# uncertainty-procedure_sphere-gonio

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```					The Presentation of the results of Measurements can be divided into eight steps

1. Design a measurement equation (model of evaluation) for determination of the measurand including all input
quantities that significantly contribute to the measurement result (value and associated MU).
The output quantity is stated and the model of evaluation developed as an algebraic equation combining all the
input quantities to calculate the value of the output quantity.
2. Determine the estimated value for all input quantities

3. Determine for all input quantities the associated standard uncertainty using Type A evaluation (statistical
method) or Type B evaluation (any other method).

4. Determine the covariances for all input quantities with correlated MUs.

5. Calculate measurement results from input quantities with the model of evaluation.

6. Determine the combined standard MU from the standard MUs and covariances of the input quantities and
from the related sensitivity coefficients.

7. Determine the effective DOF and the related value for the coverage factor for the intended confidence level.

8. Report the result of the measurement together with the associated expanded MU
Calibration of Luminous Flux by and Integrating Sphere
Incandescent reference / Incandescent test lamp (secondary standard)
current set using a voltmeter to measure the current through a calibrated shunt, R
broadband detector with lumen photpic filter used to obtain signals
Model
����������������=(1−D��������−gD����)
〖����������������〗_����=(1−〖∆��������〗_����−����_���� 〖∆����〗_���� )

F=F_����·����/����_���� ·����_��������/����_���� ·((����·����)/(����·����))−����_����·((����_����·����)/(����_����·����)) ����_��������·(����_����/����

variables relating to test lamp have no subscript
subscript 'R' refers to reference lamp standard
subscript 's' refers to sphere
Table
urel,iy
Abs. std.                                  Abs.           Abs.             Relative
Value                                     DOF
No                       Quantity Xi                Symbol Unit                        uncertainty           Type               sensitivity   contribution       contribution
xi                                       n
u(xi)                                     ci           ui(y)              urel(y)


3   sphere spatial response factor -test lamp D S f

0.001         0.0012               B                 -1.0000       -0.00120           -0.00120
4   relative aging coeff.-test lamp                    g        1/h      0.0003         0.0003               B                 -0.1000       -0.00003           -0.00003
5   burning time-test lamp                            Dt         h        0.10              0                B       
6   correction factor -test lamp

corS               0.9990                                                               0.00120             0.0012
9   sphere spatial response factor-REF               DSfR                0.000          0.00050              B                  -1.000       -0.00050           -0.00050
14   relative aging coeff.-REF                         gR        1/h     0.0002          0.0001               B                 -10.000       -0.00100           -0.00100
15   burning time-REF

DtR         h       10.00             0                 B       
12   correction factor-REF
X   i
corS R              0.9980             u      xi   
    vi
0.00112            0.00112
13   correction factor-REF                           corS R              0.9980          0.00112              A                  7026.4       7.855739           0.001120

14   correction factor-test lamp                      corS               0.9990          0.00120              A                 -7019.6       -8.426121          -0.001202

15   luminous flux-REF                                 FR        lm      2800.0           4.800               B                  2.504        12.021144          0.001714

16   photometer-source
X   i
y          V       4.579          0.0085
u      xi   
A       9    vi
1531.4       13.017000          0.001856

17   photometer-REF                                    yR         V       1.765          0.0007               A       9          -3973.0       -2.781096          -0.000397

18   photometer AUX-test lamp                          yA         V      3.1234           0.001               A       9          -2245.1       -2.245097          -0.000320

19   photometer AUX-REF                                y AR       V      3.1243           0.001               A       9           2244.4       2.244450           0.000320

20   shunt voltage-test lamp                           U          V      0.88000         0.00012              A       9          -55461.2      -6.655344          -0.000949

21   shunt voltage-REF                                 UR         V      0.58000        0.000075              A       9          86082.5       6.456184           0.000921
-3.284       -1.248087          -0.000178
22 current-lumen exponent-test lamp                    mJ                  6.96            0.38               B       

23   current-lumen exponent-REF                       m JR             7.12                0.22               B                 -30.862       -6.789553          -0.000968

26   spetral mismatch-test lamp                        F                 1                0.001               B                 -7012.3       -7.012341          -0.001000

27   spectral mismatch-REF                             FR                1               0.0005               B                  7012.3       3.506167           0.000500
28   shunt resistor                                    R        Ohm 0.100042            0.000006              B                -499068.6      -2.994412          -0.000427
29   cal. factor current DVM                           c             1.00032            0.000041              B                  559.96       0.022958           0.000003
32   nominal current-source                             J         A  8.7950                  0
33   nominal current-REF                               JR         A  5.8250                  0                                                                    0.002631

34   luminous flux - test lamp                         F1        lm   7012.3                                         124                         25.86             0.0037

found from approximation formula: k = 2.03                                      52.5              0.0075

variance - Test Lamp         u dev  y        0.26%
variance - REF               uin st y        0.26%
Measurement of Luminous Flux by and Integrating Sphere
Incandescent reference / SSL or CFL test lamp
spectral detection
current read as DVM voltage with a shunt resistor, R
Model
corS=(1+a〖∆����〗_����−D������������−����(����)−gD����)
����������������=(1+a〖∆����〗_����−D ����−gD����)

〖����������������〗_����=(1+����_���� 〖∆����〗_��������−〖∆��������〗_����−����_���� (����)−����_���� 〖

F=F_����·����/����_���� ·����_��������/����_���� ·((����·����_����)/����_0 ) ����_����·((����_����·����_

test lamp variables do not have subscripts
subscript 'R' refers to reference lamp standard
subscript 's' refers to sphere
Table                                                                manual entries are highlighted in blue
urel,iy
Abs. std.                                                     Abs.                 Relative
Value                                   DOF         Abs. sensitivity
No                       Quantity Xi              Symbol Unit                     uncertainty         Type                                    contribution          contribution
xi                                     n                 ci
u(xi)                                                       ui(y)                 urel(y)
1   ambient temp. difference

D Ta       °C           2.0       1.0              A       29              0.0020            0.00200              0.00199
2   ambient temp. coeff.                             a       1/K      0.002        0.001              A       29              2.0000            0.00200              0.00199
3   sphere spatial response factor                 Dsf                     0.0     0.0012             B                      -1.0000           -0.00120            -0.00120
4    stray light                                    S( q )               0.0        0.0050             B                      -1.0000           -0.00500            -0.00498
5    relative aging coeff.                           g        1/h      0.0003       0.0003             B                      -0.1000           -0.00003            -0.00003
6    burning time                                    Dt        h        0.10           0               B         
7    correction factor -test lamp                   corS               1.0040                                2.15E+03                             0.00587             0.0058
8    ambient temp. difference-REF

DTaR        °C        2.0          1.0              A        29             0.00015            0.00015             0.00015
9    ambient temp. coeff. -REF                      aR        1/K     0.00015      0.00002             B                        2.000            0.00004             0.00004
10   sphere spatial response factor-REF            DsfR                  0.0       0.00050             B                       -1.000           -0.00050            -0.00050
11   stray light-REF                               SR(q)                 0.0       0.00200             B                       -1.000           -0.00200            -0.00200
12   relative aging coeff.-REF                      gR        1/h      0.0002       0.0001             B                       -2.000           -0.00020            -0.00020
13   burning time-REF                               DtR        h        2.00           0               B         
14   correction factor-REF
X   i
corS R              0.9999        u      xi   
1066138 vi
0.00208              0.00208
15   correction factor-REF                         corS R              0.9999      0.00208             A     1066138            909.44           1.888946            0.002077
16   correction factor-test lamp                    corS               1.0040      0.00587             A     2.15E+03           -905.78          -5.315723           -0.005846
17   luminous flux-REF                               FR        lm      1715.0       8.600              B                      0.53023           4.560005            0.005015
18   photometer-test lamp                            y         lm       920          9.6               A         9              0.988            9.488867            0.010435
19   photometer-REF                                  yR        lm      1715.0        5.0               A         9              -0.530           -2.651188           -0.002915
20   photometer - AUX test lamp                      yA        lm      790.0         2.0               A         9              -1.151           -2.302166           -0.002532
21   photometer-AUX REF                             y AR       lm      805.0         1.0               A         9              1.130            1.129627            0.001242
22   measured voltage-test lamp                      U          V      119.99       0.012              A        29                0.0            0.000095            0.000000
23   cal. factor AC voltage                          cU                0.9986      0.00104             B                       910.62           0.947050            0.001041

24 voltage-lumen expoent - test lamp                mU                      0.5       0.1              A        9
25   shunt voltage-REF                               UR        V 0.08490           0.000006            A       29              76261.14          0.457567            0.000503
26   cal. factor DC voltage                          cR           0.9965           0.000043            B                      6497.31           0.279384            0.000307
27   shunt resistor                                  R       Ohm 0.099999          0.000071            B                     -64746.62          -4.597010           -0.005055
28   current-lumen exponent-REF                     m JR           7.12              0.22              B                      -3.18103          -0.699827           -0.000770
29   nominal voltage - source                        U0        V  120.00               0
30   nominal current-REF                             JR        A  0.8490               0                                                                             0.012226
29   luminous flux- test lamp                        F        lm   909.3                                        35                                13.38               0.0147

found from approximation formula: k =            2.09                                28.0               0.0308

variance - Test Lamp      ud ev  y        1.22%
variance - REF            uin st y        0.82%
Measurement of Luminous Intensity by and a Goniometer
Incandescent reference / Any type of test lamp
current read by DVM using calibrated shunt
Model
����������������=(1+〖a〖∆����〗_����+2D����〗∕����+ℎ(����)+����(j)−����(q)−gD����)

〖����������������〗_����=(1+〖����_���� 〖∆����〗_��������+〖2∆����〗_����〗∕����_���� +ℎ_���� (����)+����_���� (j)−����_����−����_

����=����_����·����/����_���� ·((����·����)/(����·����))−����_����·((����_����·����)/(����_����·����)) ����_��������·����_����/����·〖

test lamp variable do not have subscripts
subscript 'R' refers to reference lamp standard

Table                                                                                 manual entries are highlighted in blue
Abs. std.
Value
No                          Quantity Xi                   Symbol           Unit                   uncertainty          Type
xi
u(xi)
1    amb.temp. difference - test lamp

DT a              °C            2.0        1.0               A
2    rel.temp.coeff. - test lamp                             a              1/K          0.0007     0.0003              B
3    relative dist. variation - test lamp                  D d /d                          0.0     0.000300             B
4    angular tilt - test lamp                              h ( q)                          0.0     0.001500             B
5    angular turn - test lamp                              k ( j)                          0.0     0.000650             B
7    stray light - test lamp                               S(q)                           0.001      0.001              B
6    rel.aging coeff. - test lamp                            g              1/h          0.0003     0.0003              B
8    burning time - test lamp                                Dt              h             0.10        0                B
9    correction factor - test lamp                          corS                         1.0004
10   amb.temp. difference - REF

DTaR               °C            2.0        1.0               A
11 rel.temp.coeff. - REF                                    aR              1/K         0.00015    0.00002              B
12 relative distance variation - REF                     D d R /d R                        0.0     0.00050              B
13 angular tilt - REF                                      h R ( q)                        0.0     0.00020              B
14 angular turn - REF                                      k R ( j)                        0.0     0.00040              B
16 stray light - REF                                      SR(q)                           0.005      0.001              B
15 rel.aging coeff. - REF                                   gR              1/h          0.0002     0.0001              B
17 burning time - REF                                       DtR              h             5.00        0                B
18 correction factor source - REF
X   i
corS R                        0.9943
u      xi   

19 correction factor - REF                                 corS R                        0.9943    0.001573             A
20 correction factor -test lamp                             corS                         1.0004    0.002210             A
21 luminous intensity - REF                                  IR              cd          280.00      0.680              B
22 photometer signal - test lamp                             y               V            4.579     0.0085              A
23 photometer signal - REF                                   yR              V            1.765     0.0007              A
24 shunt voltage                                              U              V          0.88000    0.00012              A
25 shunt voltage - REF                 UR           V        0.58000    0.000075       A
26 current-intensity exponent          mJ                     6.96        0.38         B
27 current-intensity exponent - REF    m JR                   7.12        0.22         B
28 Spectral mismatch - test lamp       F            K         2900         25          B
29 Spectral mismatch - REF             FR           K         2800         10          B
30 detector non-linearity-test lamp   H(q)                    1.002      0.002         A
31 detector non-linearity-REF         HR(q)
d   P   S
0.995      0.002         A
32 Distribution sample - test lamp     Ds                     1.000      0.01          B
33 Distribution sample - REF           Ds R
c
d   P
P   S
1.000      0.001         B
34 shunt resistor                     m
R TS   1
Ohm      0.100042    0.000006       B
35 cal. factor - DVM                    c                   1.00032     0.000041       B
36 nominal current of test lamp        T
J A
A        8.7950         0
37 nominal current - REF                JR          A        5.8250         0
38 intensity at nominal current            I       cd         668.7

found from approximation formula: k =
ighted in blue
Abs.           Abs.         Relative
DOF
sensitivity   contribution   contribution
n
ci            ui(y)         urel(y)
29       0.0007        0.00070        0.00070
         2.000        0.00060        0.00060
         2.000        0.00060        0.00060
         1.000        0.00150        0.00150
         1.000        0.00065        0.00065
        -1.000        -0.00100       -0.00100
        -0.100        -0.00003       -0.00003

2,880                     0.00221        0.00221
29       0.00015        0.00015        0.00003
         2.0000         0.00004        0.00000
         2.0000         0.00100        0.00101
         1.0000         0.00020        0.00023
         1.0000         0.00040        0.00040
         -1.0000       -0.00100        0.00000
         -5.0000       -0.00050       -0.00050

350,645                       0.00157        0.00023
vi

350,645         672.5         1.05785        0.00158
2,880      -668.5        -1.47718       -0.00221
         2.388         1.62399        0.00243
9         146.0         1.24131        0.00186
9         -378.9        -0.26521       -0.00040
9          -5289        -0.63466       -0.00095
9       8209      0.61567     0.00092
      -0.3132    -0.11902    -0.00018
      -2.9430    -0.64746    -0.00097
      -0.2306    -5.76509    -0.00862
      0.2388     2.38822     0.00357
9       -667.4    -1.33474    -0.00200
9       672.1     1.34412     0.00201
       -668.8    -6.68767    -0.01000
       668.7     0.66870     0.00100
       -1069     -0.00642    -0.00001
       107.0     0.00439     0.00001

0.01355
31,018               9.8217     0.0147

2.00                 19.6      0.0294

variance   test lamp    1.36%
variance      REF       0.57%

```
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