Extreme Ultraviolet Explorer spectrometer Michael C. Hettrick, Stuart Bowyer, Roger F. Malina, Christopher Martin, and Stanley Mrowka Applied Optics Vol. 24, Issue 12, pp. 1737-1756 (1985) http://dx.doi.org/10.1364/AO.24.001737 © 1985 Optical Society of America. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modifications of the content of this paper are prohibited. Extreme Ultraviolet Explorer spectrometer Michael C. Hettrick, Stuart Bowyer, Roger F. Malina, Christopher Martin, and Stanley Mrowka The design and calculated performance is described for a spectrometer included on the Extreme Ultraviolet Explorer (EUVE) astronomical satellite. The instrument is novel in design, consisting of three plane reflec- tion gratings mounted in the converging beam behind a grazing incidence telescope. This configuration is based on new varied line-space (VLS) gratings which have recently been proposed. A sample EUVE grating has been mechanically ruled and experimentally characterized. It recovered over 80%of the theoretical efficiency of perfectly formed grooves, reaching 38% absolute at a wavelength of 114 A. The grating was used to construct a laboratory spectrographic version of the EUVE spectrometer and recorded the spectrum of helium from 228 to 320 A. The spectral resolution was A/AX - 2000 and the image heights were -10 sec of arc. Individual spots were -25 X 50 Am, which is a significant improvement over existing grazing incidence spectrographs. A line profile measurement at 1 A away from first order 304 A showed <1.5%/A of grating stray light and a rapid decline toward the wings. In visible light, no grating stray or ghost light could be seen. Three flight spectrometer channels in combination span the 70-760-Aband with an effective collect- ing area of 0.3-1 cm2 over the 80-600-A region. The spectrometer has an inherent resolution of A/AX - 300, but if combined with a worst-case satellite performance will yield a spectral resolution of A/AX = 110-240 and a spatial resolution of 1-2 min of arc. For a 40,000-sec observation, the average 3ar sensitivity to continuum flux is -2 X 10-27 erg/cm 2 /sec/Hz. This is a factor of 100 dimmer than a bright known EUV source and is comparable to the sensitivity of the all-sky survey which will be carried out on the EUVE. At a 5crdetec- tion threshold, the spectrometer sensitivity to individual spectral lines is 1-4 X 10-3 photons/cm2 /sec, which is a factor of 50 better than available with the EUVE wide bandpass telescopes. Simulated observations of two known classes of extrasolar EUV sources reveal rich spectra. During a six-month spectroscopic phase, target selection will be conducted by guest investigators chosen by NASA. 1. The first exploration of any new spectral region in Introduction The detection of extrasolar objects emitting in the extreme ultraviolet (EUV)I 4 has prompted a dedicated mission to discover and identify these sources. The Extreme Ultraviolet Explorer (EUVE) is a NASA ob- servatory which will conduct the first all-sky survey in the entire EUV band (XX100-912A).5 The scientific data retrieved from this photometric mission will be a catalog of all stellar sources above a limiting magnitude of .10-27 erg/cm 2 /sec/Hz. The entire celestial sphere will be surveyed in a six-month time period. Ap- proximately 4 X 106 sky bins (0.10 X 0.10) will be individually scanned, and fluxes will be obtained separately in four spectral bands. astronomy has always been accompanied by two events: (1) the discovery of new and serendipitous sources, and (2) the requirement for spectroscopic observations to determine the underlying physical phenomena. The feasibility of EUV spectroscopy on stellar sources has been demonstrated in recent years.6 - 8 In addition to known EUV-emitting sources, such as hot white dwarfs,1t2,6-8the coronas of late-type stars,3 cataclysmic variables,4 and planets,9 the scientific return expected from spectroscopy on newly discovered sources is par0 ticularly high.'0, 1 In response to this need, NASA has included a spectroscopic phase to the EUVE mission. Immediately followingthe six-month duration survey, the satellite will be pointed for long integrations on spectroscopic The authors are with University of California, Space Sciences Laboratory, Berkeley, California 94720. Received 26 December 1984. 0003-6935/85/121737-20$02.00/0. C 1985 Optical Society of America. targets. Any object within at least +450 of the celestial equator (ecliptic plane) will be accessible by the spectroscopic instrument. This instrument is contained within an imaging telescope which points in the antisun direction during the survey. To perform a useful first spectroscopic EUV mission, it was determined that the following performance requirements should be met: 15 June 1985 / Vol. 24, No. 12 / APPLIED OPTICS 1737 DETECTOR A DETECTOR C (DEEP SURVEY) DETECTOR B MEDIUM WAVE COLLIMATOR SECONDARY MIRROR PRIMARY MIRROR COLLIMATOR -ENTRANCE BAFFLE \ EJECTABLE FRONT COVER Fig. 1. Exploded view of the EUVE flight spectrometer consisting of three channels which share the telescope aperture. (1) simultaneous coverage of the XX100-600-A spectral region; (2) a spectral resolution A/A > 100; (3) a sensitivity 100 times better than necessary to observe the spectrum of the brightest known EUV source HZ43 (a hot white dwarf)'; and (4) sufficiently short exposure times per target (-12 h = 40,000 sec) to allow at least 100 separate pointings over a six-month spectroscopy phase. These scientific requirements were to be met with minimal impact on the EUVE survey mission. This required meeting the following constraints: (a) use of a single grazing incidence telescope with a 40-cm diam aperture to collect the incident starlight; (b) simultaneous sharing of this telescope aperture with a deep survey imaging channel; (c) an image size requiring satellite pointing reconstruction no finer than 1-min of arc sky bins; (d) a minimum overall length for the telescope plus spectrometer, not to exceed -150 cm; (e) use of existing 50-mm microchannel plate imaging detectors having 100-Itm pixels; and (f) no moving components. General Approach II. Several design options were investigated. 12 Concave grating spectrometers13 -17 were considered and found to violate our length constraint due to the requirement of a slit. In addition, the sensitivity would be degraded 1738 APPLIED OPTICS I Vol. 24, No. 12 15 June 1985 at grazing incidence due either to large astigmatism or the need for additional correcting elements.18 "19 Transmission grating spectrometers2 >2 6 were carefully studied but found to yield lower efficiency than reflection gratings. Practical limits on groove densities (<104 mm-') resulted in a common disadvantage in resolution for both transmission gratings and conical diffraction reflection gratings. Other approaches2 7 28 were found to be inconsistent with either the deep survey instrument or the intended EUVE spectroscopy mission. On the basis of spectral resolution, sensitivity, instrument packaging, and technical feasibility, we converged to a slitless design employing new varied line-space grazing incidence gratings. 2 9 30 In Fig. 1 we show an exploded view of the spectros- copy instrument. Incident starlight is collected by a grazing incidence telescope. Following reflection by the primary and secondary mirror elements, the light converges as an annular cone to a focus on the deep survey detector, which uses half of the aperture. The remaining half of the light is devoted to spectroscopy, which is accomplished through the presence of three plane reflection gratings in the converging beam. Each grating picks off one-sixth of the collected light and defines a channel spanning approximately one octave in EUV wavelength. The combined coverage extends over the 70760-A region and provides highest efficiency (>50% of peak) in the 80-600-A range. The channels are separately optimized by appropriate choice of grating groove densities, reflective coatings, and filters but are otherwise geometrically identical. Each grating features a smoothly varying line (groove) spacing across its aperture, which constrains the diffracted beams to form a well-imaged spectrum. The use of varied linespacing (VLS) in converging light also results in excellent spatial imaging normal to the dispersion.2 9 Each of the three spectra is imaged on a dedicated microchannel plate imaging detector with a flat surface normal to the diffracted light. To suppress undesirable background, dominantly the diffuse sky at hydrogen Lye (1216 A) and starlight in the far UV, each detector is preceded by a thin-film filter. In addition, fieldrestricting collimators placed in front of the telescope prevent EUV lines in the diffuse sky (304 and 584 A) from contaminating the entire spectrum. A cross section of the instrument is shown in Fig. 2. The optical path is indicated for one of the three spectroscopy channels. The use of VLS gratings in this unconventional converging beam geometry results in a total of only three optical surfaces. As each one is at grazing incidence, a highly efficient instrument is realized. Fig. 2. 111. Detailed Instrument Design In Table I we list the major design parameters of this instrument. The optimum spectrometer performance Cross-sectional view of the flight spectrometer illustrating the three grazing reflections. The optics for one of three grating channels are shown with the optical path of a 304 Aphoton. The mechanical collimator acts as a field-limiting slit. is a balance between several contributions, as shown in Fig. 3. In this section we describe the individual components of the spectroscopyinstrument and their effects on the instrument resolution and efficiency. These two principal criteria for performance are sufficiently decoupled to permit separate optimization, however both determine the ultimate sensitivity achieved. The dominant aberrations are specifiedto correspond to a blurring no more than 1 min of arc of sky. This specification is driven both by the practical constraints outlined in Sec. I and by the fact, derived below, that an Table1. EUVESpectrometer Characteristics Performance: Spectral channels (simultaneous) A, 70-190 A B, 140-380 A C, 280-760 A Spectral resolution (averages) A, 0.5A B, 1.oA C,2.oA Spatial resolution 1.5 min of arc 0.4 cm2 optimized design will convert this error into an acceptable spectral resolution of X/AX- 200. In addition, a 5c sensitivity level of 10-3 photons/cm 2 /sec over a 40,000-secobservation translates to an effective area of Collecting optics: This requirement will imply an instrument efficiency >0.5%, including the detector. Grating: varied line-space in-plane mounting 0.3 cm2 , assuming background is not the limiting factor. A. Effective area (80-600 A) Wolter-Schwarzschild 40-cm diameter F/3.4 Reflective coating Gold Plate scale (averages) Telescope This optical component both collects and focusesthe incident radiation. It is primarily responsible for the Groove density variations overall physical size of the instrument and its collecting Plane surface ruled area area and indirectly determines the resolution delivered by the grating and detector. Longer focal lengths Blaze angle Angle of incidence (average) Reflective coating produce more slowly converging beams and thus reduce grating aberrations and the sky pixel blurring arising from finite detector pixel sizes. However, given a telescope resolution, longer focal lengths also result in larger images at the detector. Given our fixed aperture, these competing effects result in an optimum value for the focal length, which we calculate to be 136 cm for type-2 Aperture Speed Detector: microchannel plate Aperture Resolution Filters Photocathode A, 2.4 A/mm B, 4.8 A/mm C, 9.6 A/mm A, 1675-3550 mm- 1 B, 830-1750 mm 1 C, 415-875 mm- 1 80 X 200 mm 3.00 82.9° Rhodium 50-mm diameter 100 X 100 m A, 0.3-,um Parylene-N B, 0.15-gm aluminum C, 0.15-gm aluminum Cesium iodide 15 June 1985 / Vol. 24, No. 12 / APPLIED OPTICS 1739 -Z-13rmm mr - o' 10' 20' 30' OFF-AXIS 40' ANGLE so' 60' 50' 60' - 2 2.0/ aE 1.8' Z Z=O 1.6' 2 Fig. 3. System block diagram showing the contributions from several LU 12' 2 factors to the instrument resolution and sensitivity. -0.8' 0.6'- the spectroscopy instrument. To minimize the instrument length while maximizing the collecting aperture we chose a Wolter-Schwarzschild type-2 telescope,31 whose surface functions are described by the parametric equations: Z 2 = -F/C1 + (FC1 14) sin 3 + (F/C 2 ) X [1 - C1 sin 2 (3/2)]( 2 -C1)/(l'C) X [cos(fl/2)j2Cj/(Cj-1)' (la) i~0.4' X 0.2'.~ 0' lo' 20' 30' 40' OFF-AXIS ANGLE Fig. 4. Telescope off-axis aberrations for (a) (b) section devoted to a spectrometer channel. detector by a distance AZ allows the field to be v is that between the grating dispersion and the incident ray is off-axis. The image is elongated entire telescope and A defocusing of the widened. The angle direction in which an in the nondispersive direction independent of v. r = F sinf3, (lb) Z2 = d cos3, (c) Ray traces of this telescope are shown in Fig. 4(a) for ld) full surfaces of revolution and a flat detector surface normal to the optical axis. At this Gaussian focus, the extremum image diameters are well described by r2 = d sino, where l/d = (C1IF) sin2 (3/2) + (C2 F)l - C1 sin2(3/2)ICS/(Cr-l) D(O) 2 = Xe , (2) (le) where 0 is the off-axis (field) angle of a point source, X In these equations, 3is the parameter which identifies a particular ray assumed incident in a direction parallel is -14.3, and D, 0 are in radians. The deep survey instrument (which shares half of the telescope aperture) to the optical axis of the telescope. The value of 3 is the has an imaging requirement angle such a ray will make with the optical axis on exiting the telescope. The ray intersections with the primary and secondary mirrors are given by radial coordinates ri and r2 and by axial coordinates z1 and Z2 from the focus. The dimensionless parameters C1 and C2 specify a particular solution for this mirror system. A useful feature of this telescope results from its ability field of view. Figure 4(a) also illustrates that, if the detector was displaced 13.5 mm toward the telescope, X [cos(,B/2)]2/(1- C), to fold a desired focal length into a short physical length. In our case, we chose a front-to-focus length Zma,: = 107 cm, which left adequate space for the collimators and for the detector electronics. This results in dimensionless parameters C1 = 132 and C2 3.5. To feasibly limit the required grating sizes, we chose a primary mirror aperture extending in radius from 16 to 20 cm, yielding i3 0.1178-0.1474. The axial length of the primary mirror is -28 cm. Incident rays parallel to the optical axis strike the mirror surfaces at mean graze angles (area weighted) of 9.3° for the primary and 5.6° for the secondary. These angles are sufficiently small to allow high reflection efficiencies to wavelengths somewhat below 100 A. 1740 APPLIED OPTICS / Vol. 24, No. 12 / 15 June 1985 of 0.10, permitting a 1.5° the on-axis image would be defocused to a 10-min of arc diameter, and the off-axis aberrations would be kept below this over a 2.10 field. The latter matches the detector aperture of 50 mm. However,the telescope must image to better than 0.5 min of arc in order not to dominate the spectrometer aberrations. This requirement is a factor of 12 tighter than that of the deep survey. Fortunately, only onesixth of the telescope aperture is used for any one spectrometer channel, resulting in greatly reduced field aberrations. As shown in Fig. 4(b), the aberration in the grating dispersion direction is <0.5 min of arc if the off-axis angle 0 is <0.50. [This corresponds to X 3.3 in Eq. (2), although the actual dependence of aberration on off-axis angle is no longer purely quadratic.] Thus, to maintain tolerable off-axis aberrations, the telescope optical axis need not be pointed very accurately toward a spectroscopy target. Defocusing of the on-axis image is not necessary and would in any case yield marginal gain due to the high degree of focal curvature for the W-S type-2 telescope. A final consideration is the residual size of an on-axis /SPECTROSCOPY) stellar image due to fabrication imperfections of the telescope, i.e., its figure. Recent visible light mea- surements being reported 3 2 for an EUVE scanning mirror reveal the on-axis imaging to be better than 2-sec --n- / TELESCOPE FOCUS (DEEP SURVEYI of arc FWHM (full width at half-maximum) and 5-sec of arc HEW (half-energy width). Similar results are expected for the spectroscopy telescope and represent a negligible contribution to the error budget. Fig. 5. B. the plate scales. Given detectors each with an aperture Gratings The heart of this spectroscopy instrument is the array of three reflection gratings located directly behind the telescope. A detailed view of any one such grating mount is shown in Fig. 5. The general principle on which this unusual mount is based2 9 3 0 is to allow the Grating mounting using a converging beam of incident light. of 50 mm, the three gratings cover the wavelength ranges 70-190 A, 140-380 A, and 280-760 A. (The correction wavelengths X* are 160, 320, and 640 A,and the wavelengths striking the detector center are 125, 250, and 500 A, respectively.) The average plate scales telescope to provide most of the focusing power and use are therefore 2.4, 4.8, and 9.6 A/mm in the three chan- the grating to provide the wavelength dispersion and fine corrections to the residual aberrations. A plane grating surface is chosen, thereby removing the large astigmatic aberrations present with the conventional nels. A 1-min of arc image produces an image diameter of 0.4 mm at the focal plane of the telescope (F = 1361.4 spherical surface at grazing incidence. A plane grating yields a pointlike stigmatic image in zero order when illuminated by convergent light. A defining feature of rection for the first-order image. Thus, the grating plate scales are translated into -0.5, 1.0, and 2.0A/min of arc for the three channels. At the center of each these plane gratings is the smooth variation in groove spacings which removes the dominant residual aber- channel, a resolution of X/AX -~ 250 is thereby attainable rations over a wide field centered on a preselected wavelength (X). The grating is used in an otherwise classical in-plane mounting and features grooveswhich are both straight and parallel to each other. At grazing incidence,the required space variation is approximately proportional to the square of the glancing angle (a). The precise variation is given by the grating equation: d(x) = mX./[cos0.(x) - cosa(x)], (3) where x is the ruled width. The groove spacing d(x) is approximately a polynomial.2 9 The incident and diffracted angles, a and 1, are relative to the grating tangent as shown in Fig. 5; 0,8 is the angle diffracted to a fixed detecting position for X*. To minimize the (dominant) aberration arising from instrument pointing uncertainties, we have chosen to use the inside spectral order (m = -1). At grazing in- cidence, this results in a significant deamplification of any image blur AO (FWHM) introduced prior to the grating. This is observed through inspection of the dispersive limit to the attainable spectral resolution 3 0 : X/A = I /o - llsinyo/(F/Lo)/A0, (4) where Lo is the central grating-detector separation, -yo is the reflection graze angle relative to the central groove, and : and a 0 are derived from Eq. (3). At the central wavelength for each channel, /ao 0 - 2 for the inside order (whereas /ao 1/2 if the outside order were chosen). Inserting the other parameters (yo = 10°, FILo = 2.8) yields a resolution X/AX = 250 for AG = 1 min of arc. This value may be understood in terms of mm). However the deamplification ratio of 0/ao 2 - results in a width of only 0.2 mm in the dispersion di- if AG = 1 min of arc. This dominates other contributions to the resolution budget, being larger than the telescope imaging (AG = 0.25 min of arc, V/AX= 1000), the detector pixel size (0.1 mm, V/AX = 500), and even the grating aberrations (X/AX = 350) as shown below. In each of the grating mounts, a increases from 6.02° to 8.62° over a ruled width of 173.2 mm, resulting in groove densities which vary over -415-840, 830-1675, and 1650-3350 mm-' for the long, medium, and short wavelength channels, respectively. To intercept offaxis rays, the flight gratings will have a ruled width of 200 mm. 1. ImagingProperties The spectral resolution attainable by such a grating is determined by the speed fy of the incident light along the direction of the groove heights: X,/zA\X = 8fy. (5) However, the image height H in the direction normal to dispersion depends also on f across the ruled width: HIL(O) = ImX*/d(0)j/(2amaJxfy), (6) where L(0) is the distance from grating center to telescope focus. For the flight spectrometers, fy = 6.2, resulting in a predicted extremum aberration X/AX = 350 at X*. The remaining parameters are mX*/d(0) = 0.037, L (0) = 485.5 mm, and f&= 22, resulting in a predicted image height of only 0.4 mm. This is equivalent to 1 min of arc of telescope aspect. In Fig. 6 we show the results of ray tracing the medium wavelength channel (XX140-380A). In these calculations we have optimized the use of a plane detector 15 June 1985 / Vol. 24, No. 12 / APPLIED OPTICS 1741 I I l, 1 I I I I 400 '. z aZo I- 180 g/.'. -j -r - 5, 300 _ fr - (a) 1400 ) 200I _ 0.6 I X- -/mm (b) 1600g/mm 5mm X-75 mm X-95mm Fig. 7. Electron micrographs of the varied line-space test grating u) 0.4 for the EUVE fabricated by Hitachi using a mechanical ruling engine. The groove spacings vary smoothly from 1400 to 1800 grooves/mm O across a 48-mm ruled width. The ruled width is in the vertical direction in this figure, and three small sections are relocated side- 0.2 CD , 1, . I 200 . I I I I 300 by-side for comparison. The blaze angle is -3.0°. These electron micrographs were taken for an aluminum replica prior to overcoating , 400 with rhodium. WAVELENGTH() Fig. 6. Geometrical aberrations of the short wavelength flight grating derived from numerical ray tracings of the extremum image sizes. A spectral resolution of A/AX = 300 and an image height of 0.35 mm are typical values. CONCAVE MIRROR surface for wide spectral coverage. This was achieved by orienting the detector normal to lie exactly along the ray diffracted from grating center to detector center (250 A). The detector is thereby found to make an angle of 15.50 with the grating normal and 30.00 with the optical axis of the telescope. As seen in Fig. 6, a V.L.S. i| spectral resolution of X/AX = 200-350 is obtained si- GRATING multaneously with a spatial resolution of H = 0.2-0.4 mm over the 140-380-A range in wavelength. Off-axis illumination of the grating (due to telescope pointing errors) must also be considered. However, over the FILM' specified field of ±15 min of arc, the deviations between the optimal focal surfaces of the telescope and the grating are small, resulting in only an overall shift in the absolute wavelength scale 30 (15 A). Employing the flight mounting parameters, we have experimentally verified the imaging properties of a ENTRANCE BAFFLE sample grating which was mechanically ruled by Hitachi using the technique of Harada and Kita.3 3 Electron micrographs of this test grating appear in Fig. 7, showing both the low (1400-mm-1 ) and high (1800-mm-1) PINHOLE density regions. This grating is a 50-mm section of the medium wavelength flight grating. The blaze angle was specified to be 3.00. In Fig. 8 we show a schematic diagram of the instru- MONOCHROMATOR ment used to test the imaging properties of the grating. In Fig. 9 we show the actual experimental apparatus. An entrance slit or pinhole is placed at the exit of a grazing incidence monochromator fed by a Paresce SOURCE hollow cathode source.3 4 A converging beam is provided by a small (-25.4-mm diameter) normal incidence spherical mirror placed 3000 mm from this entrance. As the mirror has a 2000-mm radius of curvature, the Fig. 8. Schematic of a laboratory spectrograph used to test the the imaging proeprties of the EUVE test grating. beam is refocused at a distance of 1500 mm with a focal speed of -f/60 in all directions. The 50- X 50-mm grating is illuminated across 40 mm of its ruled width and partially illuminated (-7 mm) along its grooves. Film sensitive to ultrasoft x rays,3 5 Kodak 101-06,was placed at the focal plane chosen for the flight spec1742 APPLIED OPTICS / Vol. 24, No. 12 / 15 June 1985 trometer. The spherical mirror functions as the collecting optic in this system and is coated with osmium for which usable reflectance is expected to extend somewhat below 300 A. B M Fig. 10. Spectrum recorded by the laboratory spectrograph showing the HE II Lyman series. The image heights (1 mm) are due to the dimensions of an entrance slit rather than due to the grating or optical system. The dim features near the bright 304-A image are lines of neutral helium, as is the 320-A image to the far right. No ghost lines a 5 are detectable in the spectrum. Fig. 9. Photograph of the laboratory spectrograph used to test the imaging of a varied-space grating. The spherical mirror (M), test grating (G), and film (F) are mounted on a common optical bench. The source of light enters from a pinhole preceding the entrance baffle (B), as shown in Fig. 8. X= 304 A +100 X= 256A 0 To obtain a polychromatic spectrum of the source and thus to demonstrate the grating resolution, the monochromator was switched to zero order, and the spectrometer entrance slit set to 0.1 X 2 mm. The spectrum we obtained (Fig. 10) shows an intense 304-A line and a series approaching 228 A. This is the Lyman series for ionized helium, the gas for which the source was operating. An additional line at 320 A, due to neutral helium, is also observed. By overexposing this spectrum, we were able to detect a cluster of neutral helium lines from 290 to 310 A, revealing a resolution in excess of 1000. Cr) 0o -100 U 0 +100 0 I )_ -100 However, the spectral resolution and image heights I I I I I I -100 0 +100 -100 0 +100 shown in Fig. 10 are due to the large dimensions of the entrance slit. To test the inherent resolution of our optical system, we replaced this slit by a 25-Am diam inhole. In Fig. 11 we show the recorded image at 304 , for which computer simulations predict a 20- X MICRONS Fig. 11. Recorded images of 304 and 256 A using an entrance pinhole of 25-pm diameter. The image widths are'-20-50 pm and the heights are -50-80 pm. The upper panels are high contrast reproductions showing only the brightest regions of the images. 20-pm spot including the aberrations of the spherical mirror at 10 off-axis. The measured resolution, including vibration of the fixture in the vacuum chamber (<30 pm) and film resolution (-5 pm), is 22 pm in the I- dispersion direction and 58 ptmin height. Given the Lz_ known plate scale (5 A/mm), the image width converts to a spectral resolution A/AX - 2500. The image di- mensions are equivalent to an incident beam of angular divergence 7 X 9 sec of arc. The recorded image at 256 A (Fig. 11) shows dimensions of 53-pm width by 75-pm height. Thus, even far away from the correction wavelength (X* = 316.4 A) the images remain small in POWER-LAWFIT: PERCENT=15/X-X 0 ) (n-z0. 4 W I-l20 cnz 2 0 ,c ncrZ Zz CLi 4 Q5 both dimensions. I 0.5 2. Stray Light The imaging apparatus also provided an efficient method of obtaining the distribution of focused stray light (FSL) near the first-order image. To obtain the halo of the 304-Aimage, we overexposed the spectrum I1 _ 1 WAVELENGTH () _ 2 Fig. 12. Microdensitometer profile of stray light in the halo of an overexposed 304-A line image. Due to unknown contributions from the entrance slit width and the film image halo, this light level is an upper limit to that produced by the grating. shown in Fig. 10, and we show in Fig. 12 a microdensi- tometer trace in the dispersion direction. We determined the total 304-A intensity by the measured relative intensities of all lines in an unsaturated exposure and using the film calibration given by Henke et al. 3 scale is in units of percent per angstrom. This profile is well described by the formula 5 The horizontal axis of Fig. 12 corresponds to the wave- length plate scale at the detector, and thus the vertical w(A-1) = 0.0151X ?- XoI', for 0.3A < -Xol < 3A. (7) This has not been corrected for either the wide entrance 15 June 1985 / Vol. 24, No. 12 APPLIED OPTICS 1743 slit (0.3-A halfwidth), the contribution of diffraction from the finite optical apertures, or the contribution from image broadening of overexposed film. Thus, it is an upper limit to the grating scatter but is still only 1.5%of the first-order intensity of 304 A within a 1-Abin located 1 A from the line center. Due to limitations of this method, the FSL level could not be obtained in the wings of the profile, however some qualitative information was obtained in the visible (6328 A) through pencil-beam illumination. Neither stray line nor ghosts could be seen, in contrast to easily visible levels pro- duced by conventional gratings ruled on other engines. A varied line-space concave grating ruled on the same engine and having a similar line spacing and ruled width has been reported3 6 to scatter <10-5 A-' = 10-3% A1 at 100 A from the line center at 304 A. For comparison,37 at 1236 A a photoresist grating has been reported at the same level and a conventionally ruled grating at '--2X 10-2% A-'. We have also made detailed efficiency measurements on the test grating. To enhance the EUV reflectance, the replica grating (aluminum surface) was overcoated with 125 A of rhodium over a binding layer of 50-A chromium. Reflectance values reported in the litera1 reveal an improvement for rhodium over other standard coatings (e.g.,gold or platinum) in the region of interest (X - 100-600 A). Monochromatic pencil-beam radiation was provided by a Henke tube,4 2 a Penning source, 43 or a hollow cathode source3 4 placed at the entrance slit of a grazing incidence monochromator. These sources provided lines at 114 A, 170 A, and at 256, 304, 584, and 1216 A, respectively. The intensities of the diffracted images were measured by translating the grating into the beam and positioning the detector of intercept the diffracted relative to the grating facets. In the negative orders, y = a + 3. The blaze angle was specified to be 3.0 in the sample grating and the nominal groove spacing to be 1/1600 mm, resulting in the detector and incident at a fixed angle to the microchannels. The grating was positioned by translating it across the incident beam and monitoring the reflected signal to locate the grating center. Aperture stops ensured that the grating would then be underilluminated. Since the detector was an imaging microchannel plate, histograms of the accumulated counts were also monitored to ensure that one (and only one) spectral order fell safely within the field of view. Spectral impurities of the monochromator were removed by switching to a nearby (off-line)background region and subtracting the counts. All counts were corrected for electronic dead times (<10% in all cases). Absolute grating efficiencies were obtained by normalizing these results to the incident beam intensity. This intensity was obtained by removing the grating and positioning the detector to intercept the beam directly. The intensity was monitored as a function of time and the results used to correct for temporal drifts (of the order of 1% between measurements). Measurements were made at severalwavelengthsand 1744 XB _ 130 A. In addition, the reflectance of rhodium is apparently increasing as the wavelength decreases from .200 to 100 A,judging by the sum of efficiencies in all observable ported by Cox et al. 38 and those which we have obtained on a flat coated as a witness sample to the grating, using the 11.40graze angle relative to the groove facets. The grating reflectance of 77% we measure at 114 We show in Fig.13(a) the absolute APPLIED OPTICS / Vol. 24, No. 12 / 15 June 1985 A is in precise agreement with the 76%value we measure for the flat. Assuming a perfectly smooth surface, the optical constants given by Henke et al. 3 9 predict a reflectance of 93%. The relative grating efficiencies are therefore confidently derived as the ratio of the measured absolute efficiency to the measured sum of efficienciesin all orders. In Fig. 13(b) we show this result, revealing relative first-order efficiencies as large as 50%. We find these results to be in excellent agreement with the theoretical efficiency curve given by orders (e.g., m = 0, 1, 2, etc.). To minimize variations in detector efficiency, the image was always centered on angles of incidence. (8) 2d sinb siny, XB where 6 is the grating blaze angle and y is the graze orders [upper data in Fig. 13(a)]. These values are in excellent agreement both with reflectance values re- 3. Efficiency ture 3 efficiencies as functions of wavelength. These were made with incident light at an 8.40 angle relative to the grating tangent, this being the mounting configuration of the flight gratings for this illuminated section of the ruled width. The first-order efficienciesare seen to rise toward shorter wavelengths, reaching 38%absolute at 114 A. This trend is explained in part on the basis of a peak in the diffraction efficiency near the blazed wavelength: erel(Xm) = I (Xm)/ /all m I(Xm), (9a) where I(X,m) = [sin(pm)/(pm)]/sin[fl(X,m)], Pm = (OrglX)cos(a+ 5) - cos[(X,m) (9b) - a (9c) are the familiar Kirchhoff/Rowland results4 4 4 5 for diffraction from a reflecting facet of width g. As shown in Fig. 14(a) our grazing incidence mounting results in significant shadowing of the incident light by adjacent grooves, yielding an illuminated width g = d os5[1 - tanb/tan(a + )]. (10) Equations (9)-(10) represent a normalized scalar Kirchhoff approximation for the grating relative efficiencies. We note that the 1/sin: term in Eq. (9b) accounts for the width of the interference patterns from a given number of grooves and that /3(X,m) is derived from the grating Eq. (3) in which for the present analysis we treat the spacing d as a constant. This theory predicts a blaze efficiency of sina/sin, which has been verified experimentally 4 6 and is in agreement with more rigorous theory.4 7 This factor also has a simple geo- 0.6 1.0 | I I I (b) a = 8.4° FIRST ORDER 0.51- 0.8 U z z )W 0.4 (J 0.6 ULi U- O , 0.3 I-_ Z [IJ n 0.4 -J 0 d 0.2I-_ In tX 0.2 Q.o WAVELENGTH(A) I I I I l0 200 300 400 500 600 WAVELENGTH(1 n. |l.V 0s -/ l I~~~~~~~~d) Ua: 84° ~~~~~~~~ZERO ORDER _/ z 5 UL Un Wi 0.6 In 0.4 o1 In 0.2 6 8 10 12 14 INCIDENT GRAZEANGLE (Deg), 0 I 200 I 400 I I I II I 600 800 1000 WAVELENGTH(A) I I 1200 1400 Fig. 13. Measured grating efficiencies. (a) Absolute efficiency in spectral orders 0, 1, 2, and 3 vs wavelength at an 8.40 graze angle to the grating tangent (11.40 to groove facets). The sum em= o + q + 2+ 3 is compared to our reflectance measurements at 11.40 of a flat witness sample (+) and those found in Ref. 38 (l). (b) Relative first-order efficiencies derived from the left-hand panel compared to theoretical curves times -0.9. (c) Relative first-order efficiencies vs angle at X = 114 A compared to theoretical curves times -0.85. (d) Zero-order relative efficiencies vs wavelength at an 8.4° graze angle compared to a theoretical curve times 1.06. metric interpretation. If the incident and diffracted directions are interchanged [Fig. 14(b)], an appeal to the (a) SHADOW INCIDENT t m = -I ) .m-l) 4 9 maintains the same theorem of optical reciprocity48' absolute grating efficiency at that wavelength. At blaze, the new incident angle f3 grazes the facet at the same angle ( - 6) as in the previous case (a + ). Therefore, the reflection coefficient is unchanged and the relative efficiency at blaze is equal to that fraction Q of the exiting beam which is not blocked by the adjacent facet: Q = [1 - tan8/tan(a + 8)1/[1+ tanb/tan(/ = sina/sinfl, for j = a + 26. Fig. 14. Geometry of groove shadowing: (a) blaze of an inside spectral order, (b) blaze of an outside spectral order. Shadow factors derived from these geometries may be used to accurately determine the blaze efficiency. - 8)] (Ila) (11b) However, away from the blaze the efficiency curve is more difficult to infer from geometrical arguments, as evidenced by the several variations in this application of the Kirchhoff theory which have been proposed.50 - 5 4 Nonetheless, we find our method generates curves in good agreement with the measured efficienciesto within the domain of validity of the Kirchhoff theory. Using Eqs. (9)-(10), the theoretical first-order curve which best fits the data ploted in Fig. 13(b) is for a blaze angle 6 = 3.5° and for 90% of the theoretical values. As 15 June 1985 / Vol. 24, No. 12 / APPLIED OPTICS 1745 Table II. an alternative (dashed) theoretical curve, we have used simply the shadow factor of Eq. (la) and the unnormalized diffraction pattern for fully illuminated facets [g = d in Eq. (9c)]. In this case a best fit to the data yields a blaze angle of 3.00 and 82% of the theoretical values. It is remarkable that, with either fit, the data attain over 80% of the theoretical efficiency values. This close agreement with the values expected from perfect grooves is startling, given that we are illuminating the groove tips and have ignored edge defects in the calculations. The worst fit is for data taken at 584 A, which may be an indication of the breakdown expected in the Kirchhoff theory for effective wavelengths comparable to the groove spacings. For graze angles of 8.40, the effective wavelength at 584 A divided by the groove spacing (6250 A) is -0.7, while the Kirchhoff theory is valid only for ratios less than .4.48,55 In1.35) the theory predicts a deed, at 1216 A (eff/d relative efficiency of 4%, whereas a single mesurement at this wavelength yielded only -1.2%. In addition, strong polarization effects occur at the longer wavelengths, which this scalar theory neglects, and the reflection coefficient there should be derived from a generalized Fresnel equation. 5 ' Neglected effects which are not expected to be significant include polarization of the incident light and polarization sensitivity of the detector. The above measurements are not fully adequate to infer the blaze angle, as these fits are heavily based on only two data points (114 and 170 A). To further constrain our model, in Fig. 13(c) we show measurements taken as a function of angle at a wavelength of 114 A. These derived relative efficiencies show a clear blaze peak near a 90 graze angle. These data are best fit by an assumed blaze angle of 3.3° (or 2.80 with the alter- nate theory) and an efficiency of 82% (88%) times the theoretical values. Figure 13(d) shows the zero-order relative efficiencies and the theoretical curve times a factor of only 1.06. This is additional indication that very little of the diffracted light (6%) is misallocated from other orders and into the zero order. From the measurements displayed in Fig. 13, we can confidently infer several things: (1) that the total energy diffracted into the grating orders equals the reflectance of the coating at the graze angleincident to the groove facets, (2) that in excess of 80% of the efficiency expected from perfectly formed grooves has been recovered, and (3) that the blaze angle is between 2.80 and 3.5°, in agreement with the specified value of 3.00. C. Background Suppression Contamination of the spectrum by unwanted light can originate both within the instrument (e.g., order confusion) and externally (e.g., diffuse sky glow). However, these photons will be obstructed in three stages prior to reaching the detector. First, any light attempting to enter the instrument aperture from a sky position located outside the collimator field will be rejected by the medium and long wavelength channels. This causes diffuse sky lines to be restricted to narrow regions of the spectrum. 1746 At very large angles away from APPLIED OPTICS / Vol. 24, No. 12 / 15 June 1985 ImportantNightglowFeatures Average intensity Shadow intensity Wavelength A 256 304 584 600 703 718 834 911 938 950 972 991 1025-1027 1216 1304 HE II HE II + O III HEI oI 0 III o II 0 II + III 0 HI HI H N III + I I+ HI H I 0I (ecliptic) R (entire sky) R Transition <0.02 3 - 0.1 12 3 0.1 0.2 0.4 6 1.5 0.1 0.4 0.5 0.6 8.8 3500 7 - 1.3 1.5 <0.06 <0.06 <0.06 <0.06 8.8 3500 7 the optical axis, this is complemented by baffles within the telescope. Second, the low level of grating scatter expected (see Sec. III.B) prevents wavelengths from straying outside their intended spectral bin. Third, any remaining light reaching the focal plane from outside the spectral band will be largely removed by filters. Each of these three barriers permits only a small fraction (10-5-10-3) of the undesired light to be transmitted and in combination remove almost all the background. 1. Collimators The spectrum of a point source will be contaminated by diffuse night sky glow present in the geocoronal and interplanetary mediums, due dominantly to backscattered solar radiation. In Table II we list the dominant features of which these emissions are composed and the values of their nighttime intensities in units of Rayleighs (1 R = 106 /4ir photons/cm 2 /sec/s) which we have used in determining our instrument background. shadow intensities above 304A are representative The of measurements taken while viewing down the earth's shadow cone from an uplooking satellite in a polar orbit at 600 km.56 The intense hydrogen Lyman-a line at 1216 A lies outside the EUV and is thus removed by use of thin-film filters, as discussed below, and also lies in the wings of the grating scatter profile. However, helium lines at 304 and 584 A are also present in sufficient flux (10o-101R) to degrade the instrument sensitivity and unfortunately lie in the middle of the desired spectral region. At present there are no filters which can acceptably remove these lines and still provide suitable transmission at nearby wavelengths. However, we may confine these features to narrow regions of the point-source spectrum by a field stop. In the absence of a slit, we employ an array of wire grid collimators5 7 -5 9 in the medium and long wavelength spectrometer channels (Fig. 1). These collimators have a triangular response for transmission of off-axis rays: T(0,0) = T(O)[1- cosq5j/OJ, 0/Oc < /cos (12a) 0/0 = 0, molybdenum and is aligned relative to the stack by > /coso, where 0 is the off-axis angle of a field point from the telescope optical axis, and 0 is the azimuthal angle between the dispersion direction and the off-axis direction. We have employed a collimation full width at halfmaximum G, only in the dispersion direction of the grating. Thus if 0 = r/2 the radiation will not be attenuated at any off-axis angle, since the collimation is only in the normal direction. The 1-D collimation also permits minimum obstruction through the grid apertures and thus maintains high on-axis transmission T(0), -70%. Transmission of the desired light from a point source of radiation requires a pointing accuracy O < GC. Averaging over all angles X,the average transmission for the point source is (T(0)), = T(0)[1 - (2/7r0KOp/00j, (13a) where K 1, for < These leaks must also be maintained below at 1% level, which should be directly attainable with this design. A final consideration is diffraction through the narrow grid slots, which can broaden the collimator field of view.6 2 Each slot is of width W = Z tanO, 0 /Op - (15) where Z is the height of the collimator. A convenient estimate to this broadening6 3 is given by the full width at half-maximum of the 1-D Fraunhofer pattern through an individual slot opening W: AOdiff = (2.8/7r)X/W. (13b) ,, K = 1 + arccos(0/0)O mechanical registers. Through a slight oversizing of the grid bars, transmission leaks due to misalignments can be virtually eliminated. In the extreme ultraviolet, transmission directly through the wire bars is negligible due to the EUV opacity of the material. However, collimator transmission outside the desired field can occur due to reflection pathways through the stack. (16) With Z = 150 mm and Ge = 20 min of arc, the slots are V/1 -(Oj/0p) 2, for Op> Oc. (13c) 850 pm wide. The wavelengths of interest are 140-760 A which, from Eq. (16), introduce broadening in Ge <0.3 We expect a satellite pointing capability Op < 15 min of arc during more than 50% of the observing time. min of arc, in the collimator off-axis response. This (This corresponds to a 3a pointing error of 35 min of arc for Gaussian errors distributed about 0 = 0.] Adopting a collimator G, = 20 min of arc then ensures an average transmission in excess of 0.5 X T(0). principle, one might also consider the potential blurring of an incident stellar image due to slot diffraction. If each slot were positioned independently, one would Through a differential of the grating equation, one finds that the diffuse sky is restricted to a bounded spectral region A: (14a) - (do/m)(F/Lo)(Op + Ojsinao. (14b) where DX expect an incoherent superposition of the response from a single opening, as given by Eq. (16). However, to maintain usable on-axis transmission through the stack of grids, the slots must be coaligned to an accuracy much DX < X < Xsky + DX, Xsky - effect is small enough to be neglected in the design. In Therefore, sky glow at 584 A is confined to regions overlapping the point source spectrum from 522 to 646 A,and sky glow at 304 Asimilarly contaminates only the 273-335-Aregion. Thus, the astrophysically important regions near 228 A (He II edge) and 504 A (He I edge) are immune from direct sky glow. In these uncontaminated regions (140-273, 335-380, 380-522, and 646-760 A),the sensitivity rises by a factor of 5. If viewingdown the earth's shadow, the intensity of the 304-A glow drops to insignificant levels60 (Table II), however the level of a 584-A glow remains largely unchanged. 61 Thus, the collimators significantly improve the general sensitivity of the medium and long wavelength channels. Fabrication of a prototype 20-min of arc collimator is currently under way. To maintain the full sensitivity enhancement discussed above, a 1% upper limit is placed on the transmission leaks for incident angles 0 > G. This requires removal of transmission sidelobes out to L3'. The design employs an exponential spacing of intermediate grids in a coaligned stack, as originally proposed by Parkinson and also successfully employed by others.5 8 5 9 Each grid is chemically etched out of finer than their individual widths. In practice, this is achieved with openings in any one grid being equally spaced except for random location errors which are not individually reproducible between different grids in the stack. The result is that each grid acts as a coherent array of apertures, i.e., a very coarse diffraction grating. Thus, in computing the blurring of an incident stellar image, i.e.,the point-response function of the collimator, one should replace W in Eq. (16) by the total aperture of the collimator. Also being the aperture of the collecting optics, this diffraction limit is negligibly small. Even in the event of incoherent slots, the blurring of 0.3 min of arc is not a dominant contribution to the resolution budget of the instrument. 2. Filters The use of collimators and a low level of grating scatter will remove most of the stray and diffuse light prior to reaching the focalplane. However,to safeguard against possible contamination by intense Lyman-a hydrogen glow (Table II), we also employ thin-film fil- ters in front of the detector surfaces. Well-defined bandpasses are obtained by use of Parylene-N for channel A (70-190 A) and aluminum for channels B (140-380 A) and C (280-760 A). The filter transmis- sions are obtained through use of the equation Tfflt(X) = exp[-p(X)tl, 15 June 1985 / Vol. 24, No. 12 / APPLIED OPTICS (17) 1747 above for the EUVE spectrometer. The design takes advantage of a simple wedge-and-strip anode readout system.6 9 Somewhat enhanced resolution (50 gm) may be obtained in the dispersion direction of the spectrometers while maintaining the same overall number of pixels. The spectroscopy detectors will also utilize CsI photocathodes for enhancement of the EUV quantum efficiency7 0 to -30%. We note that a similar microchannel plate detector system has been measured in-flight16 to generate an internal background of 0.5 counts/cm2 /sec. z0 C,, a: IV. Instrument Performance Returning to the system flow chart presented in Fig. 3, we can now take a quantitative inventory of all the contributions to the imaging and efficiency of the spectrometer. Following these two exercises (Secs. A and B, respectively), we derive the net sensitivity of this instrument for stellar observations (Sec. C). WAVELENGTH (A) Fig. 15. Filter transmissions taken from Refs. 64 and 65. The range of each spectrometer channel is indicated at the top. where t is the filter thickness, and A(X)are the linear absorption coefficients as given by Stern and Paresce 6 4 for Pa-N and by in-house data taken by Jelinsky6 5 for aluminum and Pa-N. The filters are chosen with thicknesses capable of preventing a direct Lyman-a background from affecting the sensitivity limit for observing times <40,000 sec. This results in 3000 A of Pa-N and 1500 A of aluminum, each with transmissions at 1216 A of <2 X 10-5. The Pa-N filter also reduces most of the background in channel A due to HE II 304-A diffuse light. The measured filter transmissions within the intended EUV bands are plotted in Fig. 15, being typically 30-40% including the transmission (80%) from supporting nickel meshes. We note that a 3000-A Pa-N filter is of comparable transmission with the measured A. Resolution The resolution budget is dominated by an assumed pointing reconstruction with an error profile FWHM = 1 min of arc. Almost as large a contributor is the grating aberration, limiting the spectral resolution to A/AX= 200-350 and the spatial resolution to 0.2-0.4 mm (0.5-1.0 min of arc). The next largest aberrations are those due to detector pixels (FWHM of 0.1 mm = 0.5 min of arc in the dispersion plane), mirror off-axis aberrations (0.25 min of arc), and mirror on-axis aberrations (0.1 min of arc). Image blurring induced by misalignments is expected to be very small, corresponding to <0.1 min of arc. In the event that the instrument pointing reconstruction is significantly better than assumed (e.g., is 10 sec of arc) and that the detector pixels are redistributed to optimize for spectroscopy (50 X 200-Mmpixels filter of 2000-A Pa-N with an additional 600 A of carbon over a 1024 X 256 format), we will essentially achieve the on the front surface. Since the filters need not assume all the responsibility for background removal, a factor above aberrations do indeed arise, we must perform a of 2 improvement in these transmissions is possible by use of thinner filters (2000-APa-N and 1000-Aaluminum), which are however more susceptible to developing pinholes. D. Focal Plane The dispersed spectra will form a linear array of wavelengths which must be spatially resolved at 100gm over a 50-mm aperture. To obtain the desired resolution and sensitivity, we must be able to follow the instrument pointing through time tagging of the photon arrivals. This requires single-photon counting to permit an accurate mapping of focal plane pixel with sky position and thus determination of absolute wavelength. To obtain high sensitivity, we also desire a detector quantum efficiency of 20% or higher and low back- ground rates (<0.5 counts/cm2/sec). These properties are met with microchannel plate detectors.6 6 6 7 Siegmund et al. 68 have described laboratory results on a prototype EUVE detector which already attains the desired levels of performance outlined 1748 APPLIED OPTICS / Vol. 24, No. 12 / 15 June 1985 inherent grating resolution limits. However, if all the convolution of terms which are dominant and comparable in magnitude. This calculation must include the 1-D projections of the aberration profiles. Several of the terms described above are accurately described as normal Gaussian error distributions, such as pointing reconstruction and detector pixels. However others, such as grating aberrations and off-axis mirror aberrations, are more accurately modeled as uniformly distributed errors within a sharp boundary. The convolution of Gaussian distributions is simply a summation in quadrature of the component terms. The 1-D projection of a 2-D Gaussian is also a Gaussian with the same , which facilitates the computation. However, the convolution of two uniform and bounded distributions is a trapezoid with a FWHM equal to U = Umax+ (1/2)umin, (18a) and the generalized result for the convolution of several such square waves is U = 1 + (1/2) E ii ui = (1/2) ( + E, i) alli I (18b) where u1 = Umax. To estimate the net aberrations in our instrument, we first separately sum the Gaussian terms and the uniform terms. This results in 2.355a = 2 P(x)= E exp(-1/2a )da, ' 300- 1.12 min of arc and U = 1.0 min of arc near the spectrum center. As the second convolution is dominated by a single term (grating aberrations), we may accurately approximate this sum as a uniform distribution with a FWHM = U. This allows the final convolution to be written as a familiar probability distribution: | 400 r (L O 200 Z 3: -J 0 100 C - a* (19) * 2 where a, = (x - U/2)/crand a 2 = (x + U/2)/a, for which excellent analytical approximations exist. Inserting the above values for a and U, we find that P(x) has a FWHM equal to AG of 1.25 min of arc. From Eq. (4), where the average resolution across each channel is (X/AX) (20) 250/AO (min of arc), we find a spectral resolution of -200. resolution on the wavelength for the three spectrometer channels. Although these values meet the basic science requirement for resolution, there is room for further improvement. For example, we also include in this figure the result which is obtained given enhanced pointing reconstruction (10-sec of arc FWHM) and detector pixels (50 pmin the dispersion direction). In this case, the average resolution is 300. Calculation of the net spatial resolution proceeds in an identical manner, except to recall that (1) the grating does not deamplify sky angles in the direction normal to dispersion, resulting in an aberration of only 0.25 min of arc for a 0.1-mm pixel height, and (2) the grating contributes 0.2-0.4 mm = 0.5-1 min of arc in the image 1.03 min of arc and (U) 1.15 min of arc, yielding a net FWHM of -1.5 min of arc. This spatial resolution capability greatly reduces the instrument background and provides simultaneous observation of multiple sources within the field of view. B. Effective Area The net collecting area of each spectrometer channel is the product of the geometric aperture and several efficiency factors. Listing these in their order of occurrence in the instrument optical pathway, we have A(Am,0) = T. 011(0)X R(X,p) X erei(X~m) Tfilt(,) X QE, Ageom X X I I 200 I I I 400 WAVELENGTH () I I 600 800 Fig. 16. Spectral resolution as a function of wavelength including all aberrations of the flight spectrometer. Upper (light) curves assume a satellite pointing reconstruction of 10 sec of arc, while the lower (dark) curves assume this is 1 min of arc. As the grating dispersion increases with wavelength within each channel, the spectral resolution also increases with wavelength. In Fig. 16 we plot the dependence of this heights. Thus, 2.355a -Al 0 the functional dependences. For example, we do not expect the collimator transmission to depend strongly on wavelength or polarization of the incident beam. Nor do we find the reflection coefficient of the optics to alter significantly as a function of the off-axis angle. For convenience, we also assume that the detector efficiency is a constant for the purposes of this calculation. The geometric area devoted per spectrometer channel is 75.4 cm2 , representing exactly one-sixth of the total primary mirror aperture of 452 cm2 . Thus, the goal of 0.3 cm2 can be met only if the net efficiency of this instrument is >0.5%. Collimators are necessary only in the medium and the long wavelength channels. Each collimator is designed to transmit at least 60% on-axis, which includes obstruction from supporting structures within the wire grids. The off-axis angle of the spectroscopy target is dominated by the choiceof orbit platform for the EUVE mission. The outcomes range from a 1-min of arc capability (dominated by alignment errors between the instrument and the satellite) to a 15-min of arc average pointing error. Use of Eq. (13) then translates these values into net average transmissions of 58%and 31%, respectively. We include these two limiting cases separately in our calculations. Due to the near planarity of the reflecting surfaces in the mirror-grating system (Fig. 17), the net reflection coefficient is approximately R(Xp) = (1/2)S(X)[(1- P)aRMl(X)aRM2 (X)arRG(X) + (1 + P)rRM1(A)rRM2(X)QRG(X)1, (21) (22) three-bounce optical system as a function of the linear polarization p of the incident light, srei(Xm) is the rel- where the reflectances R are derived from the Fresnel equations, p is the linear polarization of the incident light, and S(X) is the fraction of reflected intensity which appears in the specular direction. If the electric vector is aligned along the mirror and grating tangents ative grating efficiency curve for spectral order m, Tf 1lt(X) is the filter transmission curve, and QE is the (TE = a polarization), p = -1,while the orthogonal case (TM = -7r polarization) requires p = +1. Unpolarized where T, 011 (0) is the collimator transmission at an offaxis angle 0, R (X,p) is the net reflectance curve of the detector quantum efficiency. In writing Eq. (21), we have made several simplifying assumptions regarding incident light corresponds to p = 0. In the latter case, the primary and secondary mirror elements will none15 June 1985 / Vol. 24, No. 12 / APPLIED OPTICS 1749 E 4 / L GRATING SECONDARY MIRROR I-i w LPRIMARY MIRROR U UUW Fig. 17. Three-bounce reflection system of the EUVE spectrometer. Each channel uses only one-sixth of the telescope surface of revolution, resulting in a nearly plane-parallel alignment of the reflections. This significantly improves the net reflection coefficient. 0o. I 0.6 | ] I I I I Fig. 19. ~~~~~~~~~~TE = R, _ I 200 0 I I 400 WAVELENGTH () I 600 800 Effective area as a function of wavelength for on-axis pointing toward a spectroscopy target. For off-axis pointing, these values are lowered as discussed in the text. U The upper (light) curves assume a thinner aluminum filter (1000A). z IL ULI. I 0.4- 0 z 0 w C-, a: ULI 0.2 - 1 square (rms) surface height roughness for surface i. The fraction of reflected light which is scattered, I - T1 S(X), will be distributed in a halo centered at the spec- 200 0 406 600 800 WAVELENGTH(A) Fig. 18. System reflection coefficient for three states of linear po- ular image. Because part of this halo will be enclosed by the resolution element, Eq. (23) underestimates the usable fraction of the reflected light. However, we adopt this conservative approach and assume h = 25 A for each surface. larization of the incident light using the optical alignment indicated in Fig. 17. The spectrometer reflection efficiency ocillates between the extreme case values for each 900 spin of the instrument about the line of sight. theless induce a linear polarization into the beam. Using published optical constants 38 40 for gold (mirrors) and rhodium (gratings), this separation of the polarization components results in significant enhancement (a factor of -2) in the reflective throughput, compared As we have made efficiency measurements on a sample EUVE grating (Fig. 13), we used these data as representative of rel(X)of the flight gratings. The wavelengths relevant to each channel are scaled from Fig. 13by the groove densities for the three gratings, all having the same blaze angle. For the filter transmission, we used the data6 4 65 from which Fig. 15 was derived. For the detector QE, we adopt a value of 30% as measured on microchannel plates7 0 at these wavelengths. Due to soft x-ray absorption edges of the photocathode,3 9 in practice there to a naive calculation based on reflection coefficients for will be some dependence of the QE on wavelength, re- unpolarized light. In the event that the incident light sulting in a dip near 200 A and an enhancement near 100 is itself already linearly polarized, inspection of Fig. 18 A. reveals a strong relation between R (X)and the direction of that polarization (p = -1 or p = +1). Thus, although not designed with this capability in mind, the spectrometer can also function simultaneously as a polarimeter. If during an observation the instrument were to be set into a slow spin about the optical axis, the direction of an incident linear polarization would oscillate between the TE and TM modes with a cycle of one-half the spin period. Of course, the In Fig. 19 we show the final result for the on-axis collecting area of the EUVE spectrometer. The design goal of >0.3 cm2 is met over the 80-600-A region, attaining significantly higher values over selected bands. The very high peak, over 1 cm2 near 100 A, may be due to overestimated reflectance values there. At the lon- observed modulation would also need to be deconvolved from the signal modulations caused by the collimator [Eq. (12)]. The specular fraction S(X) is derived from the ex- pressions 7 1 SQA) = S 1(X)S2 (X)S 3(X), (23a) Si(X) = expf-(47rhi sin'yi/X) 2 1, (23b) where yi is the graze angle and hi is the root-mean1750 APPLIED OPTICS / Vol. 24, No. 12 / 15 June 1985 gest wavelengths, 600-760 A, the low filter transmission results in a precipitous drop in area. This can be alle- viated by use of a thinner aluminum filter (1000 A), as displayed in the upper (light) curves. C. Sensitivity Combining all the above-mentioned effects, one can calculate the sensitivity of this instrument. At each spectral bin, X ± AX/2, the minimum detectable flux for detection of spectral lines is 2 /=(X)[1+ v/1+ (4/a )B(X)i], (24) 10 I I I I H I I B(X) (27) where ((X 5 ,p)) is an effective average scattering factor over the range Asepfrom the image center [Eq. (26)] and where AO_, is the image FWHM in the dispersion direction. As defined previously, G, is the collimator field -2 w 10- \V lo4_ 'A CHANNEL* B I l 200 0 I full width at half-maximum. The angle Oxis the offaxis angle required in order that the incoming wave i be diffracted to the wavelength bin X. This angle is 'C I I 400 600 Ox = ao(Lo/F)[N/y - 2m/do(X - I Im(X- 800 WAVELENGTH() Fig. 20. Z A(Xi)J(Xi)[(w(Xsep))OcAX + tc(OA)Ax], SENSITIVITY LI z a(X)D + AO(106 /4r) Limiting sensitivity to spectral lines as a function of wave- length. The observing time was assumed to be 40,000sec, and the detection threshold was set at 5or(and 3o). Dark curve is at the 5a level (labels are incorrectly ordered). The bump in the sensitivity curve centered at 304 A disappears for observations of sources located down the earth's shadow cone. i)/ao - 11 Xi)I/do(Lo/F)ao. (28) The two terms within the brackets of Eq. (27) represent (1) the grating scatter of light integrated over the collimator field, and (2) the directly imaged light from an off-axis sky pixel. The stray light level, (o), should be <0.01% A-' = 10-4 A-' from the distant 1216-Aline (Table II) at any of the desired wavelengths from 70 to 760 A. To be conservative, we used a value of 10-3 A- in our calculations. With Eq. (27) and inserting the measures given where A (X)is the effective area at X, i is the observing time, a is the sigma level of the detection (e.g., a = 5 is a 5a detection), e is the fractional energy encircled by a resolution element, and B (X)is the background rate. As a worst-case estimate for e, we consider the limiting spectral resolution FWHM. This corresponds to an aspect uncertainty of -1 min of arc. The encircled energy from the mirror figure is essentially unity, as discussed above. If the image profile is dominantly a 2-D Gaussian and one integrates in the direction normal to dispersion (AOy),then e = 0.76 at the limiting spectral resolution and e = 0.98 at twice as coarse a resolution. We adopt e = 0.76 for all calculations. We consider the case where there is no direct con- tinuum from the cosmic source. The background rate per pixel is then previously for the individual terms contained therein, in Fig. 20 we plot the limiting sensitivity of the EUVE spectrometer in the three channels as a function of wavelength. These curves assume a 5a detection threshold and an observing time of 40,000 sec. Background is a significant factor within the collimator transmission bumps near 304 and 584 A, the former being eliminated for observing lines of sight down the earth's shadow cone. Outside these bands, the sensitivity is simply equal to a2 /r/A(X)/e from Eq. (24). An optimal sensitivity value is 10-3 photons/cm 2 /sec. The sensitivity curves can be easily converted into continuum flux units by the transformation Fmin(X) = h(X/AX)Iin(), where X/AXmay be lowered, to provide better sensitivity, by binning the data followingan observation. V. B(X) = a(X)D + (10 6 /4-7r)AOYAXZA(X)J(Xi) X Jf (25) t,(exP(XXie)5eX where a (X) is the image area at the detector, D is the detector background (counts/cm 2 /sec), AOYis the image height projected on the sky ( = H/F), AX is the spectral bin size, J(Xi) is the sky background (in Rayleighs) for emission line i (Table II), t (0) is the relative collimator transmission at an off-axis angle 0 in the dispersion direction, and P(Xdiff)is the point-response efficiency profile of the grating (in units of A-i). The wavelength separation from the image center is Xsep X - Xi i O(do/m)(F/Lo)ao. (26) The point-response function P can be decomposed into the geometrical aberration response (Fig. 6) and the scattering profile co. If focused stray light dominates over hemispheric scatter, a convenient approximation is made on Eq. (25): (29) Applications The sensitivity of the spectroscopy instrument is most usefully illustrated by way of simulated observations on example targets. At present only a sparse sample of data exists on extrasolar EUV sources.1 - 4'6 -8 It is the primary function of the EUVE mission to survey the sky and generate a complete catalog of these sources. These data will be invaluable in identifying the brightest targets for the subsequent spectroscopic observations performed by EUVE and by other follow-onmissions. This exploratory nature precludes an exhaustive or even representative listing of the objects likely to provide useful spectra. However, it is illustrative to at least consider the quality of spectra which can be estimated for the few classes of EUV sources presently known. In this section, we consider two such objects: hot white dwarfs and stellar coronas. A. Hot White Dwarfs 'White dwarf stars have been studied extensively at 7 2'7 3 The hot white visual and ultraviolet wavelengths. 15 June 1985 / Vol. 24, No. 12 / APPLIED OPTICS 1751 6000, I o-24 I I I I I I - I (a) H43 NH 2XI0 HeG EDGE 1 zI If Hel EDGE (ISM) 0 2000 'l-26 :2 cm sec 4000 -25 I 40,000 i l o-27 20 z 400 U T SENSITIVITY( 3 60080 0, 200 400 600 860o - z (b) G191-13213 0 ~~~~~~~~NH 3 X10I7C,,- Mh, U- In-28 0 I 200 I I 400 I Il 600 1500 20,000 (ISMI Soo WAVELENGTH (A) Fig. 21. Hel EDGE sec 6) zF Continuum flux from a known EUV source, HZ43, as a 1000 0 function of wavelength. This is compared to the limiting 3a-spectrometer sensitivity after a 40,000-sec observation, assuming a 500 wavelength-binding resolution of X/AX = 100. Sources approximately a factor of 100 dimmer than HZ43 will still be spectroscopically 0O 400 detectable. 440 460 520 WAVELENGTH dwarfs were the first extrasolar objects discovered at EUV wavelengths.'1 2' 6'7 Due to their bright continua, these stars are likely to serve as in-flight calibration standards for the EUVE scanning telescopes and the spectrometer. Extensive EUV observations 6'8 exist generate Eddington surface fluxes, H(X), for HZ43. The surface flux at the earth can then be calculated: F(X) = 47rH(X)(R*/D) 2 exp[-(X)NH], (30) 600 Fig. 22. Accumulated counts per AX = /100 bin for observations of two hot white dwarfs: (a) HZ43 for 40,000 sec, and (b) Gl91-B2B for 20,000 secs. The smooth bumps and the long wavelength decline are primarily due to the instrument effective area as plotted in Fig. 19. The noise is due to Poissonian counting statistics. The lower panel shows only a part of the long wavelength spectrometer channel near a simulated interstellar helium edge at 504 A., for one hot white dwarf, HZ43. These data can be used to constrain several model parameters (temperature, density, and helium abundance) as well as the source distance and the intervening interstellar absorption. We have used a white dwarf atmosphere's code8 to 560 () provides an excellent measure of a HE I interstellar edge at 504 A. The broad EUV continuum shape is alsovery sensitive to the abundance of neutral hydrogen and thus several pieces of information on both the white dwarf and the interstellar medium are accessiblethrough EUV spectroscopy. The predicted space densities of hot white dwarfs7 5 and measured interstellar hydrogen where D is the distance to the source (65 pc), R* is the column densities7 6'77 should permit a fair sample of such star's radius (8.4 X 108 cm), NH is the column density objects for EUVE spectroscopy. of neutral hydrogen along the line of sight, and v(X)is an effective atomic cross section per neutral hydrogen atom in the interstellar medium. The atomic cross sections (X) were taken from Cruddace et al. 7 4 for cosmic elemental abundances, and a value of NH = 2 X 10'7 cm-2 was adopted8 along the line of sight. To determine the ability to spectroscopically detect small amounts of helium, we included a fraction of 2 X 10-5 helium in the atmosphere. In Fig. 21 we show these results compared to the sensitivity of the EUVE spectrometers [Eqs. (24) and (29)]after 12 h of observing. This plot reveals an EUV sensitivity -2orders of magnitude fainter than HZ43 from 100 to 600 A. If even trace amounts of helium are present in the stellar atmosphere they should be easily detectable in absorption at 228 A. A raw count spectrum [Fig. 22(a)], which includes Poissonian counting statistics, also reveals the presence of an interstellar helium edge (504 A). As another example, in Fig. 22(b) we show a simulated observation of another known hot white dwarf, G191-B2B,6'7 after a 20,000-secexposure. The higher column density of hydrogen (8 X 1o7 cm-2 ) and thus helium along the line of sight to this source 1752 APPLIED OPTICS / Vol. 24, No. 12 / 15 June 1985 B. Stellar Coronas Hot plasmas surround severaltypes of star, producing strong line emissions in the EUV3 and soft x-ray7 -83 bands. An estimate to the EUV brightness of these sources can be obtained from EUV observations of line emission in the solar corona8 4'8 5 scaled by the ratio of measured broadband quiescent luminosities in the soft x ray, LSX: I* (X) = I(X)LSX 4 ILSX,/4.2 X 1010 /D(pc) 2 exp[-NHo'(X)], (31) where I,(X) are the measured solar line intensities at the earth (in units of 106 photons/cm 2/sec), I, (X) are the predicted source line intensities (photons/cm2 /sec) at the earth, and the other quantities have been defined previously. As an example, we consider the RS CVn source HR109980 ,81 ,86,87 for which LSX./LSX , 9000, D 33, and NH 5 X 1017 cm- 2 . In Figs. 23(a)-(c) we show the raw counts of the predicted spectrum folded through the EUVE spectrometer and accumulated over 20,000 sec of observation. As in the previous example, back- 0 0OD 0 =) Cc,- L - I - ...- ~ - co co . m M- r~~~~~~~~~~~~~~~~~~~~~~1 17_ 0Nl Nl C - en In .- e ! -- GZ < tD 3. > 0 0 0 CD 0 0 0 0 (D v1' I 8- I . . . . ,. . . . I / SiNnoo 0~~~~~~~~0 cli W~~~~~~~c DO bc0 0 1 - 1! O 0) .,.........I 0 , ,,,_ I 3 0 NtM (D O0 0 0 OI 8 o F bo D5( V' t' / SiNfloo ____ _ ~0) l .Z O>> oo 0o 00 I 00 0 o 3c z'o / SiNlno 0 - C- 0toU oo '1' oo rnr 0 0 V 8-0 / SINnOo In o O A 0 t, ~1,18 0LO) 0 '~' 0r or 0N - 0 V b,-O / SNnoo ts tbD ,- " '9 Z-O / E4 SiNnoo 15 June 1985 / Vol. 24, No. 12 / APPLIED OPTICS 1753 ground has been included in the simulation [Eq. (27)]. The multitude of lines dramatically illustrates the advantage of spectroscopy for observations of sources for which the emissions are concentrated into specific wavelength features. We note that during a flare8 0 such a spectrum could be recorded in -3000 sec. In Figs. 23(d)-(f) we also show the spectrum of another RS CVn star, Capella (LSX*/LSXO, 3000) after a 50,000-sec observation. Although the higher column density (NH c 2 X 1018cm- 2) to this source lowers the intensities observed in the long wavelength channel, the short wavelength features are prominent. In addition, such sources are known to have higher coronal temperatures (-107 K) than does the sun, and thus our scaling [Eq. (31)] underestimates the intensities of the highly ionized short wavelength emissions. Other sources for which similar spectra are expected include dM stars7 8 79 and cataclysmic variables.4 and R. Stern, "Extreme Ultraviolet Observations of a Flare on Proxima Centauri and Implications Concerning Flare-Star Scaling Theory," Astrophys. J. 213, L119 (1977). 4. B. Margon, P. Szkjod, S. Bowyer, M. Lampton, and F. Paresce, "Extreme-Ultraviolet Observations of Dwarf Novae from Apollo-Soyuz," Astrophys. J. 224, 167 (1978). 5. S. Bowyer, R. Malina, M. Lampton, D. Finley, F. Paresce, and G. Penegor, "The Extreme Ultraviolet Explorer," Proc. Soc. Photo-Opt. Instrum. Eng. 279, 176 (1981). 6. J. B. Holberg, B. R. Sandel, W. T. Forrester, A. L. Broadfoot, H. L. Shipman, and D. C. Barry, "Extreme UV and Far-UV Observations of the White Dwarf HZ43 from Voyager 2," Astrophys. J. 242, L119 (1980). 7. J. B. Holberg, "The Local Interstellar Medium," Proc. Int. Astron. Union Coll. 81 (Sept. 1984). 8. R. F. Malina, C. S. Bowyer, and G. Basri, "Extreme Ultraviolet SpectroPhotometry of the Hot DA White Dwarf HZ43: Detec- tion of HE II in the Stellar Atmosphere," Astrophys. J. 262,717 (1982). 9. B. R. Sandel, et al., " Extreme Ultraviolet Observations from Voyager 2 Encounter with Jupiter," Science 206, 962 (1979). VI. Conclusions We have described the instrument design for the Extreme Ultraviolet Explorer spectrometer. The individual components of this design have been discussed in detail. A test grating has been characterized and performs as required in terms of efficiency and resolution. In the process we have demonstrated that varied line-space mechanically ruled gratings can attain levels of performance comparable with the highest quality conventional gratings. A laboratory experiment featuring the test grating has revealed performance very competitive with existing high resolution laboratory spectrographs. Measurements of the grating performance have been included in calculations of the flight instrument's sensitivity and imaging properties. The resulting performance figures have been discussed in terms of resolution and sensitivity. Predicted emissions from extrasolar EUV objects have been folded through these performance curves and reveal readily detectable features of current scientific interest. The authors would like to thank T. Harada for fabrication of the grating, J. Edelstein for invaluable technical support, and the staff of the Space Astrophysics Group without whom this project would not have been possible. We also thank A. Bunner and H. Shipman for helpful comments, B. Henke and C. Dittmore for supplying soft x-ray film, and C. Romanik and the Berkeley Astronomy Department for the use of a PDS microdensitometer. This work was funded by NASA contract NASW-3636. References 1. M. Lampton, B. Margon, S. Bowyer, R. Stern, and F. Paresce, "Discovery of a Non-Solar Extreme Ultraviolet Source," Astrophys. J. 203, L71 (1976). 2. B. Margon, M. Lampton, S. Bowyer, R. Stern, and F. Paresce, "An Intense Extreme Ultraviolet Source in Cetus," Astrophys. J. 210, L79 (1976). 3. B. M. Haisch, J. L. Linsky, M. Lampton, F. Paresce, B. Margon, 1754 APPLIED OPTICS / Vol. 24, No. 12 / 15 June 1985 10. F. Paresce, "Compact Sources of EUV Radiation," Earth Extraterr. Sci. 3, 55 (1977). 11. A. K. Dupree, "The Astrophysical Interest of EUV Observations of Extra-Solar Objects," Space Sci. Rev. 29, 479 (1981). 12. M. C. Hettrick, "Spectrometer Option Study," MCH/EUVE/ 321/82, U. California, Berkeley (1982). 13. H. A. Rowland, "Preliminary Notice of the Results Accomplished in the Manufacture and Theory of Gratings for Optical Purposes," Philos. Mag. 13, 469 (1882); "On Concave Gratings for Optical Purposes," 16, 197 (1883). 14. D. L. Garrett and R. Tousey, "Solar XUV Grazing Incidence Spectrograph on Skylab," Appl. Opt. 16, 898 (1977). 15. J.-D. Bartoe, G. E. Brueckner, J. D. Purcell, and R. Tousey, "Extreme Ultraviolet Spetrograph ATM Experiment S082B," Appl. Opt. 16, 879 (1977). 16. S. Bowyer, R. Kimble, F. Paresce, M. Lampton, and G. Penegor, "Continuous-Readout Extreme-Ultraviolet Airglow Spectrometer," Appl. Opt. 20, 477 (1981). 17. J. H. Underwood and W. M. Neupert, "GSFC EUV and x-Ray Spectroheliograph on OSO-7," Sol. Phys. 35,241 (1974). 18. W. A. Rense and T. Violett, "Method of Increasing the Speed of a Grazing-Incidence Spectrography," J. Opt. Soc. Am. 49, 139 (1959). 19. R. C. Chase, A. S. Krieger, and J. H. Underwood, "Grazing Incidence Relay Optics," Appl. Opt. 21, 4446 (1982). 20. H. Gursky and T. Zehnpfennig, "An Image-Forming Slitless Spectrometer for Soft X-Ray Astronomy," Appl. Opt. 5, 875 (1966). 21. T. Zehnpfennig, "Development of a Slitless Spectrograph for X-Ray Astronomy," Space Sci. Rev. 9, 342 (1969). 22. J. H. Dijkstra, L. J. Lantwood, and C. Timmerman, "X-Ray Transmission Gratings," in New Instrumentation for Space Astronomy, K. A. van der Hucht and G. S. Vaiana, Eds. (Pergamon, London, 1978), p. 257. 23. K. P. Beuermann, H. Brauninger, and J. Trumper, "Aberrations of a Facet-Type Transmission Grating for Cosmic X-Ray and XUV Spectroscopy," Appl. Opt. 17, 2304 (1978). 24. A. C. Brinkman, J. H. Dijkstra, W. F. P. A. L. Geerlings, F. A. van Rooijen, C. Timmerman and P. A. J. de Korte, "Efficiency and Resolution Measurements of X-Ray Transmission Gratings Between 7.1 and 304 A," Appl. Opt. 19, 1601 (1980). 25. P. Predehl, H. Brauninger, H. Kraus, and J. Trumper, "Fabrication of Transmission Gratings for Use in X-Ray Astronomy," Proc. Soc. Photo-Opt. Instrum. Eng. 316, 128 (1981). 26. F. D. Seward et al., "Calibration and Efficiency of the Einstein Objective Grating Spectrometer," Appl. Opt. 21, 2012 (1982). 27. M. Stedman and B. Gale, in Proceedings, X-Ray Optics Symposium, Mullard Space Sciences Laboratory of University CollegeLondon, Hoimbury St. Mary (1973),pp. 122-136. Am. 68, 1106 (1978). 47. D. Maystre and R. Petit, "Quelques Recents Resultats en Theorie 28. S. 0. Kastner and C. Wade, Jr., "Aspheric Grating for Extreme Ultraviolet Astronomy," Appl. Opt. 17, 1252 (1978). 29. M. C. Hettrick and S. Bowyer, "Varied Line-Space Gratings: New Designs for Use in Grazing Incidence Spectrometers," Appl. Opt. 22, 3921 (1983). 30. M. C. Hettrick, "Aberrations of Varied Line-Space Grazing Incidence Gratings in Converging Light Beams," Appl. Opt. 23,3221 (1984). 31. H. Wolter, "Spiegelsysteme Streifenden Einfalls als abbildende Optiken fur Rbntgenstrahlen," Ann. Phys. 10,94 (1952); "(Generalized Schwarzschild Systems of Mirrors with Glancing Reflection as Optical Systems for X-Rays) Verallgemeinerte Schwarzschildsche Spiegelsysteme Streifender Reflexion als Optiken fur Rdntgenstrahlen," Ann. Phys. 10, 286 (1952). 32. D. Finley, R. Malina, and S. Bowyer, "Fabrication of Mirrors for Ultraviolet," Nouv. Rev. Opt. 7, 165 (1976). 48. D. Maystre and R.C. McPhedran, "Le Theorem de Reciprocite the Extreme Ultraviolet Explorer Satellite," in Proceedings, Optical Fabrication Conference,Space Flight Center, Greenbelt to Comment," Appl. Opt. 20, 530 (1981). 53. M. Bottema, "Echelle Efficiency and Blaze Characteristics," Proc. Soc. Photo-Opt. Instrum. Eng. 240, 171 (1980); "Echelle Ef- (Jan. 1985). 33. T. Harada and T. Kita, "Mechanically Ruled Aberration-Corrected Concave Gratings," Appl. Opt. 19, 3987 (1980). 34. F. Paresce, S. Kumar, and C. S. Bowyer, "Continuous Discharge Line Source for the XUV," Appl. Opt. 10, 1904 (1971). 35. B. L. Henke, S. L. Kwok, J. Y. Vejio, H. T. Yamada, and G. C. Young, "Low Energy X-Ray Response of Photographic Films. I. Mathematical Models," J. Opt. Soc. Am. B 1, 818 (1984); B. L. Henke, F. J. Fujiwara, M. A. Tester, C. H. Dittmore, and M. 38. J. T. Cox, G. Hass, and W. R. Hunter, "Optical Properties of Evaporated Rhodium Films Deposited at Various Substrate 43. 44. 597-608. 51. A. P. Lukirskii and E. P. Savinov,"Use of Diffraction Gratings and Echelettes in the Ultra-Soft X-Ray Region," Opt. Spektrosk. 14, 285 (1963); Opt. Spektrosk. 14, 147 (1963). 52. D. L. Schroeder and R. L. Hilliard, "Echelle Efficiencies: Theory and Experiment," Appl. Opt, 19, 2833 (1980); "Author's Reply ficiencies: Theory and Experiment; Comment," Appl. Opt. 20, 528 (1981). 54. S. Engman and P. Lindblom, "Blaze Characteristics of Echelle Gratings," Appl. Opt. 21,4356 (1982). 55. E. G. Loewen and M. Neviere, "Simple Selection Rules for VUV and XUV Diffraction Gratings," Appl. Opt. 17, 1087(1978). 57. M. Oda, "High-Resolution X-Ray Collimator with Broad Field 3108 (1978). 42. and Applications of the Theory," in Electromagnetic Theory of Gratings, R. Petit, Ed. (Springer, 1980), Chap. 6. 50. R. P. Madden and J. Strong, in Concepts of Modern Optics, J. Strong Ed. (Freeman, San Francisco, 1958), Appendix P, pp. Am. B 1, 828 (1984). Gratings for Ultraviolet Space Instrumentation," Appl. Opt. 17, 41. Applications" Opt. Commun. 12, 164 (1974). 49. D. Maystre, M. Neviere, and R. Petit, "Experimental Verifications A. Palmer," "II. Experimental Characterization," J. Opt. Soc. insky, "Extreme UV Measurements on a Varied Line-Space Hitachi Reflection Grating: Efficiency and Scattering," Appl. Opt. 23, 3267 (1984). 37. G. H. Mount and W. G. Fastie, "Comprehensive Analysis of 40. Pour Les Reseaux de Conductivity Finie: Demonstration et 56. S. Chakrabarti, R. Kimble, and S. Bowyer,"Spectroscopy of the EUV (350-1400 A) Nightglow," J. Geophys. Res. 89, 5660 (1984). 36. J. Edelstein, M. C. Hettrick, S. Mrowka,C. Martin, and P. Jel- 39. des Reseaux: Application a Leur Utilization dans L'Extreme Temperatures in the Vacuum Ultraviolet from 150-2000 A," J. Opt. Soc. Am. 61, 360 (1971). B. L. Henke, P. Lee, T. J. Tanaka, R. L. Shimabukuro, and B. K. Fujikawa, "Low-Energy X-Ray Interaction Coefficients: Photoabsorption, Scattering and Reflection," Atom. Data Nucl. Data Tables 27, 1982); B. L. Henke, Proc. Soc. Photo-Opt. Instrum. Eng. 316, (1981). L. R. Canfield, G. Hass, and W. R. Hunter, "The Optical Prop*erties of Evaporated Gold in the Vacuum Ultraviolet from 300 A to 2000A,",J. Phys. 25, 124 (1964). W. R. Hunter, D. W. Angel, and G. Hass, "Optical Properties of Evaporated Platinum Films in the Vacuum Ultraviolet from 2200 A to 150 A," J. Opt. Soc. Am. 69, 1695 (1979). B. L. Henke and M. L. Tester, "Techniques of Low-Energy X-Ray Spectroscopy (0.1-2 KeV Region)," Adv. X-Ray Anal. 18, 76 (1975). D. S. Finley, S. Bowyer, F. Paresce, and R. F. Malina, "Continuous Discharge Penning Source with Emission Lines Between 50 A and 300 A," Appl. Opt. 18, 649 (1979). H. A. Rowland, "Gratings in Theory and Practice," Philos. Mag. 35, 397 (1883); Astron. Astrophys. 12, 129 (1883); Physical Papers of Henry A. Rowland (Johns Hopkins U.P., 1902), p. 525-544. of View for Astronomical Use," Appl. Opt. 4, 143 (1965). 58. R. L. Blake, P. F. Santos, D. M. Barrus, W. Brubaker, E. Feni- more, and R. Puetter, "Collimators for Soft X-Ray Measurements," Space Sci. Instrum. 2, 171 (1976). 59. R. A. Nobles, L. W. Acton, E. G. Joki, J. W. Leibacher, and R. C. Peterson, "Large-Aperture High-Resolution X-Ray Collimator for the Solar Maximum Mission," Appl. Opt. 19, 2957 (1980). 60. F. Paresce, H. Fahr, and G. Lay, "A Search for Interplanetary HE II, 304 A Emission," J. Geophys. Res. 86, 10,038 (1981). 61. F. Paresce, S. Bowyer, and S. Kumar, "Evidence for an Interstellar or Interplanetary Source of diffuse HE I 584 A Radiation," Astrophys. J. 183, L87 (1973). 62. R. L. Blake, D. M. Barrus, and E. Fenimore, "Diffraction Effects on Angular Response of X-Ray Collimators," Rev. Sci. Instrum. 47, 889 (1976). 63. C. A. Lindsey, "Effect of Diffraction in Multiple-Grid Telescopes for X-Ray Astronomy," J. Opt. Soc. Am 68, 1708 (1978). 64. R. Stern and F. Paresce, "Mass Absorption Coefficientsof Parylene-N at Soft X-ray and Vacuum-Ultraviolet Wavelengths," J. Opt. Soc. Am. 65,1515 (1975). 65. P. Jelinsky, Space Sciences Laboratory; private communication (1982). 66. M. Lampton, "The Microchannel Image Intensifier," Sci. Am. 245, 62 (1981). 67. 0. H. W. Siegmund and R. F. Malina, "Detection of Extreme UV and Soft X-Rays with Microchannel Plates: A Review," in Multichannel Image Detectors, Vol. 2, Y. Talmi, Ed. (American Chemical Society, Washington, D.C., 1983), pp. 253-275. 68. 0. H. W. Siegmund, R. F. Malina, K. Coburn, and D. Werthimer, "Microchannel Plate EUV Detectors for the extreme Ultraviolet 45. R. D. Hatcher and J. H. Rohrbaugh, "Theory of the Echelette Explorer," IEEE Trans. Nucl. Sci. NS-31, 776 (1984). 69. C. Martin, P. Jelinsky, M. Lampton, R. F. Malina, and H. 0. Grating. I," J. Opt. Soc. Am. 46, 104 (1956); "Theory of the Echelette Grating. II," 48, 704 (1958). 46. M. Neviere, D. Maystre, and W. R. Hunter, "Use of Classical and Conical Diffraction Mountings for XUV Gratings," J. Opt. Soc. Anger, "Wedge-and-Strip Anodes for Centroid-Finding Position-Sensitive Photon and Particle Detectors," Rev. Sci. Instrum. 52, 1067 (1981). 70. C. Martin and S. Bowyer, "Quantum Efficiency of Opaque CsI 15 June 1985 / Vol. 24, No. 12 / APPLIED OPTICS 1755 Photocathodes with Channel Electron Multiplier Arrays in the Extreme and Far Ultraviolet," Appl. Opt. 21, 4206 (1982). 71. P. A. J. de Korte et al., "EXOSAT X-Ray Imaging Optics," Appl. Opt. 20, 1080 (1981). 72. J. Liebert, "White Dwarf Stars," Ann. Rev. Astron. Astrophys. 18, 363 (1980). 73. R. F. Green, "The Luminosity Function of Hot White Dwarfs," Astrophys. J. 238, 685 (1980). 74. R. Cruddace, F. Paresce, S. Bowyer, and M. Lampton, "On the Opacity of the Interstellar Medium to Ultra-Soft X-Rays and Extreme-Ultraviolet Radiation," Astrophys. J. 187,497 (1974). 75. D. Koester, "The Space Density of Hot White Dwarfs," Astron. Astrophys. 65, 449 (1978). 76. F. C. Bruhweiler and Y. Kondo, "The UV Spectra of Nearby White Dwarfs and the Nature of the Local Interstellar Medium," Astrophys. J. 259, 232 (1982). 77. P. C. Frisch and D. G. York, "Synthesis Maps of Ultraviolet Ob- servations of Neutral Interstellar Gas," Astrophys. J. 271,L59 (1983). 78. G. S. Vaiana et al., "Results from an Extensive Einstein Stellar Survey," Astrophys. J. 244, 163 (1981). 79. R. Rosner et al., "The Stellar Contribution to the Galactic Soft X-Ray Background," Astrophys. J. 249,L5 (1981). 80. N. E. White, P. W. Sanford, and E. J. Weiler, "An X-Ray Outburst from the RS CVn Binary HR1099," Nature London 274, 569 (1978). 81. F. Walter, P. Charles, and S. Bowyer, "Discovery of Quiescent X-Ray Emissions from HR1099 and RS CVn," Nature London 274, 570 (1978). 82. W. Cash, S. Bowyer, P. A. Charles, M. Lampton, G. Garmire, and G. Riegler, "The Soft X-Ray Spectrum of Capella: Discovery of Intense Line Emission," Astrophys. J. 223, L21 (1978). 83. S. M. Kahn et al., "HEAO-1 Observation of X-Ray Emission from Flares on dMe Stars," Astrophys. J. 234, L107 (1979). 84. A. K. Dupree, M. C. E. Huber, R. W. Noyes, W. H. Parkinson, E. M. Reeves, and G. L. Withbroe, "The Extreme-Ultraviolet Spectrum of a Solar Active Region," Astrophys. J. 182, 321 (1973). 85. M. Malinovsky and L. Heroux, "An Analysis of the Solar Extreme-Ultraviolet Spectrum Between 50 and 300 A," Astrophys. J. 181, 1009 (1973). 86. E. J. Weiler et al., "Coordinated Ultraviolet, Optical, and Radio Observation of HR1099 and UX Arietus," Astrophys. J. 225, 919 (1978). 87. F. M. Walter, W. Cash, P. A. Charles, and C. S. Bowyer, "X-Rays from RS Canum Venaticorum Systems: A HEAO 1 Survey and the Development of a Coronal Model," Astrophys. J. 236, 217 (1980). Patter continuedfrompage 1718 laser as the monochromaticsource,which is focusedonto the input ends of two single-modefibers having nominal 4.5-,umdiam cores. The external plastic jacketing and inner RTV (room-temperature-vulcanized)sleevingare removed from the first several centimeters of both ends of both fibers, and -4 cm of exposed fiber are painted with index-matching mode-stripping fluid. Approximately 2.5cm at the ends of each fiber are not painted. The sample and reference opticalsignalare opticallyrecombined,spatially filtered,and detected through an electronic output signal proportional to the instantaneous stress in the fiber. This work wasdone by John H. Cantrell,Jr., of LangleyResearchCenter and Richard 0. Clause,Janet C. Wade,and Paul S. Zerwekhof VirginiaPolytechnic Institute and State University. Refer to LAR-12965. Acoustic Gaussian far-field pattern Anew ultrasonictransducer producesa far-fieldbeam with a Gaussianspatial profile for materials evaluation. The transducer is constructed by depositing a circularlysymmetricmetallicmultielectrodearray on a 12.7-mmdiam X-cut quartz disk. Each electrode is independently connected to an impedance network optimized to produce the Gaussian distribution with less than 2% error. An electric-fielddistribution that is exclusivelya function of radius is produced by the set of concentricring electrodes. If the circumstancesof the rings are largewith respect to the spacing between successiveelectrodes,the electric field in the gaps maybe considereda linear functionof radius. From this model, a piecewise linear function that approximates the Gaussian may be then generated on the face of the piezoelectriccrystal by applyingpropervoltages to the electrodes. The degree to which this function fits the desired Gaussian is determined by the width of each electrode ring,the number of electrodes,and the distribution of the electrode radii on the radius of the transducer crystal. Because the ideal Gaussian voltage distribution is a smooth function of the radius, the electrode width should be as small as possible. The photoetching techniques used, however,required a minimum electrode width of -0.5 mm. The degree of fit to the desired Gaussian shape may also be improvedby using a largenumber of electrodes;but this approach requiresthat the interelectrode spacing be small, thereby increasing the possibility of electrical breakdown between adjacent rings when high voltages are applied. Consideringthese practical limitations, it was found that, with as fewas five electrodes, the mean absolute fit error may be reduced to less than 1.5%of the peak. Becausethe radii of the ringsare the variablesoverwhichgreatestcontrol may be exercised during design,an iterative computer routine was developed to minimize absolute error by varying ring placement. The designed electrode pattern was photoetched onto a layer of chromium and goldon a circular2.25-MHzX-cut quartz transducer. Capacitancebetween electrodesand the wear-plateground plane was calculatedand later empirically verified to be less than 2pF, producing a negligiblereactive impedance at the 2.25-MHzoperating frequency. Because this impedance is low,a simple resistive network may be used to fix the desired set of electrode voltages. Construction details of the transducer are shownin Fig. 8. The leads are attached to the electrodes with a conductive adhesive,and a dome of epoxy is applied to the electrode side of the crystal to provide mechanical support for the leads and to attenuate and disperse resonantsurface-wavemodes. Further dampingis accomplishedby a thin semiviscouslayer of electricallyconductive adhesive placedon the oppositeuncoated side of the transducer disk and under a thin aluminum-foilelectrode/wearplate. The electrode leads are connected to the resistive network and coaxialcable,and the entire transducer assembly is placed in a 1.3-cmi.d. cylindricalPVC (polyvinylchloride) case and potted in filler-loaded epoxy. ANNULAR ELECTRODES SUPPORTING EPOXY WEAR PLATE 0 CONDUCTIVE/ ADHESIVE Fig. 8. Concentric electrode rings in the ultrasonic transducer produce a beam with a Gaussian profile. The transducer is used for materials evaluations. This work was done by Richard 0. Claus and Paul S. Zerwekh of Virginia PolytechnicInstitute and State Universityfor LangleyResearchCenter. Refer to LAR-12967. continuedonpage1760 1756 APPLIED OPTICS / Vol. 24, No. 12 / 15 June 1985