diffraction grating monochromators (pgms) · 2017. 3. 30. · m. r. howells, advanced light source...
TRANSCRIPT
-
M. R. Howells, Advanced Light Source
DIFFRACTION GRATING
MONOCHROMATORS
(PGMs)
Malcolm R. Howells
Advanced Light Source
-
M. R. Howells, Advanced Light Source
PLANE GRATING SYSTEMS: GENERAL
Focus condition for a spherical grating
cos2
r− cos
R
+
cos2
′ r − cos
R
= 0 let R ⇒ ∞ → ′ r = −r
cos2
cos2
Note that if r = ∞ then ′ r = ∞ irrespective of cff i.e . the grating then does no focusing
Using cff =cos
cos and recalling that M = −
′ r r
cos
cos → M = cff
Eliminating between
m
d0= sin + sin and cff =
cos
cos
sin =
m
d−
m
d
2 1
cff2 + 1−
1
cff2
2
1−1
cff2
r
r'
B
A
Grating
α β
Source point
Virtualimage
(of the grating alone)
-
M. R. Howells, Advanced Light Source
COLLIMATED LIGHT SX700 (CLSX700)
• This is the current and deservedly the most popular of many versions (used in ALS MES project)
• The original (Petersen) held fixed focus by maintainingand introduced the still-essential mechanism for positioning the plane mirror (next slide)
• CLSX700 has constant focus position irrespective of the value of cff which therefore becomes a user-controlled variable
• This can be used to track the efficiency maximum, suppress high orders or maximize resolution
• Sagittal focusing mirrors reduce sensitivity to manufacturing errors (Jark 1992) see next slide, othertypes were paraboloid (Kunz 1968), ellipsoid (Petersen 1982), elliptical cylinder (Nyholm 1985) orsphere (Padmore 1989)
cff = cos cos = 2.25
Kunz 1968Petersen 1982Follath 1997
-
M. R. Howells, Advanced Light Source
FORGIVENESS FACTOR
Requirement: ′ s T ≤1
2′ s T → 2 ′ r T ≤
1
2
′ r r
sT
T ≤1
4
sTr
′ s S ≤12
′ s S → 2 ′ r S ≤12
′ r
r sS
S ≤14
sSr
Reasons for the factor 2's:
1. Ray deviation is twice that of the mirror
2. Quadratic sum of and /2 is 1.1 implying a 10% error which we declare acceptable
-
M. R. Howells, Advanced Light Source
THE ZEISS MIRROR MECHANISM
• Reimer 1983• Pimpale 1991
• This mechanism, patented by BESSY and Zeiss, is a major reason for the success of this design
• The idea is to find a point about which to rotate the mirror such that the central ray always hits thegrating pole - this can be done with only a few microns error
• The easy and less accurate solution is continue the mirror surfaces at maximum and minimum angle tointersect the y axis and take the average of the two points - this will be near A (0, D/2) for small angles
• More accurate solutions (Pimpale 1991) are close to B (0, 3D/2) - best solutions are good within 10µmif D ≤ 8 cm and the grazing angle is less than 10° - B itself is a good solution to within 10 µm if D ≤ 3cm and the grazing angle is less than 10°
-
M. R. Howells, Advanced Light Source
SOME WORKING CURVES FOR PGM’S
-
M. R. Howells, Advanced Light Source
• 300/mm grating
• 79°<
-
M. R. Howells, Advanced Light Source
m
d= sin + sin so
= d cosm
d
dq=
d
d
d
dq=
d cos
m ′ r
Fractional bandwidth due to the entrance slit is
source
= qr
cos
m d≡ s
r A cff( )
Angularerror
Normalizedangulardispersion
In the small - angle approximation
A cff( ) ≅ dm
2
cff2 −1( )
NB - the grating changes the angular
spread by 1cff (cff is the magnification)
Follath 1997, 2001
source
=s
r A cff( )
exit
slit
= ′ s
′ r cff A cff( )
aberr
= ′ y ′ r
cff A cff( )
preopt
= po A cff( )
focopt
= fo cff A cff( )
grating
= gr 1 + cff( ) A cff( )
total
=
i
2
i∑ = 1
R
CONTRIBUTIONS TO THE SX700 RESOLUTION
-
M. R. Howells, Advanced Light Source
BESSY U125/1-PGM
Foc optic 0.05 sec
Slit 10 µm
Grating 0.2 sec
Preoptic 0.25 sec
Source 50 µm
Follath 2001
–ve order +ve order
BESSY U125/1-PGM
Preoptic 0.25 sec
Source 50 µm
Foc optic 0.05 sec
Grating 0.2 sec
Slit 10 µm
RESOLUTION CONTRIBUTIONS FOR A BESSY PGM
TOTAL
TOTAL
-
M. R. Howells, Advanced Light Source
Petersen 1986
SGM –veorder
SGM +veorder
WORKING CURVES FOR cff=2.25 ETC
-
M. R. Howells, Advanced Light Source
BESSY CLSX700'S: SUMMARY
-
M. R. Howells, Advanced Light Source
BESSY U125/1-PGM BEAM LINE
Follath 2002
Effective total length = 27 m
-
M. R. Howells, Advanced Light Source
BESSY PGM RESOLUTION DEMONSTRATION
• Doppler width 0.4 meV
• Monochromatorcontribution 0.65 meV
• Resolving power=1.0x105
• Rotation increments- grating: 17 nrad- mirror: 9 nrad
• Measured with 1200/mmgrating at cff =10 to 12
Picture from R. Follath, BESSY
-
M. R. Howells, Advanced Light Source
1200mm
300/mm
Where we are(925/mm)
Where they are
BESSY PGM'S: RESOLUTION SUMMARY
Where we'd like to be
-
M. R. Howells, Advanced Light Source
Mono angles
75eV 2000eV
Cff = 1
Cff = 10
thermaldistortionn
good higher ordersuppression
goodefficiencywith deepgrooves
goodefficiencywithshallowgrooves
resolutioninsensitive to slopeerrors
mechanical limits
largeincludedangle
smallincludedangle
mechanical limits
Parameters for this study:150 lines/mm 25nm groove depth (operating from 75 eV to 800eV)(low dispersion)
1200 lines/mm 6nm groove depth (operating from 300 eV to 2000eV)(high dispersion)
Slide from TonyWarwick
-
M. R. Howells, Advanced Light Source
OPTICAL PATH FUNCTION: VARIED-LINE-SPACING GRATINGS
d(w) = d0 1 + v1w + v2w2 + ...( ) n w( ) = ni00wi
i=1
∞
∑
F = Cijkijk∑ ,r( )wil j zk + Cijk
ijk∑ , ′ r ( )wil j ′ z k + m
d0nijk
n100 =1n200 = −v1 2
n300 = v12 − v2( ) 3
n400 = −v13 + 2v1v2 − v3( ) 4
nijk = 0 if i or k ≠ 0
Now the groove spacing d(w) and number n(w) are functions of w and are also expressed as power series
So the optical path function becomes
Evidently the use of VLS can benefit aberrations of the form i00:
Defocus, coma, spherical aberration but not ones with j, k ≠0
-
M. R. Howells, Advanced Light Source
WHY DO VLS GRATINGS WORK?
The spherical - grating focus condition is now:
F( )200 =1
2w2
cos2
r−
cos
R
+
cos2
′ r −
cos
R
−
v1m
d0
= 0
So setting R = ∞, using the grating equation and switching to grazing angles a, b
1
′ r =
cos a − cos bsin2 b
− 1
r
sin2 a
sin2 b=
1
rv1r
−2sina + b
2
sin
a − b2
sin2 b −
sin2 a
sin2 b
Now approximating sin a ≅ a etc
1
′ r =
1
r−v1r
a2 − b2
2b2 −
a2
b2
Evidently if v1 =−2r
then ′ r = −r
IDENTICALLY (for all values of a, b
and thus . Moreover if, in addition,
v2 =1
r2 then coma and sperical aberration
are corrected as well under the same small -
angle assumption
B
Source point r
r'
A
Grating
α β
Virtualimage
This works equally well in converging or diverginglight (principle of reversibility) although the literaturediscusses only converging.
-
M. R. Howells, Advanced Light Source
-4.0E-06
-2.0E-06
0.0E+00
2.0E-06
4.0E-06
6.0E-06
8.0E-06
1.0E-05
0 20 40 60 80 100 120 140
Wavelength (Å)
0.0E+00
1.0E-03
2.0E-03
3.0E-03
4.0E-03
5.0E-03
6.0E-03
0 500 1000 1500
Wavelength (Å)
DOES v1 = –r/2, r' = –r GIVE OPTIMUM FOCUSING?
• No - the usual procedure is to write the focus equation twice for two wavelengths of exact focus and solve for r' and v1 -(this requires a fixed included angle or at least a fixed focusing principle) - the nominal focal distance then changes by asmall amount (2% in the above case) - this gives locally better focus although not much improvement over a large range
• Note that all of the design studies in the literature except one (Koike 1995) consider only fixed-included-angle cases andoffer, sometimes very good, although still approximate solutions but they have SGM-like disadvantages.
• Now that the variable-included angle schemes are available we have exact focus solutions such as CLSX700 or classicalSX700 although the latter does not give control of the included angle to the user.
• Therefore retrofitting VLS to a standard SX700 makes some sense to give user control of the included angle howevernote that the focal length or the focal distance of the mirror would have to change.
• Conclusion: VLS role in general-purpose monochromators is becoming minor but it is still strong in spectrographs.
-
M. R. Howells, Advanced Light Source
0.00001
0.0001
0.001
0.01
0.1
1
1 10 100 1000 10000Wavelength (Å)
Defocus
1 µr slope error
Mirror coma
Source size
Total
• VLS solution with cffchosen for maximumefficiency (between 1.5and 2.5)
• Wavelengths of exactfocus: 20 Å and 80 Å
• Source: size 50 µm anddistance 15 m
• Beam height: 2mm
• Inside (+ve) order
• 1200/mm
VLS RETROFIT TO AN SX700
-
M. R. Howells, Advanced Light Source
MES PROJECT CALCULATIONS
First, second and third orderefficiency calculations for alaminar grating 150/mm
-
M. R. Howells, Advanced Light Source
MES PROJECT CALCULATIONS
Source-size-limited resolving power fora source of size FWHM = 40 µm atdistance 12 m with a 150/mm grating
-
M. R. Howells, Advanced Light Source
MES PROJECT CALCULATIONS
Cylindrical mirror slope errorneeded to get a resolving power of7500 with the 150/mm grating
-
M. R. Howells, Advanced Light Source
MES PROJECT CALCULATIONS
Grating slope error needed toget 7500 resolving power with150/mm grating
-
M. R. Howells, Advanced Light Source
Mirror cooling for high heatload at low energy (75eV)
slope error for glidcop mirror 75eV
-2.00E-05
-1.50E-05
-1.00E-05
-5.00E-06
0.00E+00
0 100 200 300
mm
rad
Cff=1.25 dT=4.29
Cff=2.5 dT=1.99Cff=5 dT=1.42
slope error for glidcop mirror 300eV
-6.00E-06-5.00E-06-4.00E-06-3.00E-06-2.00E-06-1.00E-060.00E+00
0 100 200 300
mm
rad
Cff=1.25 dT=1.44
Cff=2.5 dT=0.40
Cff=5 dT=0.26
slope error for silicon mirror 300eV
-1.20E-06-1.00E-06-8.00E-07-6.00E-07-4.00E-07-2.00E-070.00E+00
0 100 200 300
mm
rad
Cff=1.25 dT=2.50
Cff=2.5 dT=0.68Cff=5 dT=0.43
slope error for silicon mirror 75eV
-5.00E-06
-4.00E-06
-3.00E-06-2.00E-06
-1.00E-06
0.00E+00
0 100 200 300
mm
rad
Cff=1.25 dT=7.80
Cff=2.5 dT=3.45Cff=5 dT=2.42
absorbed power density300eV
0
0.02
0.04
0.06
0.08
0.1
-200 -100 0 100 200
mm
W/m
m2
Cff=1.25, 2theta=173.9
Cff=2.5, 2theta=176.9
Cff=5.0, 2theta=177.5
absorbed power density75eV
0
0.05
0.1
0.15
0.2
0.25
0.3
-200 -100 0 100 200
mm
W/m
m2
Cff=1.25, 2theta=167.9
Cff=2.5, 2theta=173.8
Cff=5.0, 2theta=175.0
The rms slope error (µrad) of the pre-mirror corresponding to a resolvingpower R=7500 (FWHM) from the150l/mm grating.
11.5
5
1
500 1000eV
1
2
3
4
Cff=1.25Cff=2.5
Cff=5.0
-
M. R. Howells, Advanced Light Source
JENOPTIC SX700 MONOCHROMATOR
Three gratings
UHV rotary encoder
Grating drive arm
Mirror drive arm
Plane mirror
-
M. R. Howells, Advanced Light Source
New implementation of SX700monochromator
Legs filled with epoxy granite
Heavy pump below bellows onseparate support
6-strut alignment
Lightweight rigid honeycombtable
Aluminum structural vessel
External sine-bar drives andlinear encoders
Seal joint below beam heightfor alignment access
External grating changer
-
M. R. Howells, Advanced Light Source
Monochromator chamber,vacuum test Oct 2001
-
M. R. Howells, Advanced Light Source
monochromator scanningmechanism with integral cooling
Pressure equalized water feed
Pressure-equalized water feed
Silicon plane mirror
Double grating
Water lines on sine bar
Water manifold with no flexingparts
Grating carriage with roll andyaw adjusters for double
grating
Invar structural frame