DIFFRACTION GRATING MONOCHROMATORS (PGMs) · 2017. 3. 30. · M. R. Howells, Advanced Light Source COLLIMATED LIGHT SX700 (CLSX700) • This is the current and deservedly the most

M. R. Howells, Advanced Light Source

DIFFRACTION GRATING

MONOCHROMATORS

(PGMs)

Malcolm 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)


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


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


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°


SOME WORKING CURVES FOR PGM’S


• 300/mm grating

• 79°<


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


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


Petersen 1986

SGM –veorder

SGM +veorder

WORKING CURVES FOR cff=2.25 ETC


BESSY CLSX700'S: SUMMARY


BESSY U125/1-PGM BEAM LINE

Follath 2002

Effective total length = 27 m


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


1200mm

300/mm

Where we are(925/mm)

Where they are

BESSY PGM'S: RESOLUTION SUMMARY

Where we'd like to be


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


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


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.


-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.


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


MES PROJECT CALCULATIONS

First, second and third orderefficiency calculations for alaminar grating 150/mm



Source-size-limited resolving power fora source of size FWHM = 40 µm atdistance 12 m with a 150/mm grating



Cylindrical mirror slope errorneeded to get a resolving power of7500 with the 150/mm grating



Grating slope error needed toget 7500 resolving power with150/mm grating


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


JENOPTIC SX700 MONOCHROMATOR

Three gratings

UHV rotary encoder

Grating drive arm

Mirror drive arm

Plane mirror


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


Monochromator chamber,vacuum test Oct 2001


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

Documents

DIFFRACTION GRATING MONOCHROMATORS (PGMs) · 2017. 3. 30. · M. R. Howells, Advanced Light Source COLLIMATED LIGHT SX700 (CLSX700) • This is the current and deservedly the most