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 non-deformed object is digitized and stored by a computer. The intensity at each point of the CCD can be described by
where x,y are the coordinates on the chip, 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.
Fig.1: Optical setup for ESPI (out-of-plane)
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
where 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.
Fig.3: Optical setup with phase shifter in reference beam path
Fig.4: Phase map and subsequent unique evaluation
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)
.
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.
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 / Spatial phase shifting• Accurate / • Less accurate
• Mechanical components / • No mechanical components
• min. 4 recorded frames / • 2 recorded frames
• Less noise / • More noise
• High sensitivity to
external sources (environment) / • Low sensitivity to
external sources
• Full resolution / • 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.