# Electronic speckle pattern interferometry

The Electronic speckle pattern interferometry (ESPI), Eng. Electronic Speckle Pattern Interferometry is an interferometric measuring method for the non-contact measurement of optical path changes. These can e.g. B. caused by surface deformations of components. ESPI is used for stress and strain measurement, for vibration analysis and for non-destructive material testing.

## history

Electronic speckle pattern interferometry was proposed independently by Butters and Leendertz, Schwomma and Macovski, Ramsey and Schaefer in the early 1970s. A driver for these developments was the desire to use the recently discovered holographic interferometry (see article Holography) from the time-consuming wet chemical development of exposed photographic plates by using an electronic camera directly. This is possible by dispensing with the three-dimensional information content of holograms (this is not important for most metrological applications). Initially, analog cameras were used to record images; in the older literature the process is also known as "TV holography". This "analog" phase of ESPI development is well summarized in Lokberg's article. Later digital cameras were used, and the phase shifting methods known from classical interferometry and holographic interferometry were also introduced into speckle interferometry for quantitative phase determination.

## Principle using the example of out-of-plane deformation measurement

A laser beam is split into the reference wave and the object wave with a beam splitter (see picture).

Out-of-plane ESPI setup

The object to be examined is illuminated with the expanded object wave. The object wave diffusely scattered by the object is focused with a lens on the light-sensitive surface of a camera and there interferes with the reference wave. Today mainly CCD and CMOS cameras are used.

The source point of the reference wave is ideally in the center of the imaging optics. By closing the diaphragm, the size of the speckle (or the spatial frequency spectrum of the interference figure on the camera target) can be adapted to the resolution of the camera. From a holographic point of view, this arrangement can also be referred to as image field holography with in-line reference wave. Two images (interferograms) are recorded. The load on the object is changed slightly between the shots. This can e.g. B. thermally (heating or cooling), or by mechanical deformation. The first image is referred to below as A (x, y) , the second as B (x, y) . The two recordings are subtracted from each other point by point in the computer, then the absolute amount is formed:

${\ displaystyle D (x, y) = | A (x, y) -B (x, y)}$|

x and y denote the spatial coordinates.

This image correlation creates a striped pattern which has properties similar to a holographic interferogram. The figure shows such a speckle correlogram.

ESPI striped image

The object was tilted slightly between the shots. The stripes can be interpreted as contour lines of the deformation. With this setup, out-of-plane displacements (in the direction of the camera) can be measured. The distance between two neighboring strips corresponds (with perpendicular illumination) to a shift of half a wavelength .

The image subtraction is usually carried out in real time so that the user can observe changes in real time.

## In-plane displacement measurement

ESPI can also be used to measure in-plane displacements, see picture.

In-plane ESPI structure

The object is illuminated symmetrically from two sides at the same angles to the surface normal. A speckle pattern is created for each direction of illumination, both patterns interfere on the camera sensor. If parts of the object surface are now shifted parallel to the camera plane (in-plane shift), then the interference pattern also changes. A striped image is created by subtracting the two images recorded before and after the shift. The in-plane shift can be calculated from this correlation pattern.

## Vibration measurement

The optical structure corresponds to that of the out-of-plane deformation measurement. The object is excited to mechanical vibrations. Vibration nodes and antinodes develop on the surface. The camera continuously records images of the surface (live images); an image subtraction, as with static deformation measurement, is not required. In the picture you can see the different oscillation states (amplitudes) from the different contrast of the speckle pattern.

ESPI vibration image

## Individual evidence

1. JN Butters, JA Leendertz: Holographic and Videotechniques applied to engineering measurements. In: J Meas Control. Volume 4, 1971, pp. 349-354
2. O Schwomma: austrian patent 298.830 1972
3. A. Macovski, D. Ramsey, LF Schaefer: Time Lapse Interferometry and contouring using Television Systems. In: Appl. Opt. Volume 10, No. 12, 1971, pp. 2722-2727
4. O. Lokberg: Electron Speckle Pattern Interferometry. In: Phys Technol. Volume 11, 1980, pp. 16-22
5. K. Creath: Phase shifting speckle interferometry. In: Appl Opt. Volume 4, No. 18, 1985, pp. 3053-3058
6. KA Stetson, R. Brohinsky: Electro Optic holography and its application to hologram interferometry. In: Appl Opt. Volume 24, No. 21, 1985, pp. 3631-3637
7. U. Schnars, C. Falldorf, J. Watson, W. Jüptner: Digital Holography and Wavefront Sensing. 2nd edition, Springer, 2014, ISBN 978-3-662-44692-8 , chapter 8, https://www.springer.com/de/book/9783662446928
8. KJ Gasvik: Optical Metrology. John Wiley & Sons, 1987, ISBN 0-471-91246-8 , chapter 6.3