Electronic Speckle Pattern Interferometry:
Temporal vs. Spatial Phase-Shifting
PH564
Portland State University
Project Report
Oliver Erne
Abstract:
Electronic Speckle Pattern Interferometry is an optical full-field measurement method to
determine deformations on object surfaces with sensitivity below fractions of the
wavelength of light. An object beam back scattered of an object surface and a reference
beam, originating from the same laser light source are superimposed on a video camera
and interfere to a speckle pattern. Speckle pattern recorded before and after deformation
of the object yield to a non-unique fringe pattern. Using a phase shifting method, this
non-uniqueness can be solved and the fringe pattern evaluated using a computer
algorithm. This report summarizes two common phase shifting methods, temporal and
spatial phase shifting, and exhibits their advantages and disadvantages in a comparison.
Electronic Speckle Pattern Interferometry:
Electronic Speckle Pattern Interferometry (ESPI) is a widely used technique to measure
full-field deformation on surfaces of many kinds of objects. This optical technique allows
detecting deformation with sensitivity smaller than the wavelength of light (Jones and
Wykes 1989; Kreis and Geldmacher 1991). Laser light is used to illuminate the object
surface in a full-field manner using diverging optics (L1). The back-scattered light is
collected with a lens and imaged on the light sensitive chip of a video camera (CCD). In
addition, a divergent reference beam (diverging optics L2), originating from the same
laser light source is superimposed via a beam splitter (BS) on the CCD. This setup is
commonly called out-of-plane setup due to its measurement sensitivity nearly
perpendicular to the object surface (Fig.1). Both wave fronts, back scattered from the
object and of the reference beam interfere and form a speckle pattern, which can be
detected using a CCD camera. For later reference, this speckle pattern of the nondeformed object is digitized and stored by a computer. The intensity at each point of the
CCD can be described by
I x, y   I 0 x, y 1   ( x, y) * cos ( x, y)
where x,y are the coordinates on the chip, I 0 is the intensity of the laser light,  describes
the contrast function and  the phase of the wave front(Burke, Helmers et al. 1998).
After deformation of the object surface, the wave front, emanating from the object is
slightly deformed, whereas the wave front of the reference beam remains constant. The
new resulting speckle pattern on the CCD is then as well digitized and stored in the
computer. A subtraction of the two images result in a fringe pattern, which reflects the
deformation of the object surface between the original and deformed state (Fig.2).
However, this fringe pattern is not unique and requires additional information for
subsequent evaluation.
Object
M1
L1
BS
L2
M2
CCD
BS
Lens
Laser
Fig.1: Optical setup for ESPI (out-of-plane)
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PV = 18.663
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108.8 128.9 148.1 168.1 187.6 207.7 Def or mat i on [ µm]
P V = 18.663
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Dr . E t t emeyer GmbH & Co.
Fringe
Pattern
Dr . E ttemeyer GmbH & Co.
Positiv
Negativ
Fig.2: Fringe pattern and sign ambiguity
Temporal phase shifting:
While the fringe pattern describes the surface deformation of the object, its appearance is
not unique. The direction of the deformation, towards the optical setup or away, can only
be detected with the determination of the phase  . This is commonly done by application
of phase shifting techniques. The optical setup is altered with a phase shifter in one of
both beams (Fig.3). This phase-shifter (e.g. piezo element behind mirror) allows adding a
known phase shift to the random phase  . Several images (i.e. ≥3) are recorded in a
temporal manner, using different known phase shifts (i.e. /2, 3/2, 5/2). Subsequently,
the phase angle  can be calculated utilizing
 I 3 ( x, y)  I 2 ( x, y) 

 I 1 ( x, y)  I 2 ( x, y) 
 ( x, y)  tan 1 
where I n describes the intensity at x,y in accordance to the additional applied phase shift
(Creath 1991). The phase difference (after subtraction) is usually displayed in a phase
map, which contains still the information of the fringe pattern and in addition the
directional information of the deformation (Fig.4). Phase maps are unwrapped using a
computer algorithm to display the deformation in e.g. color-coded plots.
Phase shifter
Fig.3: Optical setup with phase shifter in reference beam path
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2.12
Z
1.41
0.70
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103.75
122.02
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61.28
62.62
Phase map
2-image
40.04
Y
32.91
X
18.80
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PV= 3.537
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Fig.4: Phase map and subsequent unique evaluation
Ettemeyer LLC
aoutofplane-entlastung.TFD
This temporal phase shifting method does not only solve the ambiguous sign of the
deformation it improves as well the resolution of the system up to /100 (Kreis and
Geldmacher 1991). Although ESPI with temporal phase shifting is a powerful tool to
measure small deformations over the full field of object surfaces, only quasi-static
deformations can be accessed. Even small deformations during acquisition of the 3 phase
shifted images would result in an additional unknown phase shift and might disturb the
phase calculation. There are more stable algorithms available, which involve 4 or more
images to determine the phase (Creath 1991; Kreis and Geldmacher 1991). However due
to large acquisition times, fast dynamic deformations, with exception of harmonic
vibrations cannot be recorded.
Spatial phase shifting:
Small alterations in the optical setup allow for a different, so called spatial phase shifting
method. First, the aperture of the imaging lens needs to be decreased to create larger
speckle (≥ than 3 pixel of the CCD), originating from the object beam. Furthermore, the
reference beam needs to be positioned, so that its wave front incidents in an angle in
respect to the wave front of the object beam (Fig.5). Assuming that the phase over one
speckle is constant, this setup allows determining the resulting phase of object and
reference beam in respect to adjacent pixels (Fig.6). Using only one image the phase can
be determined by (Burke, Helmers et al. 1998)

 ( xn , y)  tan 1  3


I ( xn1 , y)  I ( xn1 , y)
 mod  .
2 I ( xn , y)  I ( xn1 , y)  I ( xn1 , y) 
This setup and algorithm can be used to detect static as well as dynamic deformations.
Fast dynamic deformations can be detected by using a pulsed laser with short
illumination times. Despite the advantages of the spatial phase shifting method, phase
gradients over the size of speckles and non-continuities between speckles add significant
noise to the system.
Object
M1
L1
BS
L2
M2
CCD
BS
Lens
Laser
Fig.5: Optical setup for spatial phase shifting.
Fig.6: Wave fronts and resulting spatial phase distribution on CCD
Comparison:
In comparison, both methods have their advantages and disadvantages and should be
considered in respect to the application. The following table summarizes the advantages
and disadvantages of both methods (Tab.1). In addition, Fig.7 displays the phase map of a
fast-deformed metal plate recorded with both methods (Burke, Helmers et al. 1998).
Temporal phase shifting
• Accurate
• Mechanical components
• min. 4 recorded frames
• Less noise
• High sensitivity to
external sources (environment)
• Full resolution
Spatial phase shifting
• Less accurate
• No mechanical components
• 2 recorded frames
• More noise
• Low sensitivity to
external sources
• Reduced resolution
(due to large speckle)
Tab.1: Comparison of temporal and spatial phase shifting technique
Temporal phase shifting
Spatial phase shifting
Fig.7: Phase map of fast deforming, centrally loaded metal plate: Comparison of temporal
vs. spatial phase shifting technique (Burke, Helmers et al. 1998)
Conclusion:
This project report gives a small summary to common phase shifting methods in ESPI.
While in ESPI for deformation measurements the sign ambiguity is not solved, phase
shifting methods are used to allow for unique evaluation of full-field deformations.
Despite the great accuracy, ESPI with temporal phase shifting is limited to quasi-static
deformations or in special cases to harmonic vibrations (stroboscopic illumination i.e.
vibro ESPI). Spatial phase shifting adds the possibility of measuring even fast dynamic
deformations, but introduces additional noise.
References:
Burke, J., H. Helmers, et al. (1998). "Messung schnell veränderlicher Verformungen mit
räumlich phasenschiebender elektronischer Specklemuster-Interferometrie (ESPI)." Z.
Angew. Math. Mech. 78: 321-322.
Creath, K. (1991). Phase-measurement interferometry: Beware these errors. SPIE Laser
interferometry IV.
Jones, R. and C. Wykes (1989). Holographic and speckle interferometry, Cambridge
University Press.
Kreis, T. M. and J. Geldmacher (1991). Evaluation of interference patterns: a comparison
of methods. SPIE.