the first instrument specifically designed for use with infraredsynchrotron radiation that takes advantage of the spatial coherence of this radiation. Beam splitting isachieved by wave-front division. We show data taken with the instrument over the wavelength regionfrom 10 to 1000 pum (1-mm wavelengths) and discuss the advantages of this instrument over aconventional one.

Introduction

We describe a new class of instrument that wedeveloped that uses the spatially coherent propertiesof infrared synchrotron radiation. We were particu-larly interested in building an instrument capable ofcovering a very wide wavelength range (10-pm-1-cmwavelengths) without changing beam splitters andalso of operating in the asymmetric mode.

Synchrotron radiation is 1000 times brighterthan a conventional mercury source across the entireinfrared region. It is also less noisy than a conven-tional source, thus offering signal-to-noise-ratio ad-vantages of several orders of magnitude for infraredspectroscopy. To date all experiments reported thatused synchrotron radiation at Berlin,' at Daresbury(Great Britain),2 and at Okasaki (Japan)3'4 used com-mercial spectrometers to analyze the source.

At the National Synchrotron Light Source at Brook-haven National Laboratory, the U4IR beam line wasalso initially equipped with a commercial spectrome-ter,5 in this case a new vacuum rapid-scan6 Nicolet20F Michelson interferometer covering the rangefrom 10 iim to 1 mm. This instrument is wellcharacterized and hence provided a useful standardwith which to compare the performance of the newinstrument described in this paper. In addition, the

K. D. M6ller, D. Scardino, and P. Petrone are with the Depart-ment of Physics, Fairleigh Dickinson University, Teaneck, NewJersey 07666. The other authors are with the National Synchro-tron Light Source, Brookhaven National Laboratory, Upton, NewYork 11973.

Received 6 December 1990.0003-6935/91/304297-05$05.00/0.© 1991 Optical Society of America.

commercial instrument was used to make an accurateconfirmation of the spectral properties of the newsource. In fact, the brightness and the flux in theinfrared region agree well with the calculations ofDuncan and Williams7 and Martin.8 References 7 and8 both indicate that in the infrared region the synchro-tron radiation would be highly spatially coherent. Itwas this property that prompted us to develop theinstrument described below.

Spatial coherence

A source is said to be spatially coherent across itslateral dimensions if an interference pattern is visiblewhen it illuminates, for example, two slits whosetransmitted beams recombine on a screen, as shownin Fig. 1(a). This condition implies that there is < 27rof phase error across the wave front. Phase errorsresult in a loss of visibility of the interference fringes.An alternative way of describing spatial coherence isshown in Fig. 1(b). This is a simplification of thegeneral treatment by Born and Wolf' for a screenilluminated by an extended incoherent quasi-mono-chromatic source. In Fig. 1(b) an observation point Pis illuminated by light from two points, S, and S2, adistance s apart on the source. The phase errorresulting from the different optical paths from dif-ferent points on the source will be small over an areaof diameter 2D, given by9

0.16XR2D = (1)

Now, since the half-angle a = DIR, the condition forspatial coherence when a is small can also be written

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bined in the beam splitter of the Michelson instru-ment, changes in the phase of the sample beamrelative to the reference beam cause the energy to beswitched back and forth between the detector armand the incident beam arm.'0 The situation is a littlemore subtle for the division of a wave-front interfer-ometer because the interference takes place in thedetector plane and there is no obvious place for thebeam energy to go under conditions of destructiveinterference. Since the waves arriving at the detectorare neither collimated nor parallel, a spatially inhomo-geneous fringe pattern is formed. This pattern can becalculated in the Fraunhofer approximation, andsuch calculations are shown in Fig. 2. The solid curvein Fig. 2(a) shows the situation for zero path differ-ence, i.e., constructive interference on axis. Thiscentral strong maximum is flanked by two weakmaxima corresponding to the next higher-order dif-fraction. For an optical path difference of half awavelength [see Fig. 2(a), dashed curve], destructiveinterference occurs on axis with symmetrically placedstrong maxima on either side. The beam energy isthus redistributed among different parts of the detec-

Fig. 1. (a) Illustrating the condition for spatial coherence: asource is said to be spatially coherent if the light passing throughthe apertures yields detectable interference fringes. (b) An alterna-tive way of expressing the condition for spatial coherence: 2D =0.16XR/s or sa << X.

in the form

sa << X, (2)

where X is the wavelength of the light. s can be seenfrom Fig. 1(b) to be the actual physical path differencebetween two extreme rays. Although we have definedspatial coherence in this way we note that spatialcoherence implies no phase relationships betweenemitting portions across the source but only thatthese portions are indistinguishable when viewed at adistant screen under the conditions of Eq. (2). Syn-chrotron radiation has the property that a, the half-angle into which the radiation is emitted, is a functionof wavelength and varies in such a way as to help tomaintain spatial coherence; i.e., as X gets shorter, agets smaller. At X = 10 Jim, for example, a = 0.01 rad,while at X = 1 cm a = 0.05 rad. Thus if we assume aheight of 200 plm for the synchrotron source we seethat we satisfy Eq. (2) over the entire 10-p1m-1-cmrange.

The main idea behind the new wave-front-dividinginterferometer is to take advantage of the spatial-coherence property of synchrotron radiation to buildan interferometer in which we spatially divide theemitted wave front, preserving one part as a phase-and-amplitude reference to compare against the probebeam. This is quite different from the operation of aMichelson interferometer, in which the two interfer-ing waves are formed by division of the amplitude ofthe incident wave. When the two beams are recom-

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Fig. 2. Calculated diffraction pattern for a two-plate interferome-ter (inset) of grating constant 2d for a wavelength of d50 forangles covering the first order on both sides. The intensity isnormalized to 1 and plotted as function of 0 [=sin (0) for smallangles], where 0 is the diffraction angle. The different curves referto different optical path differences, 2h, where h is the actual platedisplacement expressed as a function of the wavelength. (a) Solidcurve 2h = 0, dashed curve 2h = /2. (b) Heavy solid curve 2h =X/6, thinner solid curve 2h = 5/6, heavy dashed curve 2h = 4/6,thinner dashed curve 2h = 2/6.

4298, APPLIED OPTICS I Vol. 30, No. 30 I 20 October 1991

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tor plane, rather than switched between the two armsof the Michelson arrangement. Figure 2(b) showspatterns for intermediate path differences.

The use of more plates than the two used in ourdesign provides better spatial separation of thesesidelobes, and hence better fringe contrast in princi-ple, as illustrated in Fig. 3. The difficulty in fabricat-ing and aligning the multiplate instruments makes itmore attractive in practice to use only two, particu-larly at short wavelengths. It is, in any case, possibleto obtain good contrast by proper choice of theacceptance aperture of the detector.

Instrumentation Development

The instrument evolved from a conventional lamellargrating with a reflecting area of 24 cm x 24 cm and agrating constant of - 2 cm. For this instrument wewere able to restack the plates of the laminar gratingto produce grating constants of 6 and 24 cm to checkfor spatial coherence, whose existence was confirmedwhen identical interferograms were obtained for all

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Fig. 4. Optical schematic of the wave-front-dividing interferome-ter: Ml, M2, M7, M8 , flat mirrors; M3, M6, M,, spherical mirrors; Ch,chopper. The wave front is divided by the flat mirrors M4 and M5,which are situated one above another and one of which is scanned.

three grating constants. Following this the new instru-ment described below was built.

The new wave-front-dividing interferometer wasconstructed with two 4 cm x 8 cm mirrors at itsheart. The optical arrangement is shown schemati-cally in Fig. 4. One mirror was fixed; the other couldbe moved over a length of 2.5 cm in steps of 1 Jim.Interferograms were recorded point by point.

As we mentioned above, in the case of the lamellargrating for destructive interference at the detectorsite most of the power is directed into sidelobes in thedetector plane. To prevent this light from reachingthe detector we inserted a slit in the focal plane ofmirror M6. The width required for this slit is afunction of wavelength. Losses at the slit are onedrawback of this two-mirror system; neverthelessthis optical design offers scientific opportunities sincean instrument of this type may be used as an asymmet-ric Fourier-transform spectrometer for small sam-ples. For this application, mirrors M4 and M5 are tiltedvertically with respect to each other, producing twoseparate beams between mirrors M4/ M5 and M8. Twoslits are then used, and mirror M8 is split to allow thebeams to be recombined at the detector.

-0.5 0 0.5Mirror Displacement [mm]

Fig. 5. Interferogram obtained with the two-plate interferometer(Figs. 2 and 4) for a polystyrene sample. The interferogram wasrecorded with 512 data points, each averaged for 1 s. A choppingfrequency of 13 Hz was used, and the detector was a liquid-helium-cooled bolometer. The detected interferogram was limited by filtersand the detector to the 50-800-cm-1 region.

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Fig. 3. Calculated diffraction pattern for a four-plate interferome-ter (minigrating) of grating constant 2d (total grating width 4d) fora wavelength X of d/50 for angles covering the first order on bothsides. The intensity is normalized to 1 and plotted as function of 0[=sin (0) for small angles], where is the diffraction angle. Thedifferent curves refer to different optical path differences 2h whereh is the actual plate displacement expressed as a function of thewavelength. (a) Solid curve 2h = 0, dashed curve 2h = /2. (b)Heavy solid curve 2h = X/6, thinner solid curve 2h = 5X/6, heavydashed curve 2h = 4X/6, thinner dashed curve 2h = 2A/6.

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Fig. 6. Fourier transform of Fig. 5 showing the spectrum in the50-800-cm-' region. The overall shape is controlled primarily bythe filters in the detector and by the detector response. Theabsorption peaks are due to both the polystyrene sample and thefilters.

Results

Spectral Region from 1000 to 100 cm-'

The 1000-100-cm-' spectral region was studied byusing a liquid-helium-cooled bolometer manufac-tured by Infrared Laboratories (fitted with a cooled750 cm-' cut-on filter) as the detector. The slit was setto 0.5-mm width, and a sample of polystyrene wasinserted before the detector. Figure 5 shows theinterferogram recorded with a total of 512 points at 1point/s and a time constant of 1 s. Figure 6 shows thespectrum derived from this interferogram coveringthe 50-700-cm-1 range and with peaks from both thefilter and the polystyrene sample. This spectrum

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Fig. 7. Interferogram obtained with the two-plate interferometer(Figs. 2 and 4) for a wedged-shaped crystal-quartz sample. Theinterferogram was recorded with 256 data points, each averagedfor 1 s. A chopping frequency of 13 Hz was used, and the detectorwas a liquid-helium-cooled bolometer. The detected interferogramwas limited by filters and the detector to the 25-300-cm-1 region.

600

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Fig. 8. Fourier transform of Fig. 7 showing the spectrum in the25-300-cm-' region. The overall shape is controlled primarily bythe filters in the detector and by the detector response. The127-cm-1 absorption line of the crystal quartz can be clearly seen.

closely resembles spectra taken with the Nicoletfast-scanning interferometer with the same detector,demonstrating that the two-mirror interferometercan indeed be applied to such high frequencies.

Spectral Region from 400 to 50 cm-'

The 400-50-cm-' spectral region was taken with thesame liquid-helium-cooled detector as described abovebut with a 350-cm-' cut-on cooled filter. A wedge-shaped crystal-quartz plate was placed before thedetector. Figure 7 shows the interferogram recordedpoint by point with a time constant of 1 s. A total of256 points were taken at 1 point/s. The slit wasopened to 1 mm. The spectrum resulting from theFourier transform of this interferogram is shown inFig. 8. The quartz band at 127 cm-' is clearly visible.

500 10 20 30 40Frequency [Wavenumbers (cm l)]

Fig. 9. Spectra in the 10-50-cm-' region taken from an interfero-gram that used 256 points, with 1 s/point. The two spectra shownhave different water-vapor content in the optical path. The absorp-tion peaks are due to the detector response, filters, and water-vaporabsorption.

4300 APPLIED OPTICS / Vol. 30, No. 30 / 20 October 1991

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Fig. 10. Division of the two spectra shown in Fig. 9 showing threemajor peaks, at 33.0, 25.1, and 18.6 cm-', that are due to watervapor. The smaller peaks, at 30.5 and 20.8 cm-', also agree wellwith calculated values (see Ref. 6).

Spectral Region from 50-1 to 10 cm-'

The 50-10-cm'1 spectral region was studied with apumped liquid-helium-cooled boron-doped siliconbolometer with a noise-equivalent power of 10-l'W/JHz (Infrared Laboratories). Within the bolome-ter we removed a reflection plate at the back of thedetecting element to avoid an interference that wehad also observed earlier. The same chopping speedwas used, and the slit was opened to 5 mm. Figure 9shows the spectra obtained from interferograms re-corded at 1 point/s and with 256 points. Two spectraare shown, which were obtained with differentamounts of water vapor in the beam path. The peakscorrespond to a superposition of peaks from thelow-pass filter and from water-vapor absorption. Asubtraction of the two spectra is shown in Fig. 10,which reveals the water-vapor contribution; in factthe positions and intensities of these lines are inexcellent agreement with calculation.6

Discussion

We have demonstrated that infrared synchrotronradiation has a high degree of spatial coherence, andwe have developed and studied the performance of awave-front-dividing interferometer that makes ex-plicit use of this fact. Splitting the incident beam inthis way completely eliminates the need for a semi-transparent beam splitter, making it possible to cover

a wide range of wavelengths without changing opticalelements. The two-mirror instrument described aboveis particularly suitable for use in the asymmetricmode with small samples. In this mode one of thebeams passes through the sample and suffers bothphase and amplitude changes. From these changesboth the real and the imaginary parts of the opticalconstants can be determined. It will be particularlyinteresting to use the instrument in rapid-scan mode6to eliminate low-frequency noise of the kind visible inFig. 6. In this case the intensity may be increased byan additional factor of 2 at the detector since achopper is not needed. Finally, we note that inprinciple it is possible to use this type of instrumentin the vacuum-ultraviolet region and even in thesoft-x-ray region with synchrotron radiation. There isa high degree of spatial coherence for many of the newundulator sources in this region.

We thank J. Allen of Bell Communications, Inc.,Red Bank, N.J., and U. Strom, U.S. Naval ResearchLaboratory, Washington D.C., for their help andinterest in this project. Research at the BrookhavenNational Laboratory was performed under the aus-pices of the U.S. Department of Energy contractDE-AC02-76CH00016.

References1. E. Schweizer, J. Nagel, W. Braun, E. Lippert, and A. M.

Bradshaw, "The electron storage ring as a source of infraredradiation," Nucl. Instrum. Meth. A239, 630-634 (1985).

2. J. Yarwood, T. Shuttleworth, J. B. Hasted, and T. Nanba, "Anew radiation source for the infrared region," Nature (Lon-don) 312, 724-744 (1984).

3. T. Nanba, J. Yarwood, T. Shuttleworth, and J. B. Hasted,"Synchrotron radiation for long wavelength spectroscopy,"Int. J. Infrared Millimeter Waves 7, 759-769 (1986).

4. T. Nanba, "Utilization of synchrotron radiation in the far-infrared region," Rev. Sci. Instrum. 60, 1680-1685 (1989).

5. G. P. Williams, "The initial scientific program at the NSLSinfrared beamline," Nucl. Instrum. Methods A291, 8-12(1990).

6. K. D. Moeller and W. G. Rothschild, Far Infrared Spectroscopy(Wiley, New York, 1971).

7. W. D. Duncan and G. P. Williams, "Infrared synchrotronradiation from electron storage," Appl. Opt. 22, 2914-2923(1983).

8. D. Martin, "Investigation into the use of the SRS in the farinfrared region," Rep. for contract B87763/B87764 (Scienceand Engineering Research Council Daresbury Laboratory,Warrington, UK).

9. M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford,1964).

10. R. J. Bell, Introductory Fourier Transform Spectroscopy (Aca-demic, New York, 1972).

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