Polarization Fourier Spectrometer for Astronomy

Michael F. A'Hearn, Francis J. Ahern, and David M. Zipoy

A polarization Fourier spectrometer is described that improves on the previous versions built by othersand can be used from 0.3 ju to 2.5 u. Several practical problems in the construction and data reductionare discussed, and a number of typical results are presented to show the performance of the instrument.

Introduction

A number of years ago Mertz' proposed a birefrin-gent Fourier transform spectrometer for astronomicaluse in which the optical delay between the twobeams of light was obtained by polarizing the lightand passing it through an appropriately oriented bi-refringent material. Instruments of this type havebeen built for astronomical use in the ir by Sinton 2

and in the optical by Mertz,3 but these instrumentshave not received any subsequent attention from as-tronomers. Virtually all astronomical work withFourier transform techniques has centered on con-ventional Michelson interferometers for use in the irwith essentially no work shortward of the red line ofthe He-Ne laser. Since the birefringent interferom-eter offers a number of significant advantages for op-tical astronomy, we have developed an instrument ofwide versatility based on the principles of the Mertzinstrument.

Because the large attraction of Michelson interfer-ometers has been the multiplex advantage, which al-lows one to overcome to some extent the high noiseof ir detectors, some of the other advantages of inter-ferometry have not been emphasized although theyare equally applicable in the optical region where themultiplex advantage is much less important. Theseadvantages include a large etendue (compared tograting spectrometers), freedom to vary spectral res-olution over a wide range, a very wide free spectralrange, and a ready adaptability to ratioing tech-niques for reducing sensitivity to brightness fluctua-tions in the incident light. The etendue of a bire-fringent interferometer is less than that of a Michel-son interferometer due to the variation in birefrin-gence for off-axis rays, but it is still greater than for

When this work was done all the authors were with the Astron-omy Program, University of Maryland, College Park, Maryland20742. F. J. Ahern is presently at the David Dunlap Observa-tory of the University of Toronto.

Received 2 August 1973.

a grating spectrometer of otherwise similar charac-teristics. Other advantages of the birefringent inter-ferometer are that it is much less sensitive to opticalmisalignment than the Michelson interferometer, itautomatically measures the spectrum in two ortho-gonal planes of linear polarization simultaneously(thus allowing a proper determination of the spec-trum of polarized sources), and it provides automaticsky brightness subtraction without a separate mea-surement.

Optical Description

The optical schematic of the instrument is shownin Fig. 1 and follows the outlines of the previous in-struments by Sinton and Mertz. The basic theory ofthe instrument is described quantitatively by Steel4and qualitatively by Mertz.5 We have varied fromthe previous designs primarily in recording all fourbeams of the instrument separately rather than dis-carding two as in the Mertz design or combining op-posite polarizations as in the Sinton design. To re-view the principles, the Wollaston prism W1, whichimmediately follows the collimator, splits the lightinto two orthogonally polarized beams that are thentreated entirely independently in the rest of the in-strument. As one of these beams passes through theBabinet-Soleil compensator (which has its opticalaxis oriented at 450 to the Wollaston splitting), itcan be thought of as having two components of equalintensity polarized parallel and perpendicular, re-spectively, to the optical axis of the compensator.The component polarized perpendicular to the axissuffers a delay relative to that polarized parallel tothe axis since it sees a greater index of refraction.Since these two components are orthogonally polar-ized, they of course cannot interfere with each other,but the subsequent Wollaston prism W2 resolves thetwo polarizations into components parallel and per-pendicular to the original plane of polarization of thebeam and thus permits interference. It can easily beshown that this results in the two beams emergingfrom W2 having fringes that are exactly out of phasewith each other. The second beam emerging from

May 1974 / Vol. 13, No. 5 / APPLIED OPTICS 1147

TELESCOPE

Di

LTI

FILTERS

BABINET -ISOLEIL

D2

W2L3

CERAMIC

PM TUBES

Fig. 1. Optical schematic diagram of instrument. For detailssee discussion in text. Orientation of polarizing components toproduce the appropriately polarized beams can be seen, for exam-

ple, in Fig. 1 of Mertz. 3

W1 follows a similar path and emerges from theother W2 as another pair of beams with complemen-tary fringes. Automatic sky subtraction takes placebecause the first Wollaston W1 superimposes oneach of the two beams an additional beam of the op-posite polarization from an adjacent area of sky.This results in a cancellation of the fringes due tothe sky, leaving only an additional bias level in thesignal.

The heart of the instrument is, of course, the Ba-binet-Soleil compensator that determines both theresolution and the etendue of the instrument. Thecompensator in the present instrument is a crystal ofcalcite; calcite was chosen because of its high trans-mission throughout the optical and near ir regioncombined with its high birefringence and relativeimperviousness to humidity. The effective free spec-tral range of the instrument thus runs from the at-mospheric cutoff near 3000 A to the absorptionbands of water (adsorbed in the calcite) near 2.5 M.All other optical components have been chosen tocover this range also. We have used a compensatorwith a clear aperture 18 mm square and a delay at5000 A which can be varied from several hundredwaves advance to somewhat over 2000 waves retar-dation. Unlike the conventional Michelson interfer-ometer in which the spectral resolution in wavenum-ber units is nearly independent of wavenumber, thevariable birefringence of calcite leads to a slow varia-

Lion in the spectral resolution that is nearly linear inwavenumber from roughly 8 cm-' at 33,000 cm-' (3/4A at 3000 A) to roughly 11 cm-' at 4000 cm-' (70 Aat 2.5 A).

The specification of the field available with thistype of interferometer is a bit difficult because thefringe pattern is hyperbolic (due to the change in bi-refringence for off-axis rays) rather than circular.The fringe pattern as seen in both narrow bandpasslight and white light is shown in Fig. 2. Further-more, the field is usually not centered on the fringepattern because one must allow for two adjacentfields corresponding to the two orthogonal polariza-tions of incident radiation. The Wollaston prismW1 separates the two fields along one of the asymp-totes of the hyperbolae by an amount depending onthe splitting angle of the Wollaston. The images ofthe field are displaced along the asymptote such thatwhen the instrument is used at maximum field thetwo field images are tangent at the center of the pat-tern. The splitting angle of the Wollaston is deter-mined by the resolution limit and the field. Wehave rather arbitrarily taken the maximum circularfield to be that size at which a uniform source fillingthe field would yield 90% fringe visibility in theworst cast (maximum delay and 3000-A light). Thiscorresponds to a cone of radiation having a total di-vergence of 1 entering the compensator, which inturn implies that the Wollaston splitting angleshould be 1 and that the field of view in the tele-scope focal plane subtends an angle of 1 as seenfrom the collimator lens L1. (The collimator alsoserves as a field lens, imaging the telescope objectiveinside Wollaston prism W1.) Combining these factswe find that the angular field of view on the sky inmin of arc is equal to 40/D, where D is the telescopediameter in inches. Our criterion for field size interms of fringe visibility yields a field in which twopoints on the edge of the field have very large phaseerrors relative to the vertex of the hyperbolae. Thismeans that serious sampling errors will arise if apoint source is allowed to wander over the entirefield; similar effects can occur with extended sourcesof very nonuniform brightness. Thus many of theobservations with the instrument have been madewith fields smaller than that determined above.

After these basic considerations the parameters ofthe remaining components can be specified. Ourpresent collimator is designed for use at a focal ratioof 13.5 since this covers the majority of moderatesized telescopes. The lens itself is a doublet of fusedquartz and calcium fluoride, with a focal length of200 mm and achromatized for 3400 A and 1.0 a.The focal length is thus constant to within 1 mmfrom 3000 A to 1.3 A but deviates considerably atlonger wavelengths. Despite the chromatic effects,lenses were chosen over mirrors to eliminate spuriouspolarization effects that might occur with off-axismirrors. In addition, lenses have smaller losses thando mirrors over such a wide spectral range.

The Wollaston prism W1, which splits the lightinto two orthogonally polarized beams, is of quartz

1148 APPLIED OPTICS / Vol. 13, No. 5 / May 1974

Fig. 2. Hyperbolic fringe pat-tern. Fringe pattern photo-graphed in different colorsthrough the entire instrumentwith field stop diaphragms re-moved. a, b, and c are rela-tively narrow-band photographsin blue, green, and red light, re-spectively, taken at the samewedge position while d is awhite light photograph. Allphotographs were taken with thewedge set nominally for thewhite light fringe. The varia-tions with colors of the centralfringe are due to the large phaseshift introduced by the air gapin the Babinet-Soleil compensa-

tor.

rather than calcite despite the relatively large (10)splitting angle. If calcite had been used, the varia-tion in splitting angle with wavelength would havebeen a significant fraction of the splitting angle it-self. This would have led, in effect, to measuringthe uv light from a different part of the field thanthe visible light. With a quartz prism this effect ismuch smaller. In order to minimize reflections,components are optically contacted with DC-200(Ref. 6) silicone fluid wherever possible. The mainproblem encountered in the instrument has been theexistence of an air gap between the two wedges of

the compensator. Refraction at this gap varies withwavelength and with angle of incidence leading tosignificant displacements of the beam in the gap.Thus short wavelengths are displaced more thanlong wavelengths, and certain parts of the field aredisplaced more than others. This displacementleads in turn to delays that vary across the field.This variation can be minimized only by makingthe air gap as small as possible. At present we usean air gap of a few thousandths of an inch since anysmaller air gap would lead to danger of scratchingthe calcite surfaces by small dust particles. An ob-

May1974 / Vol. 13, No. 5 / APPLIED OPTICS 1149

vious improvement would be either to seal hermeti-cally the unit and reduce the air gap to a matter oftens of microns or to seal it and fill it with a fluidsuch as DC-200.

After leaving the compensator the light passes tothe camera lens L2, which reimages the field. Thislens is similar to the collimator lens in all respectsexcept focal length, which is 165 mm, a number cho-sen entirely for convenience in subsequent mechani-cal design. It was positioned as close to the com-pensator as was mechanically convenient. The lensforms two polarized images of the field that are tan-gent to each other. The field of view is then deter-mined by various readily interchangeable dia-phragms D2 inserted at the instrumental focal plane.Although two diaphragms are required to isolate thefield in this focal plane, the alternative of definingthe field in the telescope focal plane has an evenworse drawback. The automatic sky subtractionfeature of this instrument requires that adjacentareas of sky on either side of the desired field be iso-lated as well, thus requiring three accurately posi-tioned diaphragms of accurately equal area ratherthan the two of nominally equal area that are re-quired at the instrumental focal plane. At times,however, one would like to suppress the automaticsky subtraction feature, either because the sky isstrongly polarized and the sky subtraction conse-quently does not work properly or because the adja-cent areas of sky contain another part of the objectof interest or other objects. Alternatively, one mightsometimes wish to define the field at the telescopefocal plane to eliminate the slight chromatic effectsin the images at the instrumental focal plane. Ineither eventuality a diaphragm can be inserted atthe telescope focal plane either to suppress sky sub-traction or to define the field.

Immediately following the rear diaphragms arefused quartz prisms that are used to separate theemerging beams spatially and for mechanical conve-nience to send the beams to the side of the instru-ment. Wollaston prisms W2 are then contacted tothe exit faces of these prisms thus forming the fouroutput beams of the instrument. The two beamsout of one Wollaston show complementary fringes forone plane of incident linear polarization, while thetwo beams from the other Wollaston show comple-mentary fringes for the orthogonal plane of incidentlinear polarization. Finally on the exit faces of thetwo Wollastons are contacted Fabry lenses L3 thatimage the telescope objective onto the four detectorswhich are arranged in a square array. A viewingeyepiece at this point allows the observer to view thefield in all four output beams.

Wedge Control System

The principal decisions to be made in determiningthe wedge control system are the choice between acontinuous drive or a step and integrate mode of op-eration and the choice of a method for monitoringthe wedge position. The only truly satisfactorymethod for monitoring the wedge position is actually

to observe fringes through the interferometer itself.Any monitoring method that does not pass lightthrough the interferometer is subject to numerousproblems including, for example, the change in delayproduced by a change in temperature of the instru-ment. Temperature changes in astronomical appli-cations can be extreme, and so an internal monitor-ing system is essential. Since the sampling theoremrequires that samples be taken every half-fringe ofthe shortest wavelength being observed, it is desir-able that the fringe reference light be of this wave-length or shorter. We use the 2537-A line of a mer-cury discharge lamp to produce two beams withcomplementary fringes. The difference betweenthese two outputs has a zero every half-fringe of thereference wavelength, and the position of the zero isnot affected by brightness fluctuations of the refer-ence light source.

The light from the discharge lamp is passedthrough a small diaphragm (D3 in optical schemat-ic), filtered to eliminate the visible lines, polarizedwith a Glan-Taylor prism (GT), and collimated byL4. It is then passed through an unused corner ofthe compensator in the reverse direction, i.e., towardthe telescope, in order to prevent this intense lightfrom being scattered into the main detectors. Afterpassing through the compensator the beam is splitinto two polarized components by Wollaston prismW1, and these two beams, which show complemen-tary fringes in the 2537-A line, are incident on twoRCA 1P28 photomultipliers. The outputs of the twophotomultiplier amplifiers are adjusted so that thetwo signals have equal amplitudes. The differencebetween these two signals then has a null at everyhalf-fringe of the 2537-A line. Unfortunately thephase of these two signals is critically dependent onthe thickness of the air gap between the two wedgesof the compensator, and any variation in the spacingwill lead to severe sampling errors. Thus the twowedges must be aligned with the direction of motionwith extreme care. This problem would also be con-siderably alleviated if the compensator were im-mersed in a fluid of appropriate index as describedabove.

The choice between continuous drive or step andintegrate is a difficult one. With a continuous drivesampling errors are easily introduced by smallamounts of wow or flutter in the driving motor. Onthe other hand this method allows rapid scanning, atechnique that can entirely eliminate the effects ofatmospheric scintillation. The step and integratemethod is severely limited in its ability to rapidscan, but there are other methods for reducing scin-tillation that have been combined with the step andintegrate method to produce some of the best Fouriertransform data to date. We have therefore chosenthe step and integrate method.

The principal drive control is an 8-phase steppingmotor that is geared to a micrometer that in turndrives the wedge. The gearing has been chosen sothat each step of the stepping motor corresponds ap-proximately to one-half fringe of the fringe reference

1150 APPLIED OPTICS / Vol. 13, No. 5 / May 1974

system. To obtain more precise sampling we use aservosystem that operates a piezoelectric ceramicthat is capable of driving the wedge through ap-proximately one whole fringe of the 2537-A line.The servosystem zeroes the integral of the differ-ence of the two reference signals, and damping isprovided by the derivative of the difference signal.When the circuit is switched on it causes the sys-tem to lock on the nearest zero crossing of the differ-ence signal.

In present operations a time of 20 msec is suffi-cient to step a single half-fringe and lock on it. Thisstep time allows scanning through several datapoints but not a whole spectrum in times short com-pared to atmospheric scintillations. (These are typi-cally strongest at frequencies below 10 Hz.) Thisdoes mean a relatively inefficient duty cycle for rapidscanning, but the stepping speed could be improvedby increasing the natural frequency of the mechani-cal system.

In order to check periodically on the operation ofthe instrument, it is possible to observe standardlamps through the system itself. A moveable prismcan be inserted in front of the collimator lens, andthis permits the instrument to view light from eithera line source or a continuum source imaged asthough it were coming through the telescope.

Control and Data Handling System

The output data from the system can be handledin several ways depending on the nature of the de-tectors being used and various other considerations.Most observations to date have been made with pho-tomultipliers operated in a dc mode. The signalsfrom the photomultipliers are amplified and convert-ed from currents to voltages by means of FET inputoperational amplifiers with adjustable feedback.The outputs are then sent to voltage to frequencyconverters, and the outputs of these converters arefed into binary counters. The integration time iscontrolled by opening and closing electronic gates tothe counters.

The control of the system is accomplished eitherby means of a Varian 620L mini-computer or by asimple but not very efficient hardwired backup sys-tem. The computer normally accepts the basic pa-rameters desired for a particular scan and then com-pletely controls positioning of the wedge, setting in-tegration times at each point and taking and storingthe data. It also does a minimal amount of process-ing and checking of the data and ultimately dumpsthe data on magnetic tape for processing in a largecomputer. Complete freedom is available to varythe total length of scan (depending on the resolutiondesired), the integration time as a function of wedgeposition, and the number of steps of the steppingmotor between data points. This latter point is par-ticularly useful because the use of the 2537-A line asa reference leads to considerable oversampling of theinterferogram. For observations longward of ap-proximately 4000 A, for example, one can take dataat every whole fringe rather than at every half-fringe

of the 2537-A line without fear of aliasing. For nar-row-band high resolution observations even highergains can be achieved. For example, the band be-tween 6540 A and 6740 A (containing the Ha, [N II]and [S II] lines common in nebulae) can be measuredby inserting a filter to isolate this band and thentaking data only on every 90th step.

The ability to vary integration times during a scanis also valuable in terms of maximizing SNR. Inmany instances it is desirable to spend more observ-ing time on the data points near the white lightfringe than on those away from the white lightfringe. For example, the points near the white lightfringe are usually used to symmetrize the entire in-terferogram (see below) thus influencing points ev-erywhere in the interferogram. If these points arepoorly determined, the interferogram will be poorlysymmetrized, thus leading to larger errors than onemight expect from the noise in the data alone. Fur-thermore, one frequently wishes to apodize the inter-ferogram to eliminate the strong sidelobes in thespectrum, and it is best to do this by varying the in-tegration time according to the apodizing function.The net gain of this approach can easily be estimat-ed as follows.

Suppose we apodize directly by multiplication inthe interferogram domain with an apodizing functionA(x). Then assuming a perfectly symmetrized inter-ferogram I(x), sampled at equally spaced points Xk,our spectral estimate B(o-) will be given by

N-1B(a) = A(xk)[I(xk) - I]

k=O

X cos(2 aX)(2 - k - kN-1),

and the noise in this estimate will be given byN-I

E2(a) = AI(xk)eki CoS2(2rofxs)(2 - 6 k k N)2,k=O

where ek is the noise in the interferogram point I(Xk),and a is the wavenumber. Now the mean squarenoise in the entire spectrum will be given by averag-ing this quantity over the interval from 0 to urn, themaximum value of . We also can assume that ek =

e/('Tk)l/2 , where e is a constant, and s is the inte-

gration time for the kth point in the interferogramsubject to the constraint that the sum of the T'sequals the total integration time for the interfero-gram. This will be true either if detector noise dom-inates, as is the case in the ir, or if all points in theinterferogram have comparable intensity, as is thecase for a continuum source away from the whitelight fringe. We then have

-2 eI(4 + 2AkI/rk + ANi2/TN-1).

This is of the general formN-1

2= e2EWk2/Tk,k=O

which is minimized ifN-1

Tk = TWk Wk.k=0

May 1974 / Vol. 13, No. 5 / APPLIED OPTICS 1151

In other words, except for anomalies at the endpoints, observing time should be weighted by theapodizing function. In that case we find that thenoise is given by

= T ( Wk2.

If we had used rt = T/N, we would have had

2 = TN ZWk2.k=O

Calculations indicate that for typical apodizing func-tions, such as for the hanning function cos2(rx/ 2xr)or for the function (1 - X2/Xr 2 )2, the mean squarenoise can be reduced by a factor of approximately 2/3

for a given observing time. This is a nonnegligiblegain for astronomical observations in which practicallimits on observing time frequently set the limits toachievable SNR's. Weighting the observing time bythe apodizing function is also consistent with our de-sire to spend more time on those points to be usedfor symmetrizing, since these are precisely the pointswhere the apodizing function is a maximum.

Since our signals are in pairs of complementaryfringes, we can use the sum and difference of eachpair in a ratio technique such as that described byHanel et al.8 This approach is essential to reducethe effects of scintillation and of atmospheric trans-parency changes. These produce a percentagechange in the total light which is coherent (at leastapproximately) over the entire spectral range. Nowthe sum of the two signals is essentially constant ex-cept for fluctuations in the total brightness, whilethe difference between the two signals produces anordinary interferogram with the same fluctuations.In the ideal situation the ratio of the difference tothe sum signals has the above intensity fluctuationsremoved. In practice, however, there are complica-tions. Hanel et al. point out that it is essential thatthe two complementary channels have the same sen-sitivity averaged over wavelength (a detail that canbe taken care of by a subsequent scaling of the dataduring analysis), and they note that differences inthe spectral sensitivity of the two channels maycause problems. In practice, however, they assumethat equalization of the average sensitivity of the twochannels will eliminate any systematic variation inthe sum of the two signals. On the contrary, this isnot the case as can be seen clearly in our data or intheir Fig. 4. The sum of the two signals shows dis-tinct residual fringes that are greater than thebrightness fluctuations in the vicinity of the whitelight fringe. These fringes must be eliminated as thefirst step in the data reduction. Since this modula-tion of the sum signal is just the Fourier transform ofthe spectrum of the star multiplied by the differencein spectral sensitivities of the two phototubes, it canbe expressed as the convolution of the observed dif-ference signal with a known function (actually ob-tained from an average of many different scans) andtherefore subtracted out of the sum signal. Thistechnique will be described further in a separatepublication.

Another step that must be considered in the datareduction is symmetrization of the interferogram.Because of the differential refraction at the air gapin the wedge, the phase of the interferogram is astrong function of wavelength. We use basically thesymmetrization technique of Forman et al.9 whichinvolves a convolution in the interferogram domain.A straightforward numerical application of this tech-nique leads, however, to convolution of noise in thesymmetrizing function throughout the spectrum.To minimize this effect the phase variation withfrequency is found by averaging the phase of the in-terferograms of many broadband sources and thenparameterizing this phase function. Slight changesin the phase from one interferogram to another arethen taken care of by allowing the values of certain.of the parameters to be determined from the individ-ual, short, double-sided interferogram. A typicalphase curve for the instrument is shown in Fig. 3where the effects of refraction at the air gap in thewedge can be seen to produce strong variations inphase with frequency. The strong variation in phaseis also evident in Fig. 2, wherein the fringe patternchanges noticeably as the light is varied from bluethrough green to red. This natural chirping of theinterferogram reduces the fringe visibility for whitelight sources to well below unity as can be seen inthe white light photograph of Fig. 2.

We note finally that the wavelength calibration of

WAVELENGTH (A]

7000 6000 5000 4000 36001.0

0.8 _

0.6 -

-0.2 _-s6-0.

1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8

WAVENUMBER

Fig. 3. Instrumental phase correction. A typical low resolutioncurve of the sine of the phase of the interferogram as a function ofwavenumber before any symmetrizing is performed. The nonsi-nusoidal nature of the curve is due primarily to the refraction at

the air gap of the Babinet-Soleil compensator.

1152 APPLIED OPTICS / Vol. 13, No. 5 / May 1974

Fig. 4. Instrument line shape.The profile of the green (5461-A) mercury line as determinedby an 8192-point transform withno apodization. Every fifthpoint is an actual data pointwhile intermediate points havebeen interpolated with an ap-propriate sinc function. Fullwidth half-maximum is 2.1 A(7.0 cm-'); full width first nulls

is 3.4 A (11.3 cm-').

WAVENUMBER

the instrument is not as convenient as with a con-ventional Michelson interferometer in air, becausethe wavenumber scale produced by the Fouriertransformation involves the birefringence of calcite.To determine the actual wavenumber calibrationwe have used published data on the birefringence ofcalcite from Jenkins and White.10 We have checkedthis calibration against scans of a mercury dischargelamp and find that at those wavelengths the calibra-tion is much better than the instrumental resolution.The birefringence also affects the shape of the spec-trum since the intensity per unit frequency intervalrefers to frequency intervals involving the birefrin-gence. This leads to an artificial suppression of theuv portions of the spectrum which is most easilytreated as a reduced sensitivity.

Observational Results

The completed instrument has been used on tele-scopes at the University of Maryland Observatory, atthe David Dunlap Observatory of the University ofToronto, and at Lowell Observatory. This has en-abled us to test most aspects of the performance ofthe instrument. All spectra were obtained eitherwith EMI 9558 photomultipliers (S-20 cathode) orwith EMI 9658 TIR photomultipliers (extended red,corrugated cathode).

Figure 4 shows the instrumental line shape as de-termined from a scan of a mercury discharge lamp,the lines of which can be considered delta functionsat our resolution. This particular scan is from an8192 point transform (nearly the full resolution ofwhich the instrument is capable) and was symme-trized by assuming a shape for the phase curve fromprevious observations and fitting the parametersfrom this scan. No apodizing was performed on thisspectrum. The line shown is the green (5461-A)line; it has a full width half-maximum of 2.1 A (7.0

cm-'), and a full width first nulls of 3.4 A (11.4cm-'). The profile between data points was ob-tained by a standard sinc interpolation (but includ-ing the birefringence of calcite) from the actual datapoints. The line profile obtained from the corre-sponding scan in the orthogonal polarization showsnearly identical widths but has a slight shift (lessthan 0.5 A) and is slightly asymmetric suggesting in-complete symmetrization of the interferogram.

Figure 5 illustrates the automatic sky subtractionfeature of the instrument. In this figure we haveplotted two low resolution spectra of Neptune ob-tained in immediate succession with the 50-cm (20-in.) telescope at the University of Maryland. Theupper spectrum was obtained with the sky subtrac-tion suppressed and is thus dominated completely atthis low resolution (approximately 100 A at 5000 A)by the night sky mercury lines from the city ofWashington, D.C., its surrounding suburbs, and theuniversity campus. The strongest mercury featuresare marked. The lower spectrum was obtained im-mediately after the first with the automatic sky sub-traction in operation. The night sky lines of theupper scan have been almost entirely eliminated, re-vealing the strong methane absorption bands charac-teristic of the Neptune spectrum. The sky subtrac-tion is, of course, not very effective if the sky back-ground is strongly polarized. As a check on the ex-pected behavior with a polarized sky, observationshave been made of the sky itself at various distancesfrom a nearly full moon. If the sky subtraction wereworking perfectly, there would be no fringes in thesescans. It was found that the visibility of the whitelight fringes increased from virtually zero very nearthe moon to about 10% at an angular distance of 75°from the moon. This indicates that the sky subtrac-tion should be quite effective under all but stronglypolarized sky conditions.

May 1974 / Vol. 13, No. 5 / APPLIED OPTICS 1153

I

zI-2

AX 2.1 A

AX=3.4 A

X 5769

aX 5790

\ 5461

SKY SUBTRACTION SUPRESSED

X4358

\ 4047

IN OPERATION

Fig. 5. Operation of automatic sky subtraction. Spectra ofNeptune obtained from 256-point interferograms obtained withthe University of Maryland 50-cm (20-in.) telescope. Spectralresolution with this number of points is roughly 410 cm- 1 (100 A

at 5000 A). The upper spectrum was obtained with the automaticsky subtraction suppressed while the lower spectrum (which hasbeen displaced vertically) was obtained immediately thereafterwith the sky subtraction operating. Night sky mercury features,due to lights of Washington, D.C. and of the university campus,are identified in the upper spectrum but are seen to be virtuallyeliminated from the lower scan revealing the methane absorptionfeatures characteristic of Neptune itself. Integration time wasone sec/data point, and the instrumental response has not been

corrected for.

The limiting accuracy of the instrument has nowbeen investigated with a reasonably large body ofdata obtained under a variety of conditions. To es-timate the statistical accuracy of the resultant spec-tra, we consider the sum of the outputs from chan-nels 1 and 2 of the instrument (complementary frin-ges for one plane of incident linear polarization) andthe sum of the outputs from channels 3 and 4 (theorthogonal polarization). Both of these sums shouldbe constants except for noise. Coherent scintillationnoise, which will be eliminated from the spectra bytaking the ratio of a difference to a sum as describedabove, will also vanish in the ratio of the two sumswhile the incoherent noise will still be present. Ifthe spectrum is obtained by Fourier transformationof either a difference or a difference divided by asum, it turns out that the rms noise in the spectrumdivided by the mean value in the spectrum is INtimes the noise in the ratio of sums where N is thenumber of data points used in the transformation.As a check that the noise in the ratio of sums is avalid measure of the noise in the resultant spectra,we have on two occasions observed a series of spectraof the same star in rapid succession and estimatedthe noise in the spectra by determining the averagefluctuation of the individual data points from onespectrum to the next. In both instances, the VNdependence was verified, and we conclude that thenoise in the ratio of sums is a valid measure of theaccuracy of the spectra provided that any residualfringes in the sums are eliminated. Note that if allnoise is uncorrelated (e.g., photon noise) among thefour channels, the noise in the ratio of sums will be afactor of \/2 greater than the noise in either sum

alone, while if the noise is strongly correlated (e.g.,scintillation) the noise in the ratio of sums will bemuch smaller that in either sum alone. An alterna-tive method of looking at the noise is to estimate thetotal power in the calculated spectrum at frequencieswhere there is known to be no light. These esti-mates are also consistent with the other estimates ofnoise.

The noise in the ratio of sums has been used to in-vestigate the performance of the instrument usinginterferograms obtained for many different sources.The principal body of data for this purpose com-prises four consecutive nights of observing with the183-cm (72-in.) Perkins telescope of the Lowell Ob-servatory. These data cover sources ranging in visu-al magnitude from 5 to 13m, include low and me-dium resolution. interferograms in white light andhigh resolution interferograms in narrow (200-A)bandpasses, include integration times ranging fromV4 sec to 3 sec/data point, and cover two very clearnights and two nights with frequent thin clouds. Asa measure of the effective brightness of the sourceswe have used the average photocurrent from thephotomultiplier tubes which automatically allows forthe varying bandpasses and the varying atmospherictransparency. As a measure of the statistical accu-racy we have taken the noise in the ratio of sumsmentioned above and normalized it by the squareroot of the integration time per data point. The va-lidity of this has also been checked by comparison ofsuccessive scans of the same star using different inte-gration times per data point. Comparison of thenoise in the individual sums with the noise in theratio of sums suggests that for typical clear condi-tions, with a large telescope, with integration timesof the order of /2 sec, and with a moderately brightstar, the noise is reduced by roughly a factor of 3 byratio techniques. On cloudy nights the noise is re-duced by as much as a factor of 50. For the fainterobjects, on the other hand, the noise in the ratio ofsums is indeed somewhat worse than the noise in theindividual sums as one would expect for uncorrelatednoise such as photon statistics. The reduction ofnoise by ratioing is not, however, nearly as impor-tant as the actual noise level achieved. For the ap-proximately 100 scans obtained on the four nights(for sources that ranged over 3 orders of magnitudein intensity corresponding to stellar magnitudes 5-13), the measured noise was within less than a factorof 2 of that predicted by photon statistics (estimatedfrom the measured photocurrents and published gaincurves for the tubes), except that for stars brighterthan stellar magnitude 6 observed in white light,roughly one-quarter of the scans yielded noticeablylarger amounts of noise. This indicates that for thebrightest stars observed we are sometimes beginningto see other sources of noise than photon statistics(such as uncorrelated scintillations) and are thus be-ginning to suffer Fellgett's disadvantage. This is ofno practical consequence, however, since on a tele-scope of this size a star brighter than magnitude 4produces such a strong signal that the photomulti-

1154 APPLIED OPTICS / Vol. 13, No. 5 / May 1974

- WAVELENGTH [A]5000 4000

1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5

WAVENUMBER -

pliers are operating in their nonlinear region. Weconclude, then, that the instrument is limited byphoton statistics for all observations except whitelight observations of the brightest sources we can ob-serve. This discussion, of course, considers only theinternal scatter in single scans. Systematic effectsand fluctuations from one scan to another must beevaluated differently.

An alternative method for testing the accuracyand stability of the instrument is to measure the fluxdistribution of various standard stars relative to theabsolute standard star Vega. Since this requires thedetermination of atmospheric extinction, it is a goodmeasure of the stability of the instrument over mod-erately long periods (typically a whole night). Thestars Regulus and Vega were observed on two differ-ent nights with the University of Maryland 50-cm(20-in.) telescope. Observing times were, 1 sec/datapoint with the interferograms being 512 points longfor a total integration time of roughly 10 min/scan.The transformed spectra were then integrated overthe standard 50-A bandpasses used in previous stud-ies of the absolute calibration of Vega.1 Atmo-spheric extinction was eliminated in the usual wayby comparison of scans through different amounts ofatmosphere. The results are shown in Fig. 6 wherewe have plotted the intensity ratio of Regulus toVega as determined from our measurements and asfound by previous investigators. The agreement isexcellent, the largest discrepancy being comparableto the standard deviations quoted by all observers.In our case, the largest part of the uncertainty isdue to the extinction coefficient which shows largevariations at our observatory.

The star Arcturus was also analyzed in a similarway. For Arcturus, however, we obtained a much

Fig. 6. Ratio of the intensityper unit wavenumber of Regulusto that of Vega. Vega is the tra-ditional standard star for abso-lute energy calibrations and isused here also because it has aspectrum similar to that of Reg-ulus, thus yielding a relativelyconstant intensity ratio. Mostof the observations, includingour own, represent integrationsover the bandpasses of Oke andSchild,1 but some of the otherobservations1 2 refer to nonstan-dard bandpasses. Since thespectrum of Regulus has fewlines, this has little effect.Error bars represent plus andminus one standard deviation asquoted by the various authors,and it is clear that the agree-ment is well within the statisti-

!.6 cal accuracy of the data.

higher resolution spectrum for purposes of compari-son with model atmosphere calculations. The inter-ferogram was 2108 points long with an integrationtime of 1 sec/data point. The spectrum was thenconvolved down to the standard 50-A bandpasses.Although this is a relatively inefficient way to de-termine an energy distribution (ideally one shoulduse a minimum number of data points), we againfind excellent agreement. Since Arcturus is a veryred star and the standard star Vega is blue, the de-termination of the absolute eneray distribution ismore difficult than

30

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Fig. 7. Spectrum of 15 CVn based on 256-point interferogramobtained in 1 min of observation with 188-cm (74-in.) telescope atDavid Dunlap Observatory. Atmospheric extinction and instru-mental response have not been removed. Points of discrete Fou-rier transform are arbitrarily connected by straight lines ratherthan interpolated. Noise is less than 1% of peak intensity and is

consistent with expected photon statistics.

May 1974 / Vol. 13, No. 5 / APPLIED OPTICS 1155

7000 6000

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Fig. 8. Spectrum of planetary nebula NGC 6572 based on 2048-point interferogram obtained in 20 min of observation with 188-cm (74-in.) telescope at David Dunlap Observatory. Atmospheric extinction and instrumental response have not been removed. Points are ar-bitrarily connected by straight lines. Line identifications are from previous investigators. Strongest lines have been cut off in figure,actual heights indicated by numbers in ( ) at top of figure. No identifications attempted in vicinity of 5000 A due to confusion with side

lobes of [0 1II] lines.

nearly the same color as Vega. In particular, previ-ous scanner measurements may well be subject tosignificant scattered light corrections. We are rela-tively free from this problem since the analogous ef-fect in a transform spectrometer is a higher noise inthe faint parts of the spectrum which will be randomrather than systematic. Previous scanner measure-ments of good quality exist for Arcturus at wave-lengths greater than 5000 A, and in that region (tosomewhat beyond 7000 A) we find agreement towithin 2% which is what one would expect based onthe extinction errors. Shortward of 5000 A the pre-vious measurements are much less certain, and wefind that Arcturus is systematically fainter by about10% than previous results indicate. These observa-tions show that the instrument is readily capable ofreaching the practical limits imposed on astronomi-cal data by the earth's atmosphere.

To illustrate the instrumental capability at higherresolutions, we present in Figs. 7 and 8 two typicalspectra obtained with the instrument, one of a starbeing representative of continuous sources and one ofa planetary nebula being representative of emissionline sources. Figure 7 shows the spectrum of thestar 15 CVn (visual magnitude 61, spectrum B 7III) as calculated from a 256-point interferogram ob-tained on the 188-cm (74-in.) telescope of the DavidDunlap Observatory with an integration time of ap-proximately 1/4 sec/data point for a total observingtime of roughly 1 min. This scan was one of a seriesof scans of the same star to determine the repeatabi-

lity of spectra obtained with the instrument, and acomparison of these individual spectra with themean indicates that the rms noise is less than 1% ofthe maximum intensity in the spectrum. Examina-tion of the power at the ends of the spectrum alsosuggests the same conclusion. This noise is consis-tent with the photon statistics expected for this ob-servation. The suppression of the blue in whatshould be a very blue star is due partly to atmo-spheric extinction, which has not been removed, andpartly to the expansion of the frequency scale due tothe rapidly increasing birefringence of calcite in theblue. The strong absorption lines are the Balmerseries of hydrogen.

Figure 8 shows the spectrum of the planetary ne-bula NGC 6572 (visual magnitude approximately81/2) as obtained from a 2048-point transform of aninterferogram observed at David Dunlap Observato-ry with an integration time of roughly 1/2 sec/datapoint for a total observing time of about 20 min.Again we have not taken out effects of atmosphericextinction or instrumental sensitivity. The strongestlines in the spectrum are completely off scale in thediagram which has been expanded to show the noiselevel and the weak lines present. Several of the linesare identified on the figure and agree with previousobservations of this nebula.

The construction of this instrument was supportedin part by the National Science Foundation throughgrant GP-17460 and by the Astronomy Program of

1156 APPLIED OPTICS / Vol. 13, No. 5 / May 1974

4

.20

z

z

3

2

0 60 00 N ED

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the University of Maryland. Much of the data re-duction was supported through NASA grant Nsg-398to the University of Maryland Computer ScienceCenter. Portions of this work were submitted (byFrancis J. Ahern) to the University of Maryland inpartial fulfillment of the requirements for the degreeof Doctor of Philosophy. Special thanks are due tothe staffs of the David Dunlap and Lowell Observa-tories for providing telescope time.

References1. L. Mertz, J. Phys. Rad. (Paris) 19, 233 (1958).2. W. M. Sinton, J. Quant. Spectrosc. Rad. Trans. 3, 551 (1963).3. L. Mertz, Astron. J. 71, 749 (1966).4. W. H. Steel, Interferometry (Cambridge U. P., Cambridge,

1967), pp. 102ff.5. L. Mertz, Transformations in Optics (Wiley, New York, 1965),

pp. 51ff.

6. DC-200 silicone fluid has an index of refraction in the visibleof roughly 1.4 and transmits from the uv to the ir. It isavailable in a wide range of viscosities from the Dow CorningCo.

7. J. Connes and P. Connes, J. Opt. Soc. Am. 56, 896 (1966).

8. R. Hanel, M. Forman, T. Meilleur, R. Westcott, and J. Prit-chard, Appl. Opt. 8, 2059 (1969).

9. M. L. Forman, W. H. Steel, and G. A. Vanasse, J. Opt. Soc.Am. 56, 59 (1966).

10. F. A. Jenkins and H. E. White, Fundamentals of Optics(McGraw-Hill, New York, 1957), p. 542.

11. J. B. Oke and R. E. Schild, Astrophys. J. 161, 1015 (1970).

12. References to previous calibrations of Regulus relative to Vegaare D. H. P. Jones, I. Astron. Union Symp. 24 (Academic,New York, 1966), p. 141; K. Bahner, Astrophys. J. 138, 1314(1963); J. B. Oke, Astrophys. J. 140, 689 (1964); D. S. Hayes,Astrophys. J. 159, 165 (1970).

Short Course on Dividing, Ruling and Mask Making

8th to 1 2th July, 1974StaffIntroduction

The Cranfield Institute of Technology, which was incor-porated by Royal Charter in December, 1 969, was formed fromThe College of Aeronautics and includes the former Depart-ments and Schools of that College. The Institute is exclusivelydevoted to teaching and research at postgraduate and post-experience level and offers a wide range of degree and shortcourses specifically orientated towards industrial needs andrequirements.

The CourseUntil recently, the techniques for making precision scales,

graticules and microcircuit masks have not been readilyavailable outside the optical or microelectronics industry.

Even today, it is not often appreciated how much themicroelectronic industry depends on precision optical andphotographic techniques for the production of high qualitygraticules and masks which form an essential part of themanufacturing process.

During this course it is proposed to describe methods ofgrinding, polishing and cleaning glass blanks, polishing singlediamond cutters, linear and circular dividing and ruling ofscales and graticules; diffraction grating ruling and replication;photocopying of graticules, including non-contact shadowprinting; production of microcircuit masks by photographicreduction; microphotography at extreme resolution; vacuumcoating and sputtering of thin films; clean liquids; clean air andenvironmental control; the application of scales, graticules,grids and gratings to instruments.

Entrance StandardThe course should benefit anyone in a management or

supervisory position in the optical, microelectronic, photo-graphic or allied industries.

Some practical knowledge of the optical, scientific instru-ment, or microelectronic industry is desirable, in order to takefull advantage of this concentrated course of lectures.

ResidenceFull board and accommodation will be provided during the

course and students will occupy single study bedrooms in oneof the Institute Halls of Residence. Joining instructions will besent to members shortly before the commencement of thecourse.

Except for the Course Organiser and Mr. A. J. Scarr,who are members of the academic staff, the 8 lecturers will allbe leading members of the optical, microelectronic or alliedindustries.

The lecturers will include:D. F. Horne, MBE., CEng., FlProdE., MRAeS.

Course Organiser. Author of "Optical Production Tech-nology" also "Dividing Ruling and Mask making".(Adam Hilger Ltd.)

A. J. Scarr, MSc., CEng., FMechE., FlProdE., MRAeS.Author of "Metrology and Precision Engineering".(McGraw Hill).

Dr. G. W. W. Stevens, MA, PhD., ScD., FRPS.(Kodak Ltd.)

Author of "Microphotography" (Chapman Hall)Dr. L. Holland, DTech., DrSc., FnstP., CEng., FEE.

(Edwards High Vacuum International)Author of "Vacuum Deposition of Thin Films" also "TheProperties of Glass Surfaces" (Chapman Hall).

SyllabusHistory of Standards and Measurement AccuracyLinear dividing and rulingCircular dividing and rulingPolishing of diamondsGrinding and polishing of flat surfacesMicrophotography at extreme resolutionMicrocircuit mask makingEnvironment conditions and air conditioningCleanliness of liquidsVacuum coating, metallizing and sputteringDiffraction grating ruling and replicationApplication of scales and graticules in instruments

There will be several visits and demonstrations of equipmentduring the week.

The Registrar (Short Courses),Cranfield Institute of TechnologyCranfield, Bedford MK43 OAL.

May 1974 / Vol. 13, No. 5 / APPLIED OPTICS 1157