Appendix B1 Reports of UME - National Physical Laboratoryresource.npl.co.uk/euromet/length/projects/reports/600-surf-texture/... · 2, 50 8, 33 0, 5 0, 9 0, 5 s t d. d e v./ n m 11,

Appendix B1 - Reports of UME July 31st, 2003

Appendix B1

Repor ts of UME

Euromet Project 600 – Comparison of Surface Roughness Standards 2/35


MEASUREMENT REPORTOF

NATIONAL METROLOGY INSTITUTEOF TURKEY, UME

EUROMET SUPPLEMENTARYCOMPARISON

SURFACE TEXTUR E

Project No. 600

UME Dimensional LaboratoryTel: 0 (262) 646 63 55 / 235

Fax: 0 (262) 646 59 14

Contact: Dr. Tanfer Yandayan [email protected]

Murat Aksulu [email protected]

Okhan ��

[email protected]



Contents

1. Description of the Measurement Method and Instrument ......................................................4

2. Results and Measurement Conditions.....................................................................................5

3. Uncertainty Budgets of Measurements...................................................................................9

3.1 Step height standard with a nominal height of 200 nm - Identification (for D)..................10

3.2 Step height standard with a nominal height of 1500 nm - Identification (for D) ................11

3.3 Step height standard with a nominal height of 8000 nm - Identification (for D) ................12

3.4 Step height standard with a nominal height of 200 nm - Identification (for Pt) .................13

3.5 Step height standard with a nominal height of 1500 nm - Identification (for Pt) ...............14

3.6 Step height standard with a nominal height of 8000 nm - Identification (for Pt) ...............15

3.7 Geometric standard Rub (P114A) - Identification (for Rz, Ra, Rmax) ...............................16

3.8 Geometric standard PTB (7070) -Identification (for Rz, Ra, Rmax)...................................17

3.9 Geometric standard PTB (8194) -Identification (for Rz, Ra, Rmax)...................................18

3.10 Roughness standard SFRN 150 (1,006) - Identif ication (for Rz, Ra, Rmax) ....................19

3.11 Roughness standard Fine (629f) - Identif ication (for Rz, Ra, Rmax) ...............................20

3.12 Roughness standard Coarse (633g) - Identif ication (for Rz, Ra, Rmax) ...........................21

3.13 Roughness standard Very coarse (686sg) - Identification (for Rz, Ra, Rmax) ..................22

3.14 Geometric standard Rub (114A) - Identification (for RSm) ..............................................23

3.15 Geometric standard PTB (7070) - Identification (for RSm)..............................................24

3.16 Geometric standard PTB (8194) - Identification (for RSm)..............................................25

3.17 Roughness standard SFRN 150 (1.006) - Identif ication (for Rk, Rpk, Rvk) .....................26

3.18 Roughness standard Fine (629f) - Identif ication (for Rk, Rpk, Rvk) ................................27

3.19 Roughness standard Coarse (633g) - Identif ication (for Rk, Rpk, Rvk)............................28

3.20 Roughness standard Very coarse (686sg) - Identification (for Rk, Rpk, Rvk)...................29

3.21 Roughness standard SFRN 150 (1.006) - Fine (629f) – Coarse (633g) – Very coarse (686sg)- Identification (for Mr 1, Mr2)...................................................................................................30

APPENDIX 1 �� "!�# $ !�%�# $ !�&�#(')� �� *+��-,

.............31

APPENDIX 2 Detail Explanations of All Uncertainty Calculations in EXCEL Sheets (see thefile “ UME-Uncertainty.xls” )



1. Description of the Measurement Method and Instrument

Type of instrument: Stylus instrument - Mahr Perthometer Concept (pick up is FRW-250, driveunit is PRK, xy table is PKT electronic)

Kind of operation: Moving stylus. A comercial column is not used. Instead, drive unit is locatedon a table with adjustable height to reduce vibration.

Conditions data collection: Stylus tip radius 2 µm, stylus tip angle 90°, vertical measurementrange ± 25 µm

Conditions of evaluation:Measurements are performed according to the datum of PRK drive unit.No skid is used.

Characterisation of instrument noise and deviation of ideal behaviour: A PTB calibratedoptical flat is used. The optical flat is set on the x-y table and different regions of the optical flatsurface are measured.

Rougness value on flat glass plate with lateral movement Rzo = 0.033 µm (Certificated Rzvalue of the optical flat is about 5 nm.)Rougness value on flat glass plate without lateral movement Rzo = 19 nmWaviness value on flat glass plate with lateral movement Wt = 30 nmVertical resolution = Measuring range / 60000 step = 0,42 nmHorizontal resolution = Standart tracing length / up to 16000 point

Environment characterisation: No vibration isolation is used. Temperature of the laboratory is20±0,3°C.

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282

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3,6

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1

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m (

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40,9

20,2

R3

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valu

e/µm

1,40

51,

364

-2,

670,

10,

90,

1

std.

dev

./nm

6,8

10,0

-2,

670,

10,

90,

1

U/n

m (

k=2)

45,2

22,0

R6

8 µ

mva

lue/

µm8,

399

8,36

3

-

2,67

0,1

0,9

0,1

std.

dev

./nm

11,8

10,8

-2,

670,

10,

90,

1

U/n

m (

k=2)

105,

525

,9

Geo

m.

Sta

ndar

d

R

aR

zR

max

RS

m

Rub

P11

4A/5

28-

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5va

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µm0,

505

1,59

31,

599

49,7

23

0,

252,

50,

10,

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2

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dev

./nm

1,2

4,9

7,1

75,4

0,25

2,5

0,1

0,9

0,2

U/n

m (

k=2)

48,6

48,6

48,6

984,

3

PT

B70

70/P

GN

10va

lue/

µm2,

978

9,73

09,

914

198,

617

2,50

8,33

0,5

0,9

0,5

std.

dev

./nm

11,9

46,8

49,1

21,1

2,50

8,33

0,5

0,9

0,5

U/n

m (

k=2)

142,

314

2,3

142,

339

20,4

PT

B81

94/P

GN

3va

lue/

µm0,

901

3,09

63,

113

119,

149

0,80

2,67

0,5

0,9

0,35

std.

dev

./nm

6,4

48,7

48,5

29,0

0,80

2,67

0,5

0,9

0,35

U/n

m (

k=2)

113,

911

3,9

113,

923

35,5

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Rk*

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Mr1

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Mr2

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686s

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14,3

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8,13

71,

231

3,11

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948

92,8

502,

508,

330,

50,

90,

5

std.

dev

./nm

32,5

258,

128

,929

7,5

125,

813

0,3

1,23

50,

807

8,

330,

50,

90,

5

U/n

m (

k=2)

497,

649

7,6

497,

663

4,4

634,

463

4,4

0,30

64,

085

Coa

rse

633g

valu

e/µm

1,53

37,

608

9,04

14,

464

0,73

92,

529

6,19

681

,968

0,80

2,67

0,5

0,9

0,35

std.

dev

./nm

8,2

197,

812

3,0

99,8

52,1

53,2

0,41

30,

469

2,

670,

50,

90,

35

U/n

m (

k=2)

399,

739

9,7

399,

752

352

352

30,

428

5,65

6

Fin

e62

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µm0,

147

1,25

51,

421

0,44

90,

137

0,29

88,

982

88,1

580,

802,

670,

50,

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std.

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./nm

2,9

40,7

51,5

11,8

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7,6

0,86

00,

654

2,

670,

50,

90,

35

U/n

m (

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98,1

98,1

98,1

136,

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6,0

136,

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979,

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0,06

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0,03

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320,

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500,

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0,78

44,

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3. Uncertainty Budgets of Measurements



A4 - Uncertainty of measurement3.1 Step height standard with a nominal height of 200 nm - Identification (for D)

Equation used:

��

� ++

+

=

∑ ∑= =

+−=� ��

��

��

� ��

Ptn : Depth of the reference setting standard known from PTB certificatePtmy : Locus dependent fraction of measured reference groove (Measured value of reference standard)b : Reproducibility of tracing of the reference groovezm : Profile of test standard (Measured value of test standard)zref : Profile of reference plane (Wt value determined using optical flat)zn : Background noise (Rz value determined using optical flat)AF : Alingnment error due to roughness and flatness error on the test depth standardno : Number of profile points of upper profile sections which is used to fit an upper straight linenu : Number of profile points of lower profile section which is used to fit a circle at the bottom of the groovezkoi : z coordinate of ith point of upper profile sectionszkui : z coordinate of ith point of lower profile section

Combined uncertainty equation:

( ) ( ) � � � !� � � ""� � � ""

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78 +++++

++++

+=

quantityXi

estimatexi

uncertaintyu(xi)

probabilit ydistribution

sensitivitycoefficient

ci

uncertaintycontribution

ui(d)

degrees offreedom

vi

Ptn 9870 nm 76 nm N 0.0040 0.154 nm 200Ptmy 9870 nm 2 nm R 0.0040 0.005 nm 200

b 10 nm 10 nm N 0.0040 0.040 nm 100zm 282 nm 5 nm N 0.1414 0.707 nm 4zref 30 nm 15 nm R 0.1414 1.225 nm 200zn 33 nm 16.50 nm R 0.1414 1.347 nm 200AF 10 nm 5 nm R 1.4142 4.083 nm 200

RES 0.42 nm 0.21 nm R 1.0000 0.121 nm 200REP 9 nm 9 nm N 1.0000 9.000 nm 49

N = normal; R = rectangular; T = triangular; U = U-shaped.RES: ResolutionREP: Repeatibili ty(Please see the Excel sheet)

Combined standard uncertainty: uc(D) = 10.1 nm

Effective degrees of freedom: veff (D) = 76.6

Expanded uncertainty: U(D) = 20.2 nm with a coverage factor k=2

Laboratory: ..National Metrology Institute of Turkey. (UME)

Date: ... 11.01.2002 ................ Signature:..................................................................




Equation used:

��

� ++

+

=

∑ ∑= =

+−=� ��

��

��

� ��

Ptn : Depth of the reference setting standard known from PTB certificatePtmy : Locus dependent fraction of measured reference groove (Measured value of reference standard)b : Reproducibilit y of tracing of the reference groovezm : Profile of test standard (Measured value of test standard)zref : Profile of reference plane (Wt value determined using optical flat)zn : Background noise (Rz value determined using optical flat)AF : Alingnment error due to roughness and flatness error on the test depth standardno : Number of profile points of upper profile sections which is used to fit an upper straight linenu : Number of profile points of lower profile section which is used to fit a circle at the bottom of the groovezkoi : z coordinate of i th point of upper profile sectionszkui : z coordinate of i th point of lower profile section


( ) ( ) � � � !� � � ""� � � ""

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78 +++++

++++

+=

quantityXi

estimatexi

uncertaintyu(xi)



ci


ui(d)

degrees offreedom

vi








Laboratory: ..National Metrology Institute of Turkey. (UME)...................................................Date: .................. 11.01.2002 .............. Signature:..................................................................




Equation used:

��

� ++

+

=

∑ ∑= =

+−=� ��

��

��

� ��

Ptn : Depth of the reference setting standard known from PTB certificatePtmy : Locus dependent fraction of measured reference groove (Measured value of reference standard)b : Reproducibility of tracing of the reference groovezm : Profile of test standard (Measured value of test standard)zref : Profile of reference plane (Wt value determined using optical flat)zn : Background noise (Rz value determined using optical flat)AF : Alingnment error due to roughness and flatness error on the test depth standardno : Number of profile points of upper profile sections which is used to fit an upper straight linenu : Number of profile points of lower profile section which is used to fit a circle at the bottom of the groovezkoi : z coordinate of ith point of upper profile sectionszkui : z coordinate of ith point of lower profile section


( ) ( ) � � � !� � � ""� � � ""

� ########### $&%(')$&%&*)+-,).).).)//0)')')' .//1) 23 4 56789 6;:9 29 26

78 +++++

++++

+=

quantityXi

estimatexi

uncertaintyu(xi)



ci


ui(d)

degrees offreedom

vi








Laboratory: ..National Metrology Institute of Turkey. (UME)................................................................................................................

Date: .................. 11.01.2002 ............ Signature:..................................................................



A4 - Uncertainty of measurement3.4 Step height standard with a nominal height of 200 nm - Identification (for Pt)

Equation used:

��

�� ++

+

=

Pt = zko - zku + 2 AF

Ptn : Depth of the reference setting standard known from PTB certificatePtmy : Locus dependent fraction of measured reference groove (Measured value of reference standard)b : Reproducibilit y of tracing of the reference groovezm : Profile of test standard (Measured value of test standard)zref : Profile of reference plane (Wt value determined using optical flat)zn : Background noise (Rz value determined using optical flat)AF : Alingnment error due to roughness and flatness error on the test depth standardzko : Highest z-value at the top of the profilezku : Lowest z-value at the bottom of the profile


( ) ( ) ��

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quantityXi

estimatexi

uncertaintyu(xi)



ci


ui(d)

degrees offreedom

vi





Combined standard uncertainty: uc(Pt) = 20.4 nm

Effective degrees of freedom: veff (Pt) = 381.1

Expanded uncertainty: U(Pt) = 40.9 nm with a coverage factor k=2


Date: .................. 11.01.2002 .............. Signature:..................................................................




Equation used:

��

� ++

+

=


Ptn : Depth of the reference setting standard known from PTB certificatePtmy : Locus dependent fraction of measured reference groove (Measured value of reference standard)b : Reproducibility of tracing of the reference groovezm : Profile of test standard (Measured value of test standard)zref : Profile of reference plane (Wt value determined using optical flat)zn : Background noise (Rz value determined using optical flat)AF : Alingnment error due to roughness and flatness error on the test depth standardzko : Highest z-value at the top of the profilezku : Lowest z-value at the bottom of the profile


( ) ( ) ��

� �� !" !$#" �" �!" ++++++++=

quantityXi

estimatexi

uncertaintyu(xi)



ci


ui(d)

degrees offreedom

vi








Laboratory: ..National Metrology Institute of Turkey. (UME)................................................................................................................Date: .................. 11.01.2002 ............ Signature:..................................................................




Equation used:

��

� ++

+

=


Ptn : Depth of the reference setting standard known from PTB certificatePtmy : Locus dependent fraction of measured reference groove (Measured value of reference standard)b : Reproducibility of tracing of the reference groovezm : Profile of test standard (Measured value of test standard)zref : Profile of reference plane (Wt value determined using optical flat)zn : Background noise (Rz value determined using optical flat)AF : Alingnment error due to roughness and flatness error on the test depth standardzko : Highest z-value at the top of the profilezku : Lowest z-value at the bottom of the profile


( ) ( ) ��

� �� !" !$#" �" �!" ++++++++=

quantityXi

estimatexi

uncertaintyu(xi)



ci


ui(d)

degrees offreedom

vi









Date: ........... 11.01.2002 ............... Signature:..................................................................



A4 - Uncertainty of measurement3.7 Geometric standard Rub (P114A) - Identification (for Rz, Ra, Rmax)

Equation used:

��

� ++

+

=

Ptn : Depth of the reference setting standard known from PTB certificatePtmy : Locus dependent fraction of measured reference grooveb : Reproducibilit y of tracing of the reference groovezs : Unknown systematic deviation. zs = a = RzPTB - RzUME

zn : Background noiseRz : Measured Rz parameter carried out on the test standardRzk : Calibrated Rz parameter


( ) ��

�� ++++++=

quantityXi

estimatexi

uncertaintyu(xi)



ci


ui(d)

degrees offreedom

vi


b 10 nm 10 nm N 0.161 1.614 nm 100zs 36.1 nm 36.1 nm R 1.000 20.842 nm 200zn 33 nm 16.50 nm R 1.000 9.526 nm 200Rz 1593 nm 5 nm N 1.000 5.000 nm 35RES 0.42 nm 0.21 nm R 1.000 0.121 nm 200

N = normal; R = rectangular; T = triangular; U = U-shaped.RES: Resolution(Please see the Excel sheet)

Combined standard uncertainty: uc(Rz) = 24.3 nm

Effective degrees of freedom: veff (Rz) = 345.2

Expanded uncertainty: U(Rz) = 48.6 nm with a coverage factor k=2


Date: .............. 11.01.2002 .............. Signature:..................................................................



A4 - Uncertainty of measurement3.8 Geometric standard PTB (7070) -Identification (for Rz, Ra, Rmax)

Equation used:

��

� ++

+

=


( ) ��

�� "! ++++++=

quantityXi

estimatexi

uncertaintyu(xi)



ci


ui(d)

degrees offreedom

vi








Date: ........... 11.01.2002 .............. Signature:..................................................................



A4 - Uncertainty of measurement3.9 Geometric standard PTB (8194) -Identification (for Rz, Ra, Rmax)

Equation used:

��

� ++

+

=

Ptn : Depth of the reference setting standard known from PTB certificatePtmy : Locus dependent fraction of measured reference grooveb : Reproducibility of tracing of the reference groovezs : Unknown systematic deviation. zs = a = RzPTB - RzUME



( ) ��

�� "! ++++++=

quantityXi

estimatexi

uncertaintyu(xi)



ci


ui(d)

degrees offreedom

vi






Expanded uncertainty: U(Rz) = 113.9 nm with a coverage factor k=2.01


Date: .............. 11.01.2002 ............ Signature:..................................................................



A4 - Uncertainty of measurement3.10 Roughness standard SFRN 150 (1,006) - Identification (for Rz, Ra, Rmax)

Equation used:

��

� ++

+

=




( ) ��

�� "! ++++++=

quantityXi

estimatexi

uncertaintyu(xi)



ci


ui(d)

degrees offreedom

vi







Laboratory: National Metrology Institute of Turkey (UME)................................................................................................................

Date: ........... 11.01.2002 ............. Signature:..................................................................



A4 - Uncertainty of measurement3.11 Roughness standard Fine (629f) - Identification (for Rz, Ra, Rmax)

Equation used:

��

� ++

+

=




( ) ��

�� "! ++++++=

quantityXi

estimatexi

uncertaintyu(xi)



ci


ui(d)

degrees offreedom

vi


b 10 nm 10 nm N 0.127 1.272 nm 100zs 35 nm 35 nm R 1.000 20.207 nm 200zn 33 nm 16.50 nm R 1.000 9.526 nm 200Rz 1255 nm 43.1 nm N 1.000 43.100 nm 35RES 0.42 nm 0.21 nm R 1.000 0.121 nm 200






Date: ......... 11.01.2002 ........... Signature:..................................................................



A4 - Uncertainty of measurement3.12 Roughness standard Coarse (633g) - Identification (for Rz, Ra, Rmax)

Equation used:

��

� ++

+

=




( ) ��

��

++++++=

quantityXi

estimatexi

uncertaintyu(xi)



ci


ui(d)

degrees offreedom

vi


b 10 nm 10 nm N 0.771 7.708 nm 100zs 61 nm 61 nm R 1.000 35.218 nm 200zn 33 nm 16.50 nm R 1.000 9.526 nm 200Rz 7608 nm 192.1 nm N 1.000 192.100 nm 35RES 0.42 nm 0.21 nm R 1.000 0.121 nm 200






Date: ................. 11.01.2002 ............ Signature:..................................................................



A4 - Uncertainty of measurement3.13 Roughness standard Very coarse (686sg) - Identification (for Rz, Ra, Rmax)

Equation used:

��

� ++

+

=




( ) ��

��

++++++=

quantityXi

estimatexi

uncertaintyu(xi)



ci


ui(d)

degrees offreedom

vi


B 10 nm 10 nm N 1.449 14.5 nm 100zs 100 nm 100 nm R 1.000 57.7 nm 200zn 33 nm 16.50 nm R 1.000 9.5 nm 200Rz 14300 nm 233.7 nm N 1.000 233.7 nm 35RES 0.42 nm 0.21 nm R 1.000 0.121 nm 200






Date: ........... 11.01.2002 ........... Signature:..................................................................



A4 - Uncertainty of measurement3.14 Geometric standard Rub (114A) - Identification (for RSm)

Equation used:

( ) ��

��++++=

Ac : Accuracy of HP laseraL : Repeatibil ity of measurements on the reference standard using laser.ap : Repeatibil ity of measurements on the reference standard using Perthometer.a : The difference between the laser and Perthometer measurement results. (PSmL - PSmp)PSmL : Mean of the measured lengths of the profile elements using laser on the reference standardPSmp : Mean of the measured lengths of the profile elements using Perthometer on the reference standardRSmg : Mean of the measured lengths of the profile elements using Perthometer on the test standard

Note 1: We assume that the ratio RSmg/PSmL is constant.Note 2: RSmg is not corrected with the value ”a”. Instead, the value “a” is taken into account in theuncertainty budget.


( ) � � � � � � � ��

��

+++++=

quantityXi

Estimatexi

uncertaintyu(xi)



ci


ui(d)

degrees offreedom

vi

Ac 0.12 nm 0.12 nm N 0.420 0.05 nm 400aL 1341 nm 1341 nm N 0.420 76.6 nm 53ap 510.7 nm 510.7 nm N 0.420 214.4 nm 8a 1768 nm 1768 nm R 0.420 428.6 nm 200

RSmg 49723 nm 75 nm N 1.000 75 nm 11RES 110 nm 55 nm R 1.000 31.8 nm 200






Date: ............ 11.01.2002 ............ Signature:..................................................................



A4 - Uncertainty of measurement3.15 Geometric standard PTB (7070) - Identification (for RSm)

Equation used:

( ) ��

��++++=




( ) � � � � � � � ��

��

+++++=

quantityXi

Estimatexi

uncertaintyu(xi)



ci


ui(d)

degrees offreedom

vi


RSmg 198617 nm 21 nm N 1.000 21.0 nm 11RES 1000 nm 500 nm R 1.000 288.7 nm 200






Date: ............... 11.01.2002 ............ Signature:..................................................................



A4 - Uncertainty of measurement3.16 Geometric standard PTB (8194) - Identification (for RSm)

Equation used:

( ) ��

��++++=




( ) � � � � � � � ��

��

+++++=

quantityXi

Estimatexi

uncertaintyu(xi)



ci


ui(d)

degrees offreedom

vi


RSmg 119149 nm 29 nm N 1.000 29.0 nm 11RES 350 nm 175 nm R 1.000 101.0 nm 200






Date: ........... 11.01.2002 ........... Signature:..................................................................



A4 - Uncertainty of measurement3.17 Roughness standard SFRN 150 (1.006) - Identification (for Rk, Rpk, Rvk)

Equation used:

�

��

��

�

−

−=

∑∑

∑∑∑

==

=== �

� �

�

� �

�

� �

�

� �

�

� ��

��

��

��

�

zi : Profile height of ith point in the central region of material ratio curveMri : Material ratio of ith point in the central region of material ratio curveN : Number of points which are used to calculate the secant in the central region of material ratio curve using

least square method.


� � �� "!�#�� $$ ++=

Note 1: Please see Appendix 1 for detail explanation of above equationNote 2: Uncertainty calculations for zk are given in Excel sheets in Appendix 2

quantityXi

estimatexi

uncertaintyu(xi)



ci


ui(d)

degrees offreedom

vi

zk 138 nm 41.8 nm N 0.853 36.209 nm 286Mr 50 % 10 % N 0.059 nm 0.006 nm 200RES 0.42 nm 0.21 nm R 1.000 0.121 nm 200

N = normal; R = rectangular; T = triangular; U = U-shaped.RES: ResolutionNote: Uncertainty of Mr are not calculated. The effect of the uncertainty of Mr is very small . The difference between the combined uncertaintiesfor u(Mr)=0 and u(Mr)=100% is less than 1%. u(Mr) is estimated to be 10%.(Please see the Excel sheet)

Combined standard uncertainty: uc(Rk) = 36.2 nm

Effective degrees of freedom: veff (Rk) = 16055.3

Expanded uncertainty: U(Rk) = 72.4 nm with a coverage factor k=2


Date: ......... 11.01.2002 ............ Signature:..................................................................



A4 - Uncertainty of measurement3.18 Roughness standard Fine (629f) - Identification (for Rk, Rpk, Rvk)

Equation used:

�

��

��

�

−

−=

∑∑

∑∑∑

==

=== �

� �

�

� �

�

� �

�

� �

�

� ��

��

��

��

�

zi : Profile height of i th point in the central region of material ratio curveMri : Material ratio of i th point in the central region of material ratio curveN : Number of points which are used to calculate the secant in the central region of material ratio curve using



� � �� "!�#�� $$ ++=


quantityXi

estimatexi

uncertaintyu(xi)



ci


ui(d)

degrees offreedom

vi

zk 1255 nm 79.7136 nm N 0.853 68.012 nm 20.5Mr 50 % 10 % N 0.383 nm 0.038 nm 200RES 0.42 nm 0.21 nm R 1.000 0.121 nm 200






Date: .... 11.01.2002 ........... Signature:..................................................................



A4 - Uncertainty of measurement3.19 Roughness standard Coarse (633g) - Identification (for Rk, Rpk, Rvk)

Equation used:

�

��

��

�

−

−=

∑∑

∑∑∑

==

=== �

� �

�

� �

�

� �

�

� �

�

� ��

��

��

��

�




� � �� !#" $ � %% ++=


quantityXi

estimatexi

uncertaintyu(xi)



ci


ui(d)

degrees offreedom

vi







Date: .......... 11.01.2002 ........... Signature:..................................................................



A4 - Uncertainty of measurement3.20 Roughness standard Very coarse (686sg) - Identification (for Rk, Rpk, Rvk)

Equation used:

�

��

��

�

−

−=

∑∑

∑∑∑

==

=== �

� �

�

� �

�

� �

�

� �

�

� ��

��

��

��

�




� � �� !�� "" ++=


quantityXi

estimatexi

uncertaintyu(xi)



ci


ui(d)

degrees offreedom

vi







Date: ........ 11.01.2002 .......... Signature:..................................................................



A4 - Uncertainty of measurement3.21 Roughness standard SFRN 150 (1.006) - Fine (629f) – Coarse (633g) – Very coarse(686sg) - Identification (for Mr1, Mr2)

Uncertainty of Mr1 and Mr2 was not calculated. Instead, we assume that the relative uncertainty of Rk with respect toRz is valid for Mr1 and Mr2 parameters.

StandardRz

(nm)U(Rk)(nm)k=2 �

��

�� Mr1

(%)U(Mr1)

(%)k=2

Mr2

(%)U(Mr2)

(%)k=2

SFRN 150 (1.006) 138 72.4 0.525 12.606 6.618 83.232 43.697Fine (629f) 1255 136.0 0.108 8.982 0.970 88.158 9.521Coarse (633g) 7608 523.0 0.069 6.196 0.428 81.968 5.656Very coarse (686sg) 14300 634.4 0.044 6.948 0.306 92.850 4.085


Date: ............. 11.01.2002 ............ Signature:..................................................................



APPENDIX 1A Model For

�� Rk, Rpk, Rvk Parameters

The following uncertainty calculation is performed for Rk parameter. It can also be applied forRpk and Rvk parameters.

According to ISO 13565-2, a line (secant) is fitted to the central region of material ratio curve inorder to obtain Rk, Rpk and Rvk parameters. The length in horizontal projection of the secant is 40%. The gradient of the secant is the smallest of the gradients of all secants which have the leng inhorizontal projection th in horizontal projection 40 % .

�

�

!"

#$�%

$�&'%

$)('%

*�+�, -�./ 01/ /2'/ 3'/ 4'/

*5 6 7 8

5 6 7 8

9

Assumptions:

1) The secant AB which is fitted to the central region is on the center of the whole curve. Sothe abscissae of the middle point of the secant is MrM = 50 % (MrA = 30 % and MrB = 70%)

2) z ordinate of middle point M of the secant is

3) Vertical measuring range of the probe MFW-250 is ± 25 µm. This renge is sampled by60000 steps. So it is assumed that at least 100 points can be used to do sampling inhorizontal axis in calculation of Rk for almost all range of standards given. Therefore 100points are used to calculate the least square best fit line.

There are N points between A and B points. 1st order polinomial (the secant) is following:

21* cMrcz += (1)

:; <

= <>

??@ +≅



From the similarity of the triangles CED and AFB, following equation can be written:

zA* : Starting point of secant

zB* : End point of secant

When we substitute Eq(1) into Eq(2) we obtain:

If we can determine c1, Rk can be found as well as with its uncertainty. The secant can bedetermined (i.e. c1 and c2 in Eq.1) using “ least square method”. The main formula for least squaremethod is written as following:

zi*:Ordinate of i th point of fitted polynomial

zi : Ordinate of i th point of the central region of material ratio curveF : Sum of the square of the differences

There are two unknowns c1 and c2 in Eq.1 . For “F” be minimum, derivetives of F with respect toc1 and c2 must be zero. Thus,

�� =

∂∂��

⇒ 0)(21

21 =−+∑=

i

N

iii MrzcMrc (5)

%40%100

**BAk zzR −= (2)

1cRk = (3)

∑=

−=N

iii zzF

1

2* )(

(4)

��

�� +−+=

��

�� −+−=



If we obtain c2 from Eq.6 and substitute into Eq.5, we obtain:

After a simple arrangement we obtain:

Combined uncertainty of Rk :

��

��

��

� ��

��

∂∂+

∂∂= ∑∑

== (8)

........)(1

1Mr

)(1

1Mr

)( 22

2

2

11

2

12

12

2

2

11

2

11

2 +

−

−+

−

−=

∑∑

∑

∑∑

∑

==

=

==

= zu

MrN

Mr

MrN

zu

MrN

Mr

MrN

RuN

ii

N

ii

N

ii

N

ii

N

ii

N

ii

k

...........)(1

12Mr2

11z

........ 12

2

22

11

2

1 1111

22

11

2

11

+

−

−

−−

−

−

+

∑∑

∑ ∑∑∑∑∑∑

==

= ======Mru

MrN

Mr

MrzN

MrzMrN

MrN

MrzN

N

ii

N

ii

N

i

N

iii

N

iii

N

ii

N

ii

N

ii

N

ii

...........)(1

12Mr2

11z

........ 22

2

22

11

2

1 1112

22

11

2

12

+

−

−

−−

−

−

+

∑∑

∑ ∑∑∑∑∑∑

==

= ======Mru

MrN

Mr

MrzN

MrzMrN

MrN

MrzN

N

ii

N

ii

N

i

N

iii

N

iii

N

ii

N

ii

N

ii

N

ii

. (9)

� =

∂∂� �

⇒ 0)(2

121 =−+∑

=

N

iii zcMrc

(6)

��

��

�

−

−==

∑∑

∑∑∑

==

=== ��

��

��

��

��

� ��

��

��

��

�� (7)

��

� =−

−+ ∑∑∑ ∑∑

=== ==

!" ""

!" "

!"

!" "

!" "" #%$&#%$#%$'&(#%$'



Above coeff icients are calculated for 4 different roughness standard by using a QBASICcomputer program. The coeff icients for N = 101 points are following:

Standard∑

=

∂∂

!" "

�&��

∑=

∂∂

!" "

�&��

∑=

∂∂

!" "

�#%$�

�

∑=

∂∂

!" "

�#%$�

��

686sg 0.728 0.00944 48.202 41.40633g 0.728 0.00944 14.507 3.75629f 0.728 0.00944 0.147 0.0003841.006 0.728 0.00944 0.00347 0.000000214Note: 4th order coefficients are used for calculation of effective degrees of freedom.

Verifying whether the extreme point of “F ” function is a minimum or not

Second derivatives of F function:

∑=

=∂∂=

��

�� Always positive

� � ��

=∂∂= Always positive

� � �� =

∂∂= ��

Discriminant:

( ) �� −= Always negative

Because ��! ""# is positive, the point is real minimum.



UME

(Only part of the comment related to changes of the uncertainty)1) We calibrated our roughness instrument by using PTB calibrated depth setting standard withsix grooves. We used only the deepest groove (Pt = 9870 and D = 9820 nm ). The relativeuncertainty is % 0.305 . Our uncertainty for R6 groove (D = 8363 nm) of the depth standard EN806 is 25.6 nm, our relative uncertainty is % 0.306 (Section 3.1–3.3, P:8–10 in UME ReportAppendix B1 in Draft A) . As can be seen, our relative uncertainty in the comparison is equal tothe uncertainty of our reference standard. This is caused by an error in the uncertainty model usedfor D parameter. In the model, z values of measured profile were being averaged according to theassumption of randomly distributed z-values. We applied this for the uncertainty of referencestandards as well as for our measurements on the sample. But Dr. Koenders explained that theuncertainty of our reference standard was systematic not random. So we can not apply averagingfor the uncertainty of reference standard. The corrected uncertainty equations and the budgets forD parameters can be seen in the attachment. According to the equations in the attachment,uncertainties for D parameters were recalculated. The results are as following:

Groove R1 (D = 282 nm), U(D) = 20.2 nm (k = 2)Groove R3 (D = 1364 nm), U(D) = 24.4 nm (k = 2)Groove R6 (D = 8363 nm), U(D) = 70.8 nm (k = 2)

2) We calculated the uncertainty only for Rz parameter (Section 3.7–3.13, P:14–20 in UMEReport Appendix B1 in Draft A) . And we used this calculated absolute uncertainty for Ra andRz1max in order to be on a safe side, because background noise level is high in our laboratory(Rzo = 33nm). But our uncertainties for Ra parameters seem very large when compared to othercountries in the comparison. So we think that two uncertainty contributions should be changed inthe budget. One of them is the systematic deviation (the difference between UME and PTB) andthe other is standard deviation of the parameter on the surface. The systematic deviation may becalculated for Ra instead of Rz. Standard deviation of Ra may be used instead of Rz on thesurface. The corrected model equation, the uncertainty equation and the budget can be seen in theattachment. According to the equations in the attachment, uncertainties for Ra parameters werecalculated. The results are as following:

Geometric Standard P114A (Ra = 505 nm), U(Ra) = 20.0 nm (k = 2)Geometric Standard 7070 (Ra = 2978 nm), U(Ra) = 46.0 nm (k = 2)Geometric Standard 8194 (Ra = 901 nm), U(Ra) = 25.2 nm (k = 2)Roughness Standard 686sg (Ra = 2346 nm), U(Ra) = 73.4 nm (k = 2)Roughness Standard 633g (Ra = 1533 nm), U(Ra) = 30.8 nm (k = 2)Roughness Standard 629f (Ra = 147 nm), U(Ra) = 20.0 nm (k = 2)Roughness Standard 1.006 (Ra = 24 nm), U(Ra) = 19.4 nm (k = 2)

Documents

Appendix B1 Reports of UME - National Physical Laboratoryresource.npl.co.uk/euromet/length/projects/reports/600-surf-texture/... · 2, 50 8, 33 0, 5 0, 9 0, 5 s t d. d e v./ n m 11,