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
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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 -
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-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""
**" °
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t
d e S
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,
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n o r m a l e
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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
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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.
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This report was done with support from the
Department of Energy. 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.