Moire thread counter

1.

Problem № 13
“Moiré Thread Counter”
When a pattern of closely spaced non-intersecting lines
(with transparent gaps in between) is overlaid on a piece
of woven fabric, characteristic moiré fringes may be
observed. Design an overlay that allows you to measure
the thread count of the fabric. Determine the accuracy
for simple fabrics (e.g. linen) and investigate if the
method is reliable for more complex fabrics (e.g. denim
or Oxford cloth).
Team Russia
Reporter: Nika Gribova

2. Basic concept

Moiré pattern is a pattern that occurs when two periodic grids are overlapped.

3.

Review
Theoretical model
Basic concepts(grid, period)
Qualitative explanation of the moiré`s pattern
Geometric moiré
Determination of the formula`s accuracy
Mathematical model and special cases
Experimental comparison(direct and indirect measurement)
calculate the number of threads
Checking our method for complex fabric
dependences(period of the moiré pattern on angle and overlay`s
period)
3

4.

Basic concepts
d f l
grid
d
Period of fabric
f
Distance between the threads
l
Width of the thread
d
f
IYPT
l
Experimental Set-up +
accuracy
Theory Model
Applicability
4

5. Complex weave

Denim (jeans fabric)
Complex weave
Fabric «Oxford»
Twodimensional
structure
IYPT
Experimental Set-up +
accuracy
Theory Model
Applicability
5

6. Quality explanation

IYPT
Experimental Set-up +
accuracy
Theory Model
Applicability
6

7.

Geometric Moiré
Transparent lines
d1
D
d1
A
d2
D
IYPT
B
d2
F
C
d1 d 2
d12 d 22 2 d1 d 2 cos
Experimental Set-up +
accuracy
Theory Model
Applicability
7

8. Физическая модель

0
Special case
D
d 1d 2
d 1 d 2 2d 1d 2 cos 0
2
2
d 1d 2
D
d1 - d 2
d 2 d1
cos 2 sin
D
D
d
2 sin
IYPT
Experimental Set-up +
accuracy
Theory Model
2
2
2
n
1
1
2 D sin
Applicability
2
9

9.

Number of threads per 1 cm
1
1
n1 d1 сm
2 d 2 cos
d
2
n1
n1
1
n1 ( , D,d 2 )
IYPT
1 сm
D
1
d2
n1
1 сm
2
2
d 1 .1
D cos d 22 D 2 sin 2
d2D
Experimental Set-up +
accuracy
d 1.2
Theory Model
Applicability
10

10. Number of threads per 1 cm

Fabric with
less period
Fabric with
bigger
period
n1 ( , D,d 2 )
IYPT
Experimental Set-up +
accuracy
D cos d 22 D 2 sin 2
d2D
Theory Model
Applicability
11

11.

Experimental set-up
overlay
0,5мм
0,2мм
0,1мм
rulers
Screw with nut
IYPT
Experimental Set-up +
accuracy
protractor
Theory Model
Applicability
12

12.

The calculation of the period of moiré
y
y
90
x
IYPT
D
Experimental Set-up +
accuracy
D
Theory Model
x
x y cos
x 2 y 2 2 xy sin
Applicability
13

13. The calculation of the period of moiré

Direct measurement of the number of threads
Errors of the
number of threads
of direct method:
n1 d1
n1 them.
We take around 20 measurements and average
d1
IYPT
Experimental Set-up +
accuracy
Theory Model
Applicability
14

14. Direct measurement of the number of threads

Error of set up
n1 ( , D,d 2 )
2
D
D
D
D
x
y
x
y
2
D cos d 22 D 2 sin 2
d2D
2
n1
n1
n1
2
2
2
n1 (
d 2 ) (
) (
D)
d 2
D
1
n
Т
nотн nабс
IYPT
Experimental Set-up +
accuracy
d 2 0,01мм
1
Theory Model
D
x y cos
x 2 y 2 2 xy sin
Applicability
15

15. Error of set up

Table values at 15
X,мм
0,1
0,15
0,2
0,079
0,03
0,87
0,031
0,105
0,031
…
6
y,мм
0,1
0,15
0,2
0,87
0,031
0,105
0,031
0,174
0,045
0,119
0,032
0,13
0,034
0,186
0, 063
0,13
0,034
0,1586
0,0356
0,195
0.65
The period of
moiré,мм
0,079
0,87
…
0,42
14,9
2,14
12,3
1,5
…
0,82
14,6
2,1
12,26
1,7
…
1,15
14,2
1,96
12,1
1,94
…
overlay, мм
…
8
IYPT
0,096
0,1
0,01
0,11
0,012
0,11
Experimental Set-up +
accuracy
5,347
1,54
The period of
moiré
error of moire
period
Theory Model
Number of
threads per cm
Error of set up
Applicability
16

16. Table values at 15

Dependence of the moiré pattern
period on the rotation angle
D
d 1 1,3mm
d 2 0,82mm
2
d1 d 2
d d 2 d1 d 2 cos
2
1
D, мм
2,5
2
2
1,5
1
D, мм
d1 1,02mm
d 2 1mm
9
8
0
5
10
15
20
25
D, мм
30
35
,
d 1 1,15mm
d 2 0,93mm
5
7
4
6
5
3
4
3
2
2
1
0
5
10
15
20
25
30
35
40
45
,
1
0
5
10
15
20
25
30
35
,

17.

Dependence of the moire period on the overlay
D, mm
5
d1 1,15mm
4,5
15
4
3,5
3
2,5
2
Optimal is the overlay with a period close to the period of fabric
1,5
1
0,5
d 2 , мм
0
0
0,5
1
1,5
2
2,5
3
18

18. Dependence of the moire period on the overlay

Comparison between direct and indirect measurement
Number of threads per cm
35
Direct measurements
30
25
20
15
10
5
coarse
calico 1
coarse
calico 2
chintz
cambric
Sateen
denim
Different
fabrics
0
IYPT
Experimental Set-up +
accuracy
Oxford
Theory Model
Applicability
20

19. Comparison between direct and undirect measurement

Applicability of designed overlay
distance
Intensity
colour
IYPT
Experimental Set-up +
accuracy
Theory Model
contrast
Applicability
21

20. Comparison between direct and indirect measurement

Set up with improved resolution
800 kilo luxsensor of (order
of 1000 luxsensor)
Receive images
60 kilo luxsensor
0,55м
laser
overlay
22

21. Applicability of designed overlay

Limitations of the visibility of a moiré pattern
Critical angle
Angular resolution
Q 1.220
Dаппертуры
23

22. Set up with improved resolution

Applicability of designed overlay
We don’t see the moiré
pattern(the distance between
our eyes or camera and overlay
with the fabric is too small)
We see the moiré pattern
We don’t see the moiré
pattern(the distance between
our eyes or camera and overlay
with the fabric is too big)
IYPT
Experimental Set-up +
accuracy
Theory Model
Applicability
24

23. Limitations of the visibility of a moiré pattern

Applicability of designed overlay
Thickness of the overlay’s line
Thickness of the
thread