fegCEi-.'ED BV OSTI |jMRl 1 Lawrence Berkeley Laboratory UNIVERSITY OF CALIFORNIA Accelerator & Fusion Research Division Presented at SPIE's 29th Annual International Technical Symposium on Optical and Electro-Optical Engineering, San Diego, CA, August 18-23, 1985; and to be published in the Proceedings VARIED LINE-SPACE GRATINGS: PAST, PRESENT AND FUTURE M.C. Hettrick August 1985 P«0M«a lent- W* U..S Ocjwrtmemu o! Emewjy mmaer Comities DE-.M3tD3-?6SP0009B &m;:u;.:r: i? w.z ir fitt DISCLAIMER This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. LBL—20115 DE86 007498 Varied line-space gratings: past, present and future Michael C. Hettrick Lawrence Berkeley Laboratory, Center for X-Hay Optics, Building 80-101, 1 Cyclotron Road, Berkeley, CA 94720. flfitf* Abstract A classically ruled diffraction grating consists of grooves which are equidistant, straight and parallel. Conversely the so-called "holographic" grating ( formed by the interfering waves of coherent visible light ) , although severely constrained by the recording wavelength and recording geometry, has grooves which are typically neither equidistant, straight nor parallel. In contrast a varied line-space (VLS) grating, in common nomenclature, is a design in which the groove positions are relatively unconstrained yet possess sufficient symmetry to permit mechanical ruling. Such seemingly exotic gratings are no longer only a theoretical curiosity, but have been ruled and used in a wide variety of applications. These include 1) aberration-corrected normal incidence concave gratings for Seya-Namioka monochromators and optical de-multiplexers, 2) flat-field grazing incidence concave gratings for plasma diagnostics, 3) =berration-corrected grazing incidence plane gratings for space-borne spectrometers, 4) focusing grazing incidt-.ce plane grating for synchrotron radiation monochromators, and 5) wavefront generators for visible interferometry of optical surfaces (particularly aspheres). Future prospects of VLS gratings as dispersing elements, wavefront correctors and beamsplitters appear promising. I discuss the history of VLS gratings, their present applications and their potential in the future. Introduction In the middle to late nineteenth century, when the imaging properties of the newly conceived concave grating were being discovered , attention was already being given to the effects of systematic variations in spacings between the grooves. The intent of these studies was primarily to explain anomalies observed in the spectra of imperfectly ruled gratings. For example, periodic spacing errors were found responsible for "ghost" lines and false images which dominated the spectra of the earliest gratings ' . Indeed, much effort has since been concentrated into reducing such variations and their undesirable effects. Cornu also considered the focal properties of gratings ruled with slow non-periodic variations in groove spacings. By invoking a linear space variation ( arising from an "error of run" inherent in early ruling engines ), he was able to explain observed anomalies in the focal curves of concave gratings, and predicted some focusing ability of a plane grating if ruled with a large linear space variation. In referring to the distance between grooves, quotes from two of Cornu's papers read "J'ai en vue les erreurs systematiques qui produisent un changement de foyer sans alterer la nettete des images." (1875). "Elle effecte, suivant le rapport existant entre R et P, des formes tres diverses, qui derivent du type de la cissoide de Diodes a laquelle d'ailleurs elle se (1893). reduit lorsque la coubure de reseau devient nulle (R=»)." unfortunately, the engineering challenges inherent in the fabrication of even a conventional grating lett"such possibilities dormant for the next eighty years. During this period, the diffraction grating found use in ever more demanding circumstances, driving the performance requirements to near perfection. Mechanical ruling^ ' or optical interferometry ^ can now form finely spaced ( up to 6000 g/mm ) grooves on the surface of a large plane or curved surface, result in the retrieval of greater than 70* o: the theoretical diffraction efficiency and with ghost line intensities negligible in most applications. Thus, we have reached the point where further engineering perfection of the basic plane or concave grating will yield limited return. Significant future enhancement in the performance of grating instruments' requires that we now turn our attention to the use of ask- ^r unconventional geometric solutions to the problem of diffractive focusing. - 3- 0 Several recent technological events are seen as responsible for a growing interest in VLS gratings, rirst, the increased sophistication of ruling engines, which now routinely incorporate cenruter control, mterferosetxic feedback and fir.e servo notions; all necessary ingredients to tt.e construction of a VLS capability. Second, tihe realization that aberra*• ion-correctior: usir-j mechanical rulmc is optional .when tlhe hi-ihest possible diffraction t h i s work was supported by the Office of Basic Energy Sciences, U.S. D*p*rti*ent of Knet^y, under Contract # DE-ACQS-MSFOQOTS- KXXZX & Km KSBRrj - 2efficiency is crucial or when the reduction of certain aberrations (such as comal re?-.. a relatively unconstrained positioning of the grooves. Third, the use of gratings ar increasingly shorter wavelengths, particularly in the soft x-ray with the availability of synchrotron and plasma radiation. The line-space variations available using visible or near UV interferons try do not closely approximate the large variations required for use at shorter-wavelengths in grazing incidence. Varied line-spacing using mechanical ruling has eadrged as a preferred method of aberration-correction in the far UV, extreme UV and'soft x-ray bands. Fourth, spectrometers are now being designed and built for long duration space flights in astronomy. Requirements on physical compactness, efficiency and signal-tonoise are extreme, and are increasingly being met by exploiting the extra degree of freedom available with varied line-spacing. Such designs have revitalized the use of unconventional plane grating geometries in both astronomical spectrometers and laboratory monochromators. Fifth, the development of high-resolution photoelectric detectors (microchannel plates, imaging proportional counters, streak cameras, etc) for which the spectrum is imaged on a flat detecting surface. Varied spacings on a grazing incidence grating can be used to obtain such required flat-field imaging. Finally, the fabrication of precisely shaped aspheric surfaces (e.g. grazing incidence telescopes, toroids, normal incidence paraboloids) has precipitated the need for more exacting methods of surface metrology. VLS gratings, including the use of circular grooves, have been used to generate wavefronts suitable for the interferometric testing of figured optical surfaces. Thus, we see a broad range of needs have arisen in which VLS gratings are crucial elements. In this paper, I have made an attempt to briefly review any work published on the subject of VLS gratings, survey their current applications, and speculate as to the future roles such devices may assume. The following sections discuss various relaxations of the classical constraints on grating design. First we consider gratings in which the grooves are straight and parallel, but not equidistant. Second we consider equally curved or concentrically curved grooves which may be either equally or unequally spaced. Lastly we discuss gratings in which the grooves are straight, but are not parallel and thus must also have space variations. In all three categories we find both plane grating and concave grating surfaces have been utilized. Non-equidistant, straight and parallel rulings Concave Surfaces In the literal sense, a curved surface contains curved grooves. The phrase "straight and parallel rulings" refers to the conventional rectilinear motion of a mechanical ruling engine for which the grooves are formed at the intersection of the grating surface and a set of parallel planes in which the tool reciprocates. Any modern ruling engine can thus, in principle, be outfitted with means of specifying the location of individual grooves in this geometry. As such, these were the first VLS gratings studied and fabricated. In a series of papers from 1875 to 1893, Cornu investigated in some detail the anomalous focal curves which result from linear space variations, i.e. o = o + w do/dw, where a is the nominal spacing., w is the ruled width coordinate and the derivative do/dw is a cons?ant. He arrived at the following equation for the spectral (meridional) focal curve: a = cos o / (cosa /R — sina /P) : (1) where R is the grating radius of curvature, P = a /( do/dw), a is the angle of diffraction (or incidence) and p is the image distance measured from the grating center. A perfectly ruled classical concave grating has an infinite value for P, which from the above equation results in the Rowland circle p = R cosa. Small space variations mainly tilt the Rowland circle in the direction of larger groove spacings. However, a significant space variation, for which i I I'M. 1. Aijosulcus fftcal curve of Caxtna 81S93J. Fig. Z. Scmuniscale of Sakayamagi il 19675 . - 3P is comparable to R, results in a non-closed focal surface reproduced in Fig. 1. Apparently unaware of Cornu's work, Sakayanagi proposed in 1967 that a concave spherical grating be ruled with varied groove spacingsll.. Sakayanagi realized the potential of apace variations in removing aberrations in the image*, with an approximately linear variation, defined by P«2R in eqn. 1, he generated a r e m n n s c a t e meridional focal curve w h i c h ' w o u l d be tangent to the sagittal (secondary) focal plane at a point in whose vicinity astigmatism would be small (Fig. 2 ) . The paper of Sakayanagi marks the beginning of an era when i"s "-• v: U V ^ - . ^ ' 5 | B f i i K ¥ 5 i § ? £ ! l fabrication of VLS gratings became practical. 13 14 In 1970, Gerasimov et al ' devised a ruling engine capable of introducing fixed variations in the groove spacings. Their setup consisted of a grating interferometer within which was inserted a cam-driven screen which modulated the moire fringes according, to the cam shape. Using a circular cam, they ruled several plane and concave gratings vith linear space variations (of order 1 % ) . In Fig. 3 are shown imaging tests of three concave gratings using a mercury light source and an entrance slit which was broken in height to test for astigmatism removal. The gratings had a radius of 1 meter and were mounted near normal incidence resulting in focal curves as illustrated below the spectra. The removal of astigmatism within a broad wavelength range centered at the intersection point of the distorted meridional curve and the sagittal plane was verified. Curve 4 in Fig. 3 shows the Rowland circle. Fig. 3. Reduction of astigmatism It is historically interesting to note that this first demonstration of a mechanically ruled aberration-corrected demonstrated by Gerasimov{1970). grating occurred within the same time period in which 15 holographic corrections were first demonstrated on photoresist gratings , mm The first instrument which effectively used a VLS mechanically ruled grating appears to ve been a far UV solar spectrograph flown on the Skylab space observatory in 1973 1 9 7 3-°. . The have main grating of the spectrograph was preceded by a cross-disperser concave grating which decreased the level of focused stray light and extended the wavelength range by separating spectral orders 1 and 2 of the main grating. However another function of this predisperser was to correct for the astiqmatism (2-3 mm) of the main grating. As shown in Fig. 4, the disperser was ruled in ten segments (multi-partite) across ''~m™™T.'.I^JLT.rr i ruled width, each segment having a discrete groove -i •~T"'""""" spacing. Although not continuous, this variation changed ~ '"* "" its meridional focal surface to approximate the sagittal plane (Sirk's position) of the main grating (POINT C ) . Astigmatism in the main spectrum was reduced a factor of I" three, and the recording speed of the spectrograph thereby increased. The segmented predisperser was ruled by B.W. Bach while at Bausch and Lomb. The instrument -'"-<-"" recorded 6400 spectra during its flight on Skylab (Fig.5). Fig.4. Bartoe segmented predisperser (1974). _. . ... . .. ' •= cr h significant advances in the engineeruu»-.?u«-.src i"9 realization and practical use of the VLS i 1 » 1 concave grating have been made over the last decade by Harada and colleagues at Hitachi's •*»il^tl*< »{H • • HI »m<f ^i ACTIVE REGION Central Research Laboratory. They have constructed ruling engines capable of placing M ^ a l ^ * ' grooves according to essentially any desired input function continuously across the grating ruled width (Fig. 6 ) 1 " * ^ . Their control system OFr­u­V •2UCSEC (Fig. 7) consists of a multi-reflection prism 1 1 •0u*T •CCtON interferometer which can determine position of the grating blank to a small fraction of the »..*. • • A" • * HI , * * . * c t i v t acGiON laser wavelength. The desired space variation is input by microcomputer and used as a reference signal to correct the blank translation by means of a servo motor driven in pulsed steps of 0.2 S. Harada has demonstrated systematic Sky lab s o l a r s p e c i r a , astigjnatasm rig control of the groove positions to less than 1 2 » \}i\ %• 15,000. Frc:n Bartoe 1197­;}. in a coma-corrected VUV seya-Namioka grating whose total required spacr. variation was only S. This accuracy sJaouli be understood as a statistical uncertainty averaged over the aber of .grooves necessary to construct an interference pattern of the observed resolution. .!s«sis Jay Bawmgati!r. er also i n v e s t i g a t e d VLS g r a t i n g s and foand s i m i l a r aresiaits. J t s T 1 e m o s t «!>«++ 7 H , 1 6 - 4Iwanaga and Oshio undertook a comprehensive analysis of the aberration-correction possible with mechanical ruling of a concave grating, and found that coma-type aberration can be reduced in addition to astigmatism for rotational mountings (e.g. Scya-Natnioka) near normal incidence At grazing incidence, much larger space variations are required to effect useful deviations from the Rowland circle. The Hitachi group has designed, fabricated and tested a grazing incidence concave grating for which a 35% space variation constrained the focal surface to,be approximately flat and normal to the diffracted beam , as illustrated in Fig. 8. In Fig. 9 is shown a scanning electron micrograph mosaic of different sections across the ruled width (50 mm) of a 1200 g/mm VLS concave grating ruled for flat-field use at grazing incidence from 50 to 3008. This grating was measured in tne extreme UV and Fig. 6. Numerically controlled found to retrieve over 70% of the theoretical efficiency ruling engine. From Harada (1980). expected from perfectly shaped grooves . The level of stray light was also quite small in comparison to conventional gratings, an effect attributed to the necessarily small random errors in groove positions attained with Niniiiital uriHivt* num *t*r :ii« :HKHit>/mm M i n . rndiusuf ,'urvaiure to m m the VLS numerically controlled ruling engine described 1­iOiWt x l O O i L i m m ­ Max. ruled area above. Nakano et al hav= used two such flat-field M.ix. aperture r.\ gratings (10-50 8 and 50-300 2) to analyze laser produced M m . »piii'« vuriiilinii 0 irj nm plasmas with photographic plates . Flat-field focusing Spherical »r i.>n>id;il ( i r ; i t i n e surtiit-e is even more crucial when electronic devices such as ! MICROi fooioTon i streak cameras are used to image the spectrum. j COMPUTER i SYSTEM ' second unique feature of the Hitachi VLS ruling engin e is its ability to tilt the ruling plane a fixed angle from the grating normal, resulting in grooves which appea r elliptically curved if projected in the plane tanye nt to the grating at its center. This tilt has been used to alter the sagittal focal curve and thus help rcduc e astigmatism in a Seya-Namioka monochromator^9. Kita and Harada have also used this effect in the const ruction of a compact concave grating (lensless) optical de-multiplexer " . By a linear space variation in nation with a tilt of the u l i n g planes, both the combi 2 1 Grating Normal t Fig. Control system of Fig. 6. Spectral Plane meridional and sagittal focal curves were distorted, and a factor of twenty reduction / in astigmatism was obtained over the 750-S5o8 251mm spectral band. The coupling efficiency of the de-multiplexer thereby rose to 55%, which is a factor of six larger than attainable with a conventional concave grating. The instrument configuration is illustrated in Concave Grating Fig.10. The grating radius of curvature was only 50 mm, the nonii:'..i: oroovc spacing was Flut-neld grazing incidence spectrorig. 1/300 mm, and the blaze angle was reset twice irauh us ir.g VLS grating. From Kita (1983). across the ruled width Itri-partitel to maintain high diffraction efficiency. W=-20imm W?0 W = 20mm Fig. 10. Optical gratma ic-~ult ijlexer js^r.c a VLS From K;tj. * K^raJia •(1'9S2P>. rcsravt. ffli'JsJ. priv OCTLTI!) - 5 - « -eridion.1 focusing along the diiper.iln dir«c£Sn * J t h f "I**** incident light and is no! curved il"g ?h. d ^ ? ? ™ £ ^ * * ? ! i " - * * * * « * « » * * * ^ ««I»ir««J space variation is approximately an exponential function" at Lt I, ^ * - £ P»«*icml ' constraints on the magnitude of S e total n v»r?f Ton fll** •*<*•* of- the grating, this design is limited to applications r«£frtn£ ™ ? " ?PP? S p a c i n 9 w o u l d r c s u l £ p t 9 r r d t h d G x v e n W l d t h t e diffraction n s i t e ^ - - n c v ^ e ' c e n t r ^ ^ Plane Surfaces In reference to Fig. 1, Cornu remarked : 4 "Enfin, passant a des conditions inverses, si le respa- »=«• =„„=<..i ^ principal. devienfune cissoiSe'donrf.LymptotfpasI^par'M " e ^ * * * au plan du reseau. On retrouve alors la disnosit?™ L S * 2 V que j-ai indiquee dans mes premieres recherche"" **" ° S f y § r S t d e S 1 , - , n o r m a l e S p e C t r e S a n ^ c u r i o ^ f a t ^ n ^ o f u n t i r r e c l n ? ! ^ " ^ ! ^ £>*£? T T " " ^ °^ intermittent Justification, as the concave grating performs foeusinnand 5 =o " ° ? ' P i t t i n g use even at ultravillet wave!eng™s where ?he n ^ r ^ f " ^ ! ^ the single concave grating geometry doeTh-™ « L V i ° ° "•incised. However, ^ P™**™* of' significant astigmatism (which ca^degrade the ultimate lint*!** • S ™ overlay a comparison spectrum) the need t n o h * - ^ sensitivity and hamper attempts to blanks, and i L practical re^rictloHo u s e ^ ^ s p e ^ ^ ^ o r d ^ f ""* ^ ^ *"""* h 3 S b e e n 3 X W i t h s o m e t i C 8 i n g l a n S m u S t b e 1 t h e ^ i n T x n t ^ ^ ^ issued in 1961 to Barnes and Collyer for a spectrometer using convergent light on a plane grating" . Monk himself deduced the meridional focal curve to be a lemniscate or the form: 10 cos a /cos S = (2) where i is the angle of incidence, S is the angle of diffraction, p is the distance from the grating center to the (virtual) source located behind the grating, and s is the focal distance from the grating center to the image. If the incident and diffracted rays lie on opposite sides of the grating normal (e.g. zero order) then , and -• are opposite in sign. In Fig. 11, the concave mirror C refocuses the light source s to the left of the diagram, and the plane grating G focuses various wavelengths along the lemniscate (dotted curve). The point I QrI;i^"^ ° consisting of a Diane grating in convergent light (Monk 1928)'. ^J; !L * ' is an equal distance from the grating as the virtual source. As the grating Ji^.racts within its plane of reflection, it provides no recusing power in the image height direction, thus the point i contains no astigmatism. Although this tero order « a"Lo\2; *? spectroscopically. the astigmatism is also absent at a second point on the opposite side of the grating normal, corresponding to the Littrow condition " »; « 19*2. Matty-' used this normal incidence mounting «Fio 12j a-d considered various methods of r«movino higfcer-order aberrations such as coma, -he existence of v.-.ich was tirst recognized by Sichards, Thomas and *oiastein3io auc by KosetuSaJUal. y inspection of Fio. 12 TV^Jt ~f It* " source. A' the spectral image ar.d P Fig. 12. Point-like focusing in J fSiat en Jhc W « ; M , it 'was sSsewen by Murty that » u f Lif-row Mertk-Cilliescn requires hyperbolic grooves (Murty ~l'962l) h r e a e C t 6 d 2 e r o o r d e r i a a e a n d i n t e ? e s t S V l a j l S p e C t r m e t e r - 6like focusing (stigmatisa) »t A is achieved if the grooves coincide with hyperboloids of revolution about the AA' axis. This is the condition for which the distance AP - A»P is stationary for all p on the grating aperture. The groove curvature removes astigmatic coma and a quadratic space variation between the grooves removes the dominant meridional coma aberration. However, the unlikely prospect of ruling hyperbolic grooves led Murty and o t h e r s * to consider less exotic means of reducing coma-type aberrations. 1 32-3 At grazing incidence, the most debilitating aberration in moderate resolution applications is D not coma, but astigmatism. Equation 2 states the focal distance S varies as the square of the ratio "ii.­ .. • in cosines of the incident and diffracted angles. For angles approaching 90° (grazing incidence), the separation between the sagittal and meridional c focal curves is even larger than for a spherical Fig. 13. VXS plane grating, corrected grating in diverging light, as in the later case for astigmatism and coma. Figure is the focal distance along the Rowland circle varies from Hettrick and Bowyer (1983) . only linearly with the cosine of the angles. Such large astigmatism, combined with the aspherical focal surface illuminated at grazing incidence, has precluded the use of the Monk-Gillieson mounting for grazing incidence spectroscopy. w 1 A solution to this problem has been given in a series of papers by Hettrick "-37 _ f straight parallel grooves whose spacing varies across the ruled width, the meridional focal curve is changed from a lemniscate to a curve which passes through the sagittal focal circle (Fig. 13) at a correction wavelength (S=p): B v u s e 0 / (c(sin0 + sini) + cos i] 2 (3) where c=(cos 0 -cos i)/(sine +sint), being the diffracted angle at the correction point. "This not only removes astigmatism but also produces a normal incidence focal surface near the correction wavelength. Meridional soma is also eliminated by the choice of space varation. Because the incident focus (source) and spectral Fig. 14. Images from convergent image are equidistant from the grating, sagittal cgma beam test of VLS plane grating at is minimized, resulting in a resolution X/4X = 8 f , where f is the beam speed (e.g. 10) along the grooves. grazing incidence (Hettrick 1985) . 2 2 Q 0 2 y The use of varied spacing to alter the meridional focal surface and thus remove astigmatism has been realized for some time in the case of a concave grating (previous section). It is therefore interesting that the analogous improvement for a plane grating was not realized until 1983, nearly 100 years after the first theoretical work on the focusing properties of plane gratings. In part, this ignorance has probably been due to the requirement of convergent incident light in the plane grating case. It is generally assumed, though incorrectly, that use of other than divergent source light requires more reflections. The realization that straight grooves could be used with small residual aberrations in a convergent beam led Hettrick to design a space observatory extreme UV spectrometer based or. this principle. Given a pre-existing large aperture telescope which collected starlight, the primary goals of maximum sensitivity and a physically compact instrument were met by a slitiess design using grazing incidence VLS gratings ?. The gratings were fabricated by Harada and the performance results on a test sample reported by Hettrick et al '. Using a convergent beara provided in the laboratory, images were recorded on film as shown in Fig. 14. The elimination of astigmatism is verified over a wide spectral band near the correction wavelength. At thu sagittal focal curve of a conventional grating, the image heights would still be approximately 50 microns, but the spectral resolution would be only ;S>, corresponding to an image width of IS,000 microns (over 300 tines as large as the iraage widths shown in Fig. 14}. This grating was also measured to retrieve in excess of 30* of the diffraction efficiency expected from perfectly formed grooves, despite the 25% space variation across its aperture. 3 3 En 1'966, Gal«3 studied the focal properties <cf VL'S plane gratings illuminated by diverging light, t'siog a physical optics approach,, Gale ^cner«at«d focal curves for two designs. ;9 - 7 Harada has designed and fabricated a high resolution IX/iX - 10 -10 ) plane grating monochromator , using the focusing properties of varied spacing when the incident light is diverging. The instrument (Fig. 15) uses only plane surfaces (mirror and grating) , which can be easily fabricated to high optical quality. As with the VLS grating monochromator proposed by Aspnes (above), the divergent incident light requires a large space variation and thus small acceptance angles. However, this is not a limitation when used with- highly collimated synchrotron radiation, where the acceptance angle need be only 1 milliradian or less across the ruled width. The monochromator is currently becoming operational a't Japan's Photon Factory synchrotron radiation light source, where it will be used to wavelengths as short as 5 A. The flat mirror preceding the grating functions not only to keep the grating in focus through the wavelength scan, but also to reduce higher-order harmonic contamination and to partially compensate for the blaze shift in the grating diffraction efficiency as the grating scans. These properties are similar to those of the FLIPPER monochromator used in synchrotron radiation beam lines, and result from the fact that both the premirror and the grating are illuminated at larger graze angles as the scanned wavelength is increased. Yet, unlike the FLIPPER, the VLS plane grating monochromator of Harada does not require a curved re-focusing mirror after the grating. 3 4 39 40 Fig. 15. V'^S plane grating monochromator for synchrotron radiation. From Harada (1984). The Perkin-Elmer Corporation has applied the technology of varied spacing on a plane grating to generate desired wavefronts in the diffracted beam ' ^. The high optical quality attainable with a flat grating surface allows diffraction-limited wavefronts to be obtained. In the case of straight and parallel grooves, these wavefronts are cylindrical, and are used to interferometrically test the precise figure of cylindrical optics, as shown in Fig. 16. This is the only non-dispersive application in which mechanicallyruled VLS gratings have been used. Gomez and Hirst at the PerkinElmer Ruling Facility Instrument Group have set up a linear ruling engine "D" which uses interferometric control to emboss varied spaced straight and parallel grooves with frequencies of 1 to 3000 per lillimeter across apertures as large as 175 x 175 irat\2. The freedom to place the grooves according to-any desired functional form allows unique wavefronts to be generated which can match those of even non-circular cross-section cylinders. 41 4 Nhen gratings are used for dispersing wavelengths, any unruled portion of the grating will simply lower the diffraction efficiency. This is a special consideration for a VLS grating, where a constant weight loading of the diamond tool cannot fully rule the groove depths required at the more coarsly ruled sections of the grating. If the grating is used at grazing incidence, this problem can be alleviated by use of a replica once removed from the master, where the imperfections are generally in the unilluminated bottom part of the grooves. However, in the case of a VLS grating to be used in optical interferometry, diffraction-limited performance demands use of the master ruling and the grating is illuminated at near-normal incidence; thus the unruled portions of the grooves are fully visible to the incident light at the groove tops. Although the resulting decrease in diffraction efficiency and shift in blaze wavelength are not crucial problems in this application, the unruled grating sections (duty cycle less than unity) result in phase disturbances in the diffracted vavefront'* (Hirst, private communication). Therefore, Hirst has experimented with means of continuously varying the loading on the diamond tool to obtain a Fig. 16. Interferogram of constant duty cycle for VLS gratings. Such conditions will also test optic using VLS flat improve the efficiency of gratings used f ° dispersive functions grating (Hirst 198S). 2 r Son-linear rulings, equidistant or varied spaced Concave Surfaces Carved ruliasas Jure generally assumed to toe impractical with mechanical ruling enginesIt thus may toe start J m c to uncover the •wot* of Sakayjmagi, Wfco in 19M d-esiqr.c-d''-. ruled 3 - 8 and tested a curved groove grating. Sakayanagi's "curved grating" design principle is shown in Fig. 17. The grating surface is a sphere with radius R and center of curvature at point 0. If projected onto the plane O'G tangent to the grating, the grooves are circular with center at 0'. The three dimensional groove is a circle with symmetry axis 0'0-on which astigmatism must vanish provided the image and source both lie on this line. This sagittal focal curve of the grating"intersects the meridional focal curve (Rowland circle) at two points. If the source and image are located at these two points, in addition to no astigmatism, the image will be in focus spectrally and contain no coma aberration. At normal incidence (within 30° of the grating normal) Sakayanagi showed there will be a useful range in wavelength where the astigmatism remains small.Subsequent theoretical w o r k ' ' , particularly that of Strezhnev and Shrnidt ' (and references cited therein) revealed that a curved groove spherical grating exhibits a broader region of astigmatism correction than would 44 1 2 4 5 4 6 4 Fig. 17. Sakayanagi curved grating (1954). result from varied spacing alone or by use of aspherical (e.g. toroidal) surfaces. In the case of Sakayanagi's curved grating, the sagittal focal surface is altered, while the uniform spacings keep the meridional focal surface intact. Sakayangi's ruling apparatus is shown in Fig. 18. This geometry constains the diamond D to move along a spherical surface with center 0' and radius p . (As discussed above, Harada has more recently realized this curved groove constraint with a linear ruling motion by Fig. 18. Apparatus used by Sakayanagi to tilting the reciprocation plane to coincide with axis GS in Fig. 17. However, Sakayanagi's rule grooves of equal curvature on a sphere. fabrication method provided a curved ruling motion even if the grating surface was flat.) A spherical grating blank of radius R=150 cm was used, and grooves of equal (not concentric) curvature o=315 cm were ruled with spacing 576 g/mm. The grating was illuminated with a Hg lamp and the spectra obtained (Fig. 19) compared to a conventional concave grating. Although the spectra suffered from a large amount of stray light, this work demonstrated clearly that astigmatism could be eliminated using curved grooves. Murty'"' has proposed a spherical zone-plate diffraction grating in reflection or transmission (Fig. 20). The grating is aplanatic due to the choice of a coma-free surface PC (the circle of Apollomus) along which the magnification between object A and image A' is constant. Varied spacing is then required to remove spherical aberration. For example, if the object is at infinity, the grating surface is a sphere with center at the image. A mirror surface, of course, would have twice this radius of curvature; thus the groove densities on the grating must be quite high to remove spherical aberration, comparable to what is required for a planar zone plate. Murty showed that the grooves are at the intersection of parallel planes spaced equally in the horizontal direction of Fig. 20. Thus, if viewed from the grating normal, the grooves are concentric with spacings which vary inverse with their radii. Murty recently has proposed a tandem ar.angoncnt of two such gratings to construct a narrow-band filter. While such gratings could be fabricated by holographic techniques, a mechanical ruling would provide _ such larger apertures and "" Kercurv stectra Ttiore easily Jttin tSe high ,ma i ran long en trance groove densities desired. ia i) carvedgrating, sin (tiji) conventional g rating. -erica! From .Sj^y^nagi 95 in. r1 3 - 9Plane Surfaces Encouraged by the prospect of mechanically-ruled curved grooves, a number of authors have proposed designs using plane grating surfaces and concentric grooves. Applications have ranged from use as fine-pitched rulers in surface metrology to spectroscopy at grazing. incidence3S,36,51 interferometry at v i s i b l e or at grazing incidence in the extreme UV or soft x - r a y . However, until recently such gratings have not been attempted witn a mechanical ruling engine. In 1982, the Perkin-Elmer Corporation constructed a prototype rotary ruling e n g i n e ' for ruling single-start concentric grooves with varied spacings. As with their linear varied-spaced gratings, the concentric gratings have been used to generate desired wavefronts for the interferometric testing of curved surfaces - in this case spheres or aspheres. The grating behaves as a zone plate in reflection, focusing to a point image either incident parallel lig.it (in first order diffraction) or a point source (second order diffraction). One such "paraboloid-sphere" is shown in Fig. 21, for which the focal length is 600 mm, corresponding to a groove density variation of approximately 50-150 g/mm for groove radii from approximately 20 to 60 mm. This grating has been used as a wavefront generator in interferometers to test spherical optics. Most recently, Hirst at Perkin-Elmer has, in addition to the prototype rotary engine, constructed an Advanced Circular Ruling Engine which is capable of providing VLS groove densities up to 1500 g/mm on ruled diameters as large as 500 mm (these p r o c e e d i n g s ) . A photograph of this new ruling engine is shown in Fig. 22. 50 52 t o 53 3 1 4 2 42 Fig. 21. Concentric groove VLS plane grating: "Paraboloid-sphere". Courtesy of G. Hirst, Perkin-Elmer Ruling Facility Instrument Group. Fig. 22. Perkin-Elmer Advanced Circular Ruling Engine. Courtesy of G. Hirst, Perki.-.-Elmer Ruling Facility. Hettrick has proposed a concentric groove plane VLS grating design which removes astigmatism at ail wavelengths at grazing incidence, and thus provides an ideal means of low-dispersion order separation in a new echelle spectrometer^!. One design variation of such a grazing incidence system is shown in Fig. 23, where the high-dispersion echelle grating is also a VLS grating (which will be discussed in the next section). A high-resolution spectrometer of this type, with the minimum number of reflections, was motivated by use in future astronomical missions. The focal length of the concentric groove grating in such applications is of order 2 meters, requiring large „ ™* ^jS*-^."*" radii of the concentric grooves. In anticipation of RULING FOCUS spectroscopic use of con- _ centric grooves, 3.W. Sach^"" at Hyperfine Inc. has recently fabricated! a grating with groove radii from -!<JtS am to .i-SO :as» and, for initial test purposes, with a constant WOOVt — SnwCTWr groove density of 6Q'G) g,/3TEtu **lS It should fee noted that fct use at gr.iair.g ir.cnier.ee. only a snill sector of a twcwmit amove groove circle is user! to WOSS­OISWHBM collect the incident ilight, •\2T\ 1 iice t:^e situation t©r ilUCJIDEMT fOCUS ione-pl-atc normal ".ncidcftce amplications as described Fig. 23. VLS 'Orazissg incidence echeile spectrometer, "using a 6 S P E < s concentric groove ajrating .ar.cl fan grating KSettricV. 19S5?. - 10 non-parallel ruling! Tan error", or successive non-parallelisa, of,grooves has bee= considered for soae tine to be one of the deaons of ruling large-grating* . Uncontrolled fanning of grooves is. of course, undesirable and will degrade the resolution of a conventional grating whose grooves are assuaed by the instrument designer to be perfectly parallel and straight. However, there are instances in which a controlled fanning of grooves can result in improved designs. 55 Concave Surfaces In 1969, Baumgardnerl briefly discursed a fan-type ruling pattern for the correction of image rotation from a concave grating when mounted for off-plane diffraction. This ruling pattern, where the grooves are straight but slanted towards the central ruling with various slopes, was shown by Baumgardner to remove first-order cross terms in the aberrant lightpath function, and thus remove image dist 'ion. 2 Plane Surfaces Hettrick has proposed a "fan grating" for use at grazing incidence in convergent light, being the off-plane version of the plane grating geometry previously described. The imaging properties of these gratings, both in-plane and off-plane, were presented in several papers"' '51 j^y Hettrick. In the fan grating design (Fig. 24), the grooves converge to a common "ruling focus" and the diffracted wavelengths lie along a cone. This is a variedspace grating with the variation being in the direction along the groove lengths. This corrects for the linearly varying focal distance to the spectral image, which without the space variation would result in a large first-order cross term in the aberrant light-path function . With fan grooves which converge to a ruling focus located behind the focal plane (and the virtual focus) by a distance 36 3 &RF = L siny tany , (4) Hettrick showed that this aberration is essentially cancelled at grazing incidence. In this equation, L is the nominal focal distance and y the nominal graze angle. A single grating can therefore be used in-focus at any graze angle, provided the focal surface and incident virtual source lie on a circle (Fig. 23) of diameter L /cosy , which intersects the grating center, the virtual source, the spectral image and the ruling focus. By an additional space variation between the grooves, the next most significant aberration (meridional coma), can be removed, resulting in potentially high resolution at grazing incidence. However, due to the inherently low dispersion of an off-plane grating of a given groove density, high resolution in practice requires use of high spectral orders This is feasible with the fan grating due to the absence of shadowing (thus high diffraction efficiency) at large blaze angles, and a unique by-product of the fan pattern beintr a nearly constant blaze wavelength across-, the grating aperture. Hettrick used these advantages of an echelle fan to design a class of grazing echelle spectrometer (Fig. 23). Cash has also proposed use of fan-type rulings in low spectral order^S. Adopting the nomenclature common in the opto-electronics industry^ and in metrological applications using this pattern^". Cash refers to this as the "radial groove grating." 7 A fan grating or "radial grating" was mechanically ruled by B.W. Bach at Hyperfine Inc. and subseguently tested in EUV and soft x-ray light by Windt . The ruling of a fan groove pattern is extremely challenging, as the groove depth varies continuously along each groove, requiring a means o:' continuously varyinq the weight loading on a diamond tool. Combined with the requirement of large blaze angles to operate as an echelle in the desired high spectral orders, and the accompanying requirement of a second space variation between the grooves for high resolution, a spectroscopically useful fan grating is perhaps the most difficult of the VLS grating designs to fabricate. 38 Fig. 24. Fan grating, mounted for conical diffraction at grazing incidence in a convergent beam. Figure for this plane grating from Hettrick and Bowyer (1983) . The future The above review has inspired sone speculation regarding the future direction in which V1^5 gratia-.as nay be headed. In addition to the plethora of proposed grating designs, a iraction OS which have actually been ruled at present, the recent construction of ruling er.451r.es dedicated to varied-space capability has provided a fcrward aoaenta3 to the art. - 11 The use of pla&e VIS gratings in converging or diverging light is a recently demonstrated geometry, and as such it is likely to quickly find applications in a ninber of diverse fields. Its advantages in being used for large area moderate resolution astronomical spectrometers are currently being explored at shorter and shorter wavelengths . In laboratory spectroscopy, nuch designs can bo adapted to time-resolved srrc.ik c i w r n s ' " , providing a powerful method of plasma diagnostics. It aay also be realistic to expect the stigraatic properties of VLS plane gratings to be used in extending interferoaetry to the soft x-ray reaion by use of grazing incidence. Interferometry at these energies will be made feasible by the development of intense coherent synchrotron radiation . Further theoretical and experimental work on the properties of gratings with varied spacing may also permit even further simplification jf dispersive systems, whereby all the optical functions required are performed in a single "monolithic" element. 59 61 A VLS concave grating design of tantalizing potential is the reflection zone plate, for which both coma and spherical aberration are absent. Such a grating should exhibit an exceptionally wide field of view, making it ideal for use as a camera or de-magnifying microprobe with loose alignment tolerances. Since such a grating is used at normal incidence, it would either be restricted to wavelengths longer than approximately 200 A , or require multi-layer coatings which reflect only an interference-limited bandpass. A multilayered aplanatic zone plate would also have minimum achromatism, allowing its use in strong continuum light such as synchrotron radiation. Varied spacing also permits higher resolution to be attained, particularly at grazing incidence. Applications to monochromator and spectrometer design are at an early stage, and likely to proceed with increased vigor given the increased availability of intense soft x-ray and extreme UV radiation. Acknowledgement s The author wishes to thank those researchers who kindly provided information, and sometimes even original drawings or photographs, regarding their work: T. Harada, G. Hirst, B. Bach, and M.V.R.K. Murty. This review would of course not have been possible without the published efforts of a large number of people, both past and present, who's foresight inspired the present work. I apologize for any misinterpretatipns of the reviewed works. References 1. H.A. Rowland, "On Concave Gratings for Optical Purposes," Phil. Mag. Vol. 16, p. 197, 18S3. 2. H.A. Rowland, "Gratings in Theory and Practice," Phil. Mag. Vol. 35, p. 397, 1893. 3. T. Lyman, "False Spectra from the Rowland Concave Grating," Phys. Rev. Vol. 12, p. 1, 1901; "An Explanation of the raise Spectra £iom Diffraction Gratings," ?hys• Rev• Vol. 16, p. 257, 1903. A. M.A. Cornu, "Sur la diffraction proprietes focales des teseaux," C.R. Acad. Sci. Vol. 80, p. 6-15, 1875 (Paris) ; "Etudies sur les reseaux dif f ringents. Anomalies focales," C.R. Acad. Sci. Vol. 116, p. 1215, 1893 (Paris); "Sur diverses methodes relatives a 1'observation des proprietes appelees anomalies focales des reseaux diffringents," C.R. Acad. Sci. Vol. 216, p. 1421, 1893 Paris); "Verifications nuraeriques relatives aux proprietes focales des reseaux diffringents plans," C.R. Acad. Sci. Vol. 117, p. 1032, 1393 (Paris). 5. G.R. Harrison, "The Diffraction Grating - An Opinionated Appraisal," Appl. Opt. Vol. 12, p. 2039, 1973. 6. Vi. Worrier. 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Any conclusions or opinions expressed in this reportrepresentsolely those of the authors) and not necessarily those of The Regents of the University of California, the Lawrence Berkeley Laboratory or the Department of Energy. Reference to a company or product name does not imply approval or recommendation of the product by the University of California or the U.S. Department of Energy te the exclusion of others that may be suitable.