Far-infrared high-resolution Fourier transform spectrometer

Bruno Carli, Massimo Carlotti, Francesco Mencaraglia, and Enzo Rossi

Design and performance of a high-resolution Fourier transform spectrometer for laboratory molecularspectroscopy in the 8-200-cm'1 region are discussed. A folding of the beam path is used to obtain themaximum path difference of 4 m with a mirror stroke of 1 m. The measured linewidth of 0.0019 cm-1 is inagreement with the expected theoretical resolution.

1. Introduction

The availability of high-sensitivity bolometers andthe use of high-efficiency and large throughput opticshave made high-resolution incoherent spectroscopypossible also in the far-infrared region. We have al-ready reported the construction of a Fourier transform(FT) spectrometer of the Martin-Puplett type' thatwas used in the 8-85-cm-1 region for both measure-ments of the stratospheric emission spectrum from aballoon-borne platform2 and laboratory measure-ments of molecular spectra.3 The unapodized resolu-tion of this instrument, defined as the spacing betweenpoints that provide independent measurements in thefrequency domain, was 0.0033 cm-'. The resultsshowed the interest of measurements at even higherresolution for the study of the many molecules thatdisplay far-infrared transitions with spacings of theorder of 10-3 cm-', and the importance-for the analy-sis of stratospheric spectra-of reference laboratorymeasurements with an accuracy appreciably betterthan that of field measurements.

These considerations motivated the construction ofa second unit with an unapodized resolution of 0.00125cm-', devoted to laboratory measurements. To have asignificant overlap with the measurements supplied byother infrared spectrometers, the instrument was de-

Massimo Carlotti is with University of Bologna, Institute ofChemical Physics & Spectroscopy, Viale Risorgimento 4, 40136 Bo-logna, Italy; E. Rossi is with University of Florence, Physics Depart-ment, Largo E. Fermi 2, 50125 Arcetri-Florence, Italy; the otherauthors are with IROE-CNR, via Panciatichi 64, 50127 Florence,Italy.

Received 9 February 1987.0003-6935/87/183818-05$02.00/0.© 1987 Optical Society of America.

signed to operate up to a nominal frequency of 200cm-.

The new instrument is described in Sec. II and theperformance obtained in recent measurements is dis-cussed in Sec. III.

II. Characteristics of the Instrument

A. Instrument Layout

The instrument was built taking advantage of themodular design of the first unit and of the availablemolds. A few changes were made, intended to intro-duce a folding of the beam path in the interferometerto obtain a maximum path difference of -4 m; and toimprove the mechanical rigidity of the instrument toachieve satisfactory alignment at high frequencies.

Figure 1 shows the optical diagram of the instru-ment. The different optical components are con-tained in separate boxes which are made airtight with0-ring couplings. This arrangement makes it easy toimplement new optical layouts whenever desirable,and eliminates the need for a large evacuable tank.

The standard configuration of the instrument is thatof the Martin-Puplett polarizing interferometer, witha polarizing beam splitter preceded by an input polar-izer and followed by an output polarizer. After remov-al of the polarizers, a Mylar beam splitter can be usedwith the same layout providing the more conventionalconfiguration of a Michelson interferometer with anamplitude-separation beam splitter (amplitude inter-ferometer).

B. Source

Measurements can be made either in emission, usinga large aperture blackbody cooled at liquid nitrogentemperature that fills the optical aperture of the in-strument, or in absorption, using a small hot source inthe focus of an off-axis paraboloid. The temperaturedifference between the source and the sample that isavailable with emission measurements is smaller than

3818 APPLIED OPTICS / Vol. 26, No. 18 / 15 September 1987

Fig. 1. Optical diagram of the far-infrared Fourier transform spec-trometer.

that available with absorption measurements. Ahigher signal is obtained, therefore, in the latter case.

The hot source operates in the vacuum of the instru-ment and is surrounded by a water-cooled housing.The same housing can accommodate either of two hotsources. The first is a high-pressure mercury-arclamp with dc power supply. The brightness tempera-ture of this source in the submillimeter region is of theorder of 1000 K, but it tends to decrease with increas-ing frequency because of the absorption of the quartzwindow through which the discharge is observed. Thesecond is an incandescent carborundum rod, which ismore efficient than the mercury arc at the high-fre-quency end of the spectral region covered by the in-strument.

C. Beam Splitter

Freestanding wire polarizers with a spacing of 25 Armare used as beam splitters in the polarizing-interfer-ometer configuration, while a 12-Am thick Mylar filmis used in the amplitude-interferometer configuration.

The polarizing beam splitter has an interferometricefficiency, defined as the modulation amplitude overmaximum intensity in the case of a monochromaticsource, that is close to unity at the low-frequency endof the spectrum, and decreases with increasing fre-quency. This loss of efficiency is due to both imper-fect polarization caused by the use of wavelengthscomparable with the wire spacing and lack of opticalflatness caused by nonuniform spacing. The Mylarbeam splitter has an interferometric efficiency thatpeaks around a frequency inversely proportional to itsthickness and can be much smaller than unity at otherfrequencies.

In the 8-200-cm-1 region, best performances areobtained using two configurations: the polarizingbeam splitter for measurements up to -100 cm-1, andthe 12-gim thick Mylar beam splitter for measurementsdown to40 cm 1.

It is important to note that when the amplitudebeam splitter is used, the two optical apertures whereinput signals can enter the interferometer (inputports) coincide with the two optical apertures where-from output signals leave the interferometer (outputports); a detector mounted at either of the two portsreceives not only the signal that enters the other portbut also the signal emitted by the detector itself. De-

pending on the position of the sample cell (either be-tween the interferometer and the detector, or betweenthe interferometer and the source), the detector-gen-erated signal may either be attenuated twice by thesample or not be attenuated at all. This fact must betaken into account when line-shape measurements aremade with the interferometer in a configuration withonly two optical ports.

D. Cells

The cells containing the gases to be measured aremade of Pyrex glass; they are 1.45 m long and have adiameter of 140 mm. Two airtight windows separatethe cell from the instrument. High-density polyethyl-ene and Mylar have been used as the materials for thewindows. Comparing windows with similar mechani-cal strength made with the two materials, the polyeth-ylene window is thicker but has less absorption in allthe far IR. Mylar is, however, preferred to polyethyl-ene in the submillimeter region where absorption isvery slight for both materials, and the use of a dielec-tric with a thickness less than the wavelength reducesreflection losses.

A configuration with two cells is adopted, aiming atdouble-beam measurements. This mode of operationcan be implemented by taking advantage of the factthat the polarizing interferometer measures a spec-trum equal to the difference between the spectra of thetwo beams that are transmitted and reflected by theinput polarizer. This instrumental subtraction can beused to subtract the background spectrum (and associ-ated channeling and source fluctuations) from thesample spectrum. To this end it is enough to mount asuitably oriented polarizer in place of mirror A (seeFig. 1). Provided the source is unpolarized, the onlydifference between the two beams differentiated bythe instrument is the absorption of the molecule con-tained in the sample cell.

E. Movement and the Optics

The design of the mechanics and of the electronics ofthe instrument is the same as that of the first unitdescribed in Carli et al.

2 We recall the main charac-teristics of the instrument. The interferometer is op-erated in a rapid-scanning mode, and the moving mir-ror is position-controlled by a closed-loop drive basedon a laser position measurement. High-resolution sin-gle-sided interferograms are recorded, together withlow-resolution double-sided interferograms for phase-error correction.

An important change is the extension of the maxi-mum path difference to -4 m by way of a 1-m carriagestroke and a beam folding. Two roof mirrors withtheir edges lying in perpendicular planes are used inthe optics of the variable-path arm, as shown in Fig. 2.

We recall that in the case of a roof mirror, the projec-tions of incident and reflected beams in the planeperpendicular to the edge of the roof are parallel.Therefore, a jaw of the moving mirror does not changethe direction of the beam at either of the two passages.Furthermore, a pitch of the moving mirror causes an

15 September 1987 / Vol. 26, No. 18 / APPLIED OPTICS 3819

Fig. 2. Perspective view of the mirrors that are used for folding thebeam path in the interferometer.

8 . ~~~~~~~~~b

~0.5-8 V

a: I M2

9.200 09.40 91360 096.400WAVENUMBER (..v) WAVENUMBER (cm-)

Fig.3. (a) Portion of the calibration spectrum of CO around theJ=4 transition at 19.2223 cm- 1 . (b) Portion of the calibration spec-trum of HCl around the J = 8 transition of the isotope 3

5Cl at186.38959 cm-'. See text for measuring conditions.

angular deviation of the reflected beam in the verticalplane, but in this plane the fixed roof mirror reflectsthe beam parallel to itself, so that the beam will besubject to an equal and opposite deviation when goingthrough the moving roof mirror the second time. Thedirection of the beam which returns onto the beamsplitter is, therefore, insensitive to yaw and pitch of themoving carriage and depends only on the alignment ofthe fixed mirror.

Another important feature of this configuration isits effect on the direction of polarization of the beam.We note that the beam is reflected an even number oftimes between two subsequent interactions with thebeam splitter. In this case, the wavefront maintainsits orientation relative to the propagation direction.Since the beam coming from the beam splitter and thebeam returning to the beam splitter travel in oppositedirections, the wavefront of the returning beam isturned over around an axis perpendicular to the direc-tion of propagation. This wavefront rotation can beused to change the direction of the linear polarizationrelative to the beam splitter, so that the beam whichwas originally reflected by the polarizing beam splitteris transmitted the second time, and the one that wastransmitted is reflected. This important property ofthe polarizing interferometer, that was originally im-plemented with one roof mirror by Martin and Pu-plett,' is obtained every time an even number of reflec-tions is used.

F. Detectors

Three detector units are used, each one includingcryostat, detector, condensing cone, filters, and pre-amplifier. The detectors are composite germaniumbolometers and operate at 1.6 K obtained by loweringthe gas pressure on a liquid helium bath. The filtersand the time constant of the detectors in each unit aretuned for maximum responsivity in a different spectralregion. The entrance pupil of each unit is chosen tomatch a solid angle of the interferometer that obeysthe Jacquinot relationship (Q = 2/R) for the resolvingpower R = max/Aa, where amax is the highest frequencyreceived by the detector, and A = 0.00125 cm-'.

Depending on the frequency interval to be investi-gated, a suitable choice of detector unit, beam splitter,source, and cell windows can be made.

Ill. Instrumental Performance

A. Resolution

When all the contingency spaces (e.g., movement-acceleration distance and portion of double-sided in-terferogram) are considered, the nominal maximumpath difference of 4 m provides in practice a maximumpath difference of 3.85 m that corresponds to an una-podized resolution of 0.0013 cm-'. This resolution isdefined by the fact that the theoretical unapodizedinstrumental function, which is a sinc function, pro-vides independent measurements in the frequency do-main with a period of 0.0013 cm-. However, for com-parison of theory and measurements, the full width athalf-maximum (FWHM) of the central peak is a moreconvenient quantity to use. In the case of the aboveinstrumental function, the FWHM is equal to 0.0016cm-l.

Figure 3 shows an expanded portion of the spectrumof CO around the J = 4 transition at 19.22223 cm-' andof the spectrum H35CI around the J = 8 transition at186.38959 cm-'. The spectrum of CO was measuredusing the polarizing-interferometer configuration, themercury-arc lamp, a detector with an 8-45-cm-1 spec-tral response, and Mylar windows on the sample cell.The pressure of CO was 2 mbar. The spectrum of HClwas measured using the amplitude-interferometerconfiguration, the carborundum source, a detectorwith a 40-200-cm-' spectral response, and polyethyl-ene windows on the sample cell. The pressure of HClwas 0.07 mbar.

The FWHM of the features shown in Fig. 3 is 0.0019± 0.0001 cm-'. The width of the observed features ingeneral is determined not only by the width of thetheoretical instrumental function, but also by otherbroadening causes: the intrinsic line shape of thefeature, and the solid angle of the instrument, mis-alignments, and aberration. The agreement betweenthe ideal and the observed FWHM is satisfactory.

B. Frequency AccuracyThe mirror movement is controlled with a frequen-

cy-stabilized He-Ne laser. To avoid the uncertaintiesin the frequency scale that may be caused by misalign-

3820 APPLIED OPTICS / Vol. 26, No. 18 / 15 September 1987

sn- -- � A

Table I. Calibration Table for H35C

ReferenceMeasureda valueb (Ref.-meas.)

(cm-') (cm-') (cm-') X 105

41.743831 41.743895 6.483.386493 83.386502 0.9

104.138208 104.138260 5.2124.826938 124.826909 -2.9145.439912 145.439949 3.7165.964928 165.964971 4.3186.389594 186.389616 2.1206.701725 206.701655 -7.0

rms deviation" = 4.5 X 10-5 cm-'

a A weight proportional to the frequency was assigned to eachmeasurement.

b Nolt et al.4

ments and angular aperture of the interfering beams,we do not rely on the laser frequency for the absolutecalibration of the scale, and use instead calibrationmeasurements with reference molecules. The laserstability of one part in 107 guarantees the reproducibil-ity of the scale. CO is used for measurements at lowfrequencies, and HCl is used for measurements at highfrequencies.4 Table I shows the typical results of aweighted calibration where line positions are mea-sured with a rms deviation of 4.5 X 10-5 cm'1 (corre-sponding to 1.5 MHz).

C. Signal-to-Noise Ratio

A single full-resolution interferogram is recorded in-10 min, but a few spectra are usually collected foreach sample to achieve an improved signal-to-noiseratio by averaging the individual spectra.

A performance close to the theoretical one has beenobtained in the submillimeter region where the instru-ment used in the polarizing configuration has uniquecapabilities, and therefore particular care has beenpaid to its optimization.

Figure 4 shows two single spectra recorded in the 20wavenumber region and their difference. The spectraare raw data without intensity-scale calibration. It ispossible to note some channeling in the continuumsignal, due to the fact that both the optical componentsof the detector system and the thickness of the win-dows have sizes comparable to the wavelength. Fromthe ratio of the average signal and the rms of thedifference between the two spectra, we obtain for eachspectrum an experimental SNR of -250.

The theoretical value of the SNR can be derivedfrom the following expression 5 :

S Im'AO 12T 12S I/ E(a)AQaVGjlG2 ( Et)

N NEP E~)ANa )G

where I is the intensity detected in the interval Aa;NEP is the noise equivalent power of the detector; E(a)is the instrument efficiency and includes the losses dueto filters and windows; AU is the throughput of theinstrument; a is a factor which accounts for the apodi-zation; aG, are the losses and gains associated with thesignal modulation; 3G2 are the losses and gains associ-ated with the spectral modulation; T is the total mea-

10- '-'.'-'An, a - b

| A"'AN''~ife 'a ft b

20he 2059WAVENUMBER (em-8)

Fig. 4. Curves a and b are two subsequent measurements of theCH3CN spectrum recorded at maximum resolution in 10 min each.The pressure of the sample was 0.3 mbar. The polarizing-interfer-ometer configuration, the mercury-arc lamp, and polyethylene win-dows were used. Raw data without intensity-scale calibration areshown. Curve c shows the difference between the two measure-ments, proving the reproducibility of the measurements. The scales

of the three curves are shifted for clarity.

surement time; Et is the time efficiency of the measure-ment; and N is the total number of measured datapoints.

In our case, the signal in each spectral point(AQImAa) is -10-11 W, and the electrical NEP of thedetector is _10-14 W/Hz. No apodization and no sig-nal modulation are used, so that aaG, = 1. Here fi =(N/8)1/2, as in all FT spectrometers, and G2 = 1 becausea single detector is used. A total measurement time of600 s and a time efficiency close to unity are used.Finally, considering an efficiency of the input polarizerequal to 0.5, a transparency of the windows of the cellsequal to 0.6, a transparency of the detector filters equalto 0.2, and a detector absorption of 0.7, we can estimatethat the instrumental efficiency is -4%.

From these numbers, it follows that the expectedvalue of the SNR is equal to 360. Considering theuncertainty in some of the numbers that have beenused for this estimate and the fact that neither geomet-rical walk-off losses nor diffraction losses have beenconsidered, we conclude that no serious unaccountedloss is present in the instrument and a performanceclose to the theoretical one has been obtained.

IV. Conclusions

The construction, the characteristics, and the per-formance of a FT spectrometer which operates in the8-200-cm-1 region with an unapodized resolution of0.0013 cm-' have been reported.

A choice of two types of beam splitter, two sources,two window materials, and three detectors is availablefor optimum performance in the full spectral range.

The measured spectra show a resolution of 0.0019-cm-' (FWHM) over the whole spectral interval, and asignal-to-noise ratio of 250 in the 20-cm-' region, closeto the theoretical values. A frequency accuracy of 4.5X 10- 5 -cm1 (rms) between 40 and 200 cm-' is ob-

15 September 1987 / Vol. 26, No. 18 / APPLIED OPTICS 3821

1

tained using the spectrum of HCl as a calibration stan-dard.

The instrument is used to measure the far-infraredspectrum and to calculate spectroscopic parameters ofspecies that are relevant in atmospheric and astro-physical studies.

References1. D. H. Martin and E. F. Puplett, "Polarized Interferometry for the

Millimetre and Submillimetre Spectrum," Infrared Phys. 10,105(1970).

2. B. Carli, F. Mencaraglia, and A. Bonetti, "Submillimeter High-Resolution FT Spectrometer for Atmospheric Studies," Appl.Opt. 23, 2594 (1984).

3. M. G. Baldecchi, B. Carli, M. Carlotti, G. Di Lonardo, F. Forni, F.Mencaraglia, and A. Trombetti, "High Resolution MolecularSpectroscopy in the Submillimeter Region," Int. J. Infrared Mil-limeter Waves 5, 281 (1984).

4. I. G. Nolt et al., "Accurate Rotational Constants of CO, HCl, andHF: Spectral Standards for the 0.3-6-THz (10-200-cm'1) Re-gion," to be published in J. Mol. Spectrosc.

5. B. Carli and V. Natale, "Efficiency of Spectrometers," Appl. Opt.18, 3953 (1979).

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3822 APPLIED OPTICS / Vol. 26, No. 18 / 15 September 1987