1. INTERFEROMETRIC TECHNIQUES
1. Moiré
shadow
projection
2. Digital fringe analysis
intensity methods
temporal phase measurement
spatial phase measurement
phase unwrapping
3. Light interference
4. Holographic
5. Speckle

2. 1. Moiré
Moiré patterns result from the interference (superposition) of high frequency gratings
or interference of electromagnetic waves :
sinusoidal grating
128 (1+sin(2px /p +f))
grating
rotated a
Moiré interference :
low frequency pattern
of black and white stripes
Superposition of gratings is equivalent to their product, and this is in turn the same
as sampling : white strips separation is the horizontal sampling period, while the vertical
period is 1 (no sampling).
Moiré patterns are just a type of aliasing , that is, sampling a grating of period p at a
frequency less than 2/p (Nyquist limit).

3. 1. Moiré
The Moiré effect can be achieved through gratings, white light projected fringes or
interference of coherent light waves : the difference is the wavelength and consequently
the period of fringes.
Often gratings are transparences with transmittances given by a square-wave function
instead of a sinusoidal one. The result is similar : all types of periodic gratings can be
descomposed as a sum of sinusoidal gratings.

4. 1. Moiré Projection Moiré
Fringes are projected on the surface and the image is interfered digitally in the computer with
a stored grating, or the images the same grating projected on two surfaces are interfered.
surface
The camera sees a
grating of period

5. 1. Moiré
Should the angle between lighting and plane normal or the viewing direction change, the
observed period p would be different but constant : fringes would be equally spaced.
Now substitute the flat surface for a curved one : u
but now
surface height with respect to the
reference plane : the plane that
would produce equally spaced
fringes with period p : t1 , the
grating used to demodulate y(x,y)

6. 1. Moiré

7. 1. Moiré level curves of the face of two
good sinks : lines are mostly parallel
level curves of a good surface (red) and one with an slight bump (green) :
lines cross ones to the others much more

8. 1. Moiré
Let be t1 a sinusoidal grating of constant frequency and vertically oriented :
a = 128
p = 40 pixels
x =
The principle behind measurement methods through Moiré interference is that somehow
the quantity to measure y(x,y) 3D shape ,
1) gets codified into the horizontal displacement u(x,y) of the grating lines from its
original position divided by the grating period p :
2) mathematically : it becomes phase modulated :

9. 1. Moiré
When the two gratings are superposed (interfere) the resulting transmittance t is :
original gratings
second grating with
doubled frequency
Moiré pattern
t(x, y) has a maximum (centers of brigh fringes) whenever
y(x,y) = n, for n = 0,  1,  2, ...
and minima (centers of black fringes) whenever
y(x,y) = n + 1/2, for n = 0,  1,  2, ...
 the Moiré pattern forms level curves of y(x,y)

10. 1. Moiré

11. 1. Moiré
If gratings were already modulated by functions y1(x,y) and y2(x,y) then the Moiré
pattern would be their difference y1(x,y)  y2(x,y) : we would obtain the level curves
of the three-dimensional difference function between two surfaces, for instance for
flaw detection or tolerance gauging in surface comparison.
We have assumed that both gratings were oriented vertically, except for the phase
introduced in t2. Were it not the case, the Moiré effect also occurs but level curves
get rotated in the same amount as the angle between the gratings. a
p /2sin(a/2)

12. Deformation detection in TV screen grids
Backlight + Moiré
Deformation detection in TV screen grids
right part
very damaged part

13. Backlight + Moiré camera test grid right reference grid
Moiré interference
Backlight setting

14. Backlight + Moiré
a simple thresholding outlines the main bumps

15. 1. Moiré
Shadow Moiré
The Moiré pattern is formed by the interference of a grating and the shadow it casts
over a surface
lighting
direction
viewing
Point P0 is projected to a point P1 on the surface which, by viewing, is projected to the
point P2 again on the grating. Thus, the displacement of the grating relative to its
shadow is
Therefore

16. 1. Moiré A bright fringe is obtained whenever
y(x,y) = n, for n = 0,  1,  2, ...
and
y(x,y) = n + 1/2, for n = 0,  1,  2, ...
In this way a topographic map is formed
over the surface. However, we have assumed
point source and camera at infinite distances
so that angles don’t change among points

17. Shadow Moiré
Shadow Moire videos :
Video 1 : deforming wet A4 paper
Video 2 : two overlaping A4 papers

18. 2. Digital fringe analysis
Temporal Phase Modulation Interferometry (TPMI)
if a1= p/4, a2= 3p/4 and a3= 5p/4,

19. Example : FringePro
phase
unwrapped phase
plot