February 1959 INCREASING SPEED OF GRAZING-INCIDENCE SPECTROGRAPH 141

only in increased density of lines but in the greaterextent of Fig. 3(b) into the ultraviolet. The exposurefor Fig. 3 (a) is four times that for Fig. 3 (b) so that thedifference in the speeds is even greater than here indi-cated. In Figs. 3 (c) and 3 (d) the source is a Lyman-typecapillary discharge in helium at low pressures. InFig. 3 (d) the mirror is used, but not in Fig. 3 (c). Hereagain, though the exposure for Fig. 3 (c) was four timesas great as for Fig. 3 (d) and though the source was not adistanct source, the increase in speed is clearly evident.The reduction of astigmatism in Figs. 3(b) and 3(d) isrecognizable by the diminished length of spectral lines.

The above described instrument was also used suc-cessfully in a rocket for detecting the resonance line ofHe II at 303.8 A in the solar spectrum.4

4 Behring, McAllister, Newman, Rense, and Violett. To bereported at International Astronomical Union, Moscow Meetings,August, 1958.

ESTIMATE OF INCREASE IN SPEED

The increase in speed of a spectrograph with themirror, over one without the mirror, for a distant sourcecan be numerically approximated. The increase in speedfactor at the wavelength for which astigmatism iseliminated= (the ratio of angular apertures) X (theratio of the effective lengths of the spectral lines for thetwo instruments) X (the reflection coefficient of themirror at grazing incidence). For the instrument de-scribed above and for the sun as source, the increase inspeed is about (4) (4) (0.5) =8. The middle term wascomputed from formulas given by Beutler.3 The spec-trograms of Fig. 3 roughly check this result. The designformulas here presented, though directly applicable toa solar spectrograph, may easily be adapted to a labo-ratory spectrograph with the source at any given dis-tance from the slit.

JOURNAL OF THE OPTICAL SOCIETY OF AMERICA VOLUME 49, NUMBER 2 FEBRUARY, 1959

An Auroral Spectrograph

K. C. CLARK* AND G. J. ROMICKGeophysical Institute, University of Alaska, College, Alaska

(Received July 16, 1958)

High sensitivity to auroral Ha, resolution in elevation angle along a narrow band from horizon tohorizon, and simplicity of components are principal features of a new automatic auroral spectrograph. Skylight reaches an all-sky convex mirror by way of an external curved slot in the vertical plane, whose calcu-lated shape gives a flat image of uniform width. This slit image of adjustable width is photographed fromabove by a standard 16-mm camera with f/0.95 lens, the light having passed through a blazed grating atminimum deviation. In this arrangement distortions in the noncollimated beam and losses by reflection arekept low, and slit adjustment to 25-A resolution enhances detection of the broadened Ha emission line.Satisfactory sensitivity to major airglow lines, hydrogen, and auroral features is obtained in successive15-min exposures, representing an approximately fivefold improvement in time resolution over that of theIGY patrol spectrograph, with a consequent loss in spectral resolution.

INTRODUCTION

VARIOUS spectrographs for routine studies ofaurorae and airglow are arranged so that the

slit image is resolved according to angle of elevationfrom horizon to horizon. The sharpness of this angularresolution is curtailed by the necessary length ofexposures, for auroral features frequently move througha considerable portion of the viewing angles in times of5 to 60 min. In studies of location and motion it istherefore generally desirable to use instruments of highspeed, good angular resolution, and satisfactory wave-length resolution.

The IGY patrol spectrographs' currently provide amoderately good combination of these features. Theyuse an all-sky lens to produce a flat sky image on theentrance slit, which is oriented to receive light from a

* On leave from University of Washington, 1957-1958.'Model 173 IGY Auroral Spectrograph manufactured by

Perkin-Elmer Corporation, Norwalk, Connecticut.

20 width in the magnetic meridian plane. After collima-tion and dispersion by a blazed transmission grating of600 lines/mm, the light is focused by a semisolidSchmidt mirror of 3-in. f/0.625 aperture. The fixed slitwidth of this instrument gives a resolution of 8 A.

Lebedinsky2 has described the use of a fast slitlessauroral spectrograph having a convex all-sky mirror,an overhead plane mirror, prism dispersion, and acamera lens of focal ratio f/0.57. Later modificationsreported by Lebedinsky3 use an off-zenith concaveupper mirror which forms a flat, real image, whosedimensions can be restricted to a narrow meridianstrip. This curved image of the meridian plane isviewed by a collimator system through an aperture in

2 A. I. Lebedinsky, The Airglow and the Aurorae (Pergamon,Press, Inc., London, 1956), pp. 388-394.

3 A. I. Lebedinsky, paper communicated to Toronto meeting ofInternational Association of Geomagnetism and Aeronomy,September, 1957.

R. C. CLARK AND G. J. ROMICK

the mirror vertex. These definitions are illustrated inFig. 1, and their relations will be described.

The relation of to o depends on the choice of h/Rand is given by the equation

sin otan0=

(h/R) + 1- cosp

FIG. 1. Coordinatesand slot shape used.

/R = p./R = 20/3.

20 _

\-

-20 -10

,- ' 1/ \ /

C _ 0 20CM

the convex all-sky mirror, dispersed by a plane reflectiongrating, and photographed by a fast camera.

The meridian mirror spectrograph developed at theGeophysical Institute, College, Alaska, has been foundsuccessful in routine operation. It emphasizes highspeed to help meet the requirements of spectroscopicposition and motion studies of auroras. A suitableexternal slot is added to the convex mirror which ispart of the basic design of the all-sky cameras describedby Elvey and Stoffregen.4 The number of reflections iskept small by simplified geometry, and a wide slot of25 A resolution improves sensitivity to broad hydrogenemission lines. The present model has the camera inan off-zenith position to give essentially unobstructed180° coverage in each straight spectrum line. The useof a standard 16-mm movie camera (/0.95) andordinary optical components makes the instrumentrelatively inexpensive.

Because of the finite value of h/R, the maximumnecessary value of o= so for horizon reception is slightlyless than 450, given by solution of the equation

sin@ tan2@o+cos p= (h/R)+1. (2)

Generally useful choices of h/R lie between 6 and 10,giving so values in the range of 42°-43°.

The astigmatism and lack of flatness of the off-axissky image require some attention. A well-resolvedimage of distant horizontal detail, such as the base ofan auroral arc, is needed in the discrimination ofelevation angles. With h/R=20/3 the displacement in1 of such images for points near the horizon is only

O.09R, which fortunately remains within the depth offocus of the camera lens. For distant vertical detail thesimilar displacement increases to O.50R; but theresolution of vertical sky detail is not critical, as thespectrograph averages intensities across the width ofthe narrow plane section of sky.

It is necessary, however, to have a flat image of theexternal slot which is of uniform width and whichresolves 1800 of elevation along its length. To satisfythese requirements, an external entrance slot in thevertical plane obscures all but a narrow section of thesky and is shaped to have those p/R values which causethe reflected image of the slot (henceforth called theimage slit) to be flat. In computing this shape, onechooses desired values of h/R (camera height) andpo/R (maximum slot height) and calculates the height770 of the image slit center from the equation

12 1

R Po(3)

OPTICAL GEOMETRY

Calculations are made assuming the reception oflight from the convex all-sky mirror at the front nodalpoint of a camera directly above it. This point is at aheight above the vertex of the mirror of radius R, andthe point of reflection determines the vertical angles orelative to the center of curvature and relative to thenodal point. Light is restricted to a narrow verticalplane by an external slot having a locus specified bythe coordinates x, y relative to the center of mirrorcurvature. Light, having traveled a distance p, strikesthe mirror at an angle of incidence (0+ p) and formsastigmatic images at general coordinates , relative to

I C. T. Elvey and W. Stoffregen, Ann. Intern. Geophys. Yr. 5,Part II, 115-151 (1957).

The determination of as a function of o is made usingEq. (1). For rays close to a vertical plane through themirror center, a simple analysis by differential anglesgives the following coordinates of the astigmatic imageof any vertical detail:

sinG-1 s +-R 2

(4)cos (0+ y)+ (R/p)

X7 cost-= (1- Cos )+R 2 cos(+ p)+ (R/p)

(5)

For coordinates of the astigmatic image of horizontaldetail the terms 2 cos(0+ p) would be replaced by2 sec(0+,o).

80

80 -

40

(1)

142 Vol. 49

AURORAL SPECTROGRAPH

The requirement of flatness for the image slit issatisfied by setting =,qo for all in Eq. (5). Theresulting values of R/p are then substituted in Eq. (4)to give the corresponding values of /R. The co-ordinates x, y of points on the external slot are relatedto the corresponding 0, o, and p by the equations

x P-=sins'+- sin(2o+O), (6)R R

V-=cosp+- cos(2o+O). (7)R R

The results of this calculation are shown to scale in thecurve of Fig. 1, which applies to a rather compactarrangement having h/R= 20/3 and po/R= 20/3.These parameters, together with the modification ofmoving the camera sidewise out of the meridian plane,were chosen for the instrument used in field operation.

VARIABLE SLIT

To provide uniform width of the image slit, the slotwidth must vary along its length. The ratio of slotwidth W to image slit width e is

W/E= x/t (8)

DISPERSION

In consistency with the aim of reducing reflectionlosses to a minimum, the collimating lens has beeneliminated. The image serving as the entrance slit isphotographed through a transmission grating placedimmediately in front of the camera lens, and thedivergence of the rays at the grating causes essentiallyno astigmatic change of focus if the grating operatesat minimum deviation.

To verify this statement, consider i and r as theangles of incidence and diffraction in the principalplane of a transmission grating, whose operation isdescribed by

mX/a= sinr-sini. (11)

Divergent rays are present, whose angles at the gratingcenter are io and r. A bundle of angular spread diabout io travels a distance I from the image slit andilluminates a length ds=ldi/cosio across the grating.The projected length of ds normal to the diffractedray is

du = ds cosro = Idi (cosro/cosio). (12)

If the distance from the grating to the apparent pointof origin of the diverging diffracted rays is q, then

du= qd tan(r-ro) = q sec2 (r-ro)dr,

and one obtains

(13)

when the widths are small relative to their respectivedistances from the mirror axis. For a fixed e set by thewavelength resolution desired, the slot width fortun-ately is proportional to the height y. This fact immedi-ately allows one to construct the slot in two adjustablehalves pivoted about a horizontal axis through thecenter of mirror curvature. Rotational adjustment ofthe separation of these slot edges will therefore controlthe wavelength resolution without disturbing thenecessary over-all uniformity of image slit width. Thischaracteristic makes the image equivalent to anordinary optical slit of adjustable but uniform width.

To verify this convenient design feature, one canevaluate the quotient F of the width ratio W/e to theheight ratio y/R. From Eq. (8) this quotient is

F= WR/ey= Rx/y. (9)

Details of the straightforward substitutions are notilluminating and may be described as the eliminationof R/p from the ratio of Eqs. (6) to (7) and from Eq.(4) by use of Eq. (5). The angle 0 is eliminated by Eq.(1), giving the result,

1- (o/R)(10)

For any given choices of h and po this ratio is indeed aconstant, depending only on the position of the flatimage slit.

I cosro cos(r-ro) di\q= -

cosio drlor

which for r- ro leads to

q= I cos2ro/cos2io.

(14)

(15)

Therefore q does not differ from I if r= tio; i.e., thegrating then gives no focusing error. The positive signapplies to the undispersed zero order. The negativesign can be realized in the condition of minimumdeviation of transmitted rays. In the case of a reflectiongrating, however, the condition cannot be simply met,as the incident and diffracted rays must coincide.

The grating used is a 52-mmX52-mm Bausch &Lomb replica with 600 lines/mm and a 280 blaze,which gives peak transmission at about 5100 A whenused at minimum deviation. In practice the grating ismounted at io= 9.20 to produce minimum deviation at5300 A, which lies in the center of the spectrum covered.The radius of curvature of the all-sky mirror is R= 7.56cm. With this geometry the desired wavelength resolu-tion of 25 A is provided by an image slit width of0.82 mm, which results from a slot separation of 11.7mm at the top.

CONSTRUCTION

The width of the acceptance angle for the narrowmeridian section of sky varies somewhat with elevation.If the slot is nearly closed, the lens aperture limits the

143February 1959

b

K. C. CLARK AND G. J. ROMICK

so

60

40

20

ADJUSTABLE SLOT SECTIONS

GRATING

DATA WHEELMIRROR rI I

PIVOT < t I I

_30 -20 -10 LJ lo 20

FIG. 2. Arrangement of optical elements.

angle to a few tenths of a degree, and if it is opened for25-A resolution, the angular width is between 1° and1.5°. The f/0.95 camera lens is of 25-mm focal lengthand is coated for low reflectance in the visible region.In standard patrol operation the linear dispersion of610 A/mm at Ha can be large because the 25-A wave-length resolution is limited by the slit width, not byfilm grain. If the slit is set for a considerably finerwavelength resolution, a camera lens of longer focallength may be substituted. To avoid obstruction of thezenith, the camera and grating assembly is mountedjust beside the meridian plane, the grating centermaking a vertical angle of 80 relative to the image slit.A diagram of the positions of the essential opticalelements is given in Fig. 2.

As illustrated in Fig. 3, the instrument is housed inan all-weather box, which has an exterior Plexiglaswindow to admit sky light from the meridian plane.The vertical sides of this window, which extend almostto the level of the grating, are tilted to prevent effectivere-entrance of sky light by reflection. The box isadequately heated electrically to operate in extremelow temperatures and to melt snow or ice from thewindow. Automatic operation controls the program ofsuccessive 15-min exposures on a pre-set nighttimebasis. Between each spectrum exposure a 10-sec data

TABLE I. Summary of characteristics of present spectrographand IGY patrol spectrograph.

All-sky Wavelength Linear Approx.Type element resolution Camera disp. Ha speed Ha

New Mirror 25 A (adjust.) 26 mm f/0.95 610 A/mm 5IGY Lens 8 A (fixed) 76 mm f1/0.625 322 A/mm 1

cycle is recorded, showing an identification card andthe day, hour, and minute on an electric synchronousclock. This information is photographed by viewing anilluminated cavity, normally dark, in the zero order ofthe grating. An exposure step wedge bordering themirror as an extension of the image slit can also beadded and recorded as a first-order spectrum.

A standard Bolex H-16 camera with Eastman 103aFFilm has been found very satisfactory. Time exposuresare actuated by constant spring pressure on a cablerelease. Frames are advanced by momentary oppositepressure from a solenoid; in this manner no vibrationis present during exposures. A latching device operatesduring the day to prevent daytime exposures. A totalof 640 frames, or over 6 nights of 12-hr operation canbe obtained with one winding of the camera. It can beindependently removed or wound in position. Thecamera mount, grating, and cable release mechanismcomprise a separate sub-assembly.

OPERATION

This spectrograph has been used in routine operationat 25-A resolution since February 12, 1958, and inexperimental operation previously. Exposure times of15 min on Eastman 103aF Film are sufficient for regulardetection of Ha and airglow NaD lines along withstronger ordinary features. Direct comparison with the

I ;Uj L j -

:,.t00 !!AkiL

FIG. 3. View of instrument, side and top removed.

144 Vol. 49

AURORAL SPECTROGRAPH

TABLE II. Calculated coordinates for shape of an external slot in vertical plane parallel to grating lines.

h 10, =8.678 Slot: - , Image Slit: R, 0.473-

0 00 2 3 5 7.5 10 12.5 15 17.5 20

0 00 0012.0' 0°18.0" 0030.0' 0044.8' 0059.6' 1°14.2' 1028.7' 1042.9' 1°56.9'

R 0 0.721 0.932 1.375 1.684 1.789 1.776 1.711 1.614 1.525

R 9.678 9.350 8.971 7.943 6.492 5.194 4.140 3.329 2.723 2.249

0 0.037 0.055 0.091 0.137 0.182 0.226 0.270 0.314 0.356R

qS 22.5 25 27.5 30 32.5 35 37.5 40 42.5 45

0 2010.5' 2°23.9' 2°36.9' 2049.5' 3001.7' 313.5' 3024.8' 3035.7' 3046.0' 3055.8'

R 1.428 1.355 1.269 1.202 1.143 1.091 1.046 1.007 0.972 0.943

R 1.885 1.624 1.399 1.226 1.088 0.975 0.883 0.807 0.744 0.691

0.398 0.439 0.478 0.517 0.554 0.590 0.625 0.658 0.689 0.720W~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

IGY patrol spectrograph on a program of simultaneousexposures with identical photographic processing in-dicated approximately 5 times the sensitivity to Hawith, however, the expected reduction in wavelengthresolution. The differing advantages of these twoauroral spectrographs are indicated in the summary ofgeometry and speed given in Table I. Comparative datafor the Lebedinsky instruments are not available.Figure 4 shows a typical spectrogram with principalemissions marked. Above the low auroral arc in thenorth there are strong oxygen red doublet and greenlines as well as hydrogen Ha. Sodium and the nitrogenpositive (red) and negative (violet) bands are wellregistered.

The present compact arrangement with R=3 in.,h= 20/3 R, po= 20/3 R, and off-zenith location of gratingrepresents in some respects an undue emphasis on smallsize, for the quality of resolution deteriorates slightlyat the extremes of the spectrum. In a second model tobe constructed, these specifications will be relaxedslightly to provide a zenith location of the grating(obstructing about 60), h= 1OR, and po =8.68R. TableII lists the design coordinates calculated for this lattermodel, differing only in minor respects from the actualinstrument illustrated in Figs. 1 and 2.

CONCLUSIONS

1. A new design of fast grating spectrograph hasbeen developed and used to resolve auroral emissionsin time and North-South elevation at 25-A wavelength

resolution. It employs a suitably shaped external slot,a convex mirror, and adequate effective collimation byuse of minimum deviation in order to reduce reflectionlosses.

2. Methods are given for calculating the shape ofthe external slot. Its width is adjustable to permit a

FIG. 4. Sample spectrogram.

choice of wavelength resolution and still maintain auniform effective slit width.

3. In normal operation at College, Alaska, thisinstrument gives adequate sensitivity to Ha in 15-minexposures and is found useful for studies of North-South progression of auroral emissions as well as forroutine spectroscopic patrol of auroral activity.

145February 1959