**8. References**

ALFIERI, D., COPPOLA, G., DENICOLA, S., FERRARO, P., FINIZIO, A., PIERATTINI, G. & JAVIDI, B. (2006). Method for superposing reconstructed images from digital holograms of the same object recorded at different distance and wavelength, *Optics Communications* **260**(1): 113–116.

URL: *http://dx.doi.org/10.1016/j.optcom.2005.10.055*


URL: *http://ao.osa.org/abstract.cfm?URI=ao-23-24-4539*

Cheng, Y.-Y. & Wyant, J. C. (1985). Multiple-wavelength phase-shifting interferometry, *Applied Optics* **24**(6): 804.

URL: *http://ao.osa.org/abstract.cfm?URI=ao-24-6-804*


14 Hologram / Book 2

Multiple-wavelength digital holographic interferometry using tunablity of laser diodes for measuring a large step-height with high accuracy was presented. The requirements for performing the phase unwrapping were discussed. We have found that precise knowledge of the recording wavelengths is required for correctly performing the phase unwrapping. The required precision of the knowledge was derived. A simple and fast algorithm for pixel size adjustment was presented. It has been demonstrated that the problem of the phase subtraction

Several holograms were recorded through the changes in the wavelength of a laser diode by injection current and operation temperature controls. A pair of holograms with a small wavelength difference less than 0.01 nm was recorded and used for realizing holographic interferometry with a large synthetic wavelength more than 120 mm. Phase differences with synthetic wavelengths from 0.4637 mm to 129.1 mm were extracted by using the holograms. The synthetic wavelengths were calibrated by the comparison between the phase differences and the object heights measured by using a slide caliper. The step-heights of 0.1 mm and 12

ALFIERI, D., COPPOLA, G., DENICOLA, S., FERRARO, P., FINIZIO, A., PIERATTINI, G.

Asundi, A. & Wensen, Z. (1998). Fast Phase-Unwrapping Algorithm Based on a Gray-Scale

Cheng, Y.-Y. & Wyant, J. C. (1984). Two-wavelength phase shifting interferometry, *Applied*

Cheng, Y.-Y. & Wyant, J. C. (1985). Multiple-wavelength phase-shifting interferometry, *Applied*

Ferraro, P., De Nicola, S., Coppola, G., Finizio, A., Alfieri, D. & Pierattini, G. (2004).

Friesem, A. A. & Levy, U. (1976). Fringe formation in two-wavelength contour holography,

Gass, J., Dakoff, A. & Kim, M. K. (2003). Phase imaging without 2*π* ambiguity by multiwavelength digital holography, *Optics Letters* **28**(13): 1141–1143. URL: *http://www.opticsinfobase.org/abstract.cfm?URI=ol-28-13-1141* Goodman, J. W. (1968). *Introduction to Fourier Optics*, McGraw-Hill, New York.

Controlling image size as a function of distance and wavelength in Fresnel-transform

de Groot, P. (1991). Three-color laser-diode interferometer, *Applied Optics* **30**(25): 3612.

& JAVIDI, B. (2006). Method for superposing reconstructed images from digital holograms of the same object recorded at different distance and wavelength, *Optics*

in two-wavelength holographic interferometry can be solved by the present method.

**7. Conclusion**

mm were correctly detected.

*Communications* **260**(1): 113–116.

*Optics* **23**(24): 4539.

*Optics* **24**(6): 804.

*Applied Optics* **15**: 3009–3020.

URL: *http://dx.doi.org/10.1016/j.optcom.2005.10.055*

Mask and Flood Fill, *Applied Optics* **37**(23): 5416. URL: *http://ao.osa.org/abstract.cfm?URI=ao-37-23-5416*

URL: *http://ao.osa.org/abstract.cfm?URI=ao-23-24-4539*

URL: *http://ao.osa.org/abstract.cfm?URI=ao-24-6-804*

URL: *http://ao.osa.org/abstract.cfm?URI=ao-30-25-3612*

URL: *http://ol.osa.org/abstract.cfm?URI=ol-29-8-854*

URL: *http://ao.osa.org/abstract.cfm?id=20668*

reconstruction of digital holograms, *Optics Letters* **29**(8): 854.

**8. References**


URL: *http://www.opticsinfobase.org/abstract.cfm?id=44295*


URL: *http://ao.osa.org/abstract.cfm?id=44347*


**4** 

*Egypt* 

**Digital Holographic Interferometric** 

Hamdy Wahba and Mamdouh Shams El-Din *Physics Department, Faculty of Science, 34517 Damietta,* 

*University of Mansoura* 

**Characterization of Optical Waveguides** 

Holography was developed by Dennis Gabor 1947. Gabor presented holography as a lensless process for image formation by reconstructed wavefronts (Gabor, 1948, 1949, 1951). Holography can be defined as a method for recording and reconstructing whole optical waveelds, which means intensity and phase (Gabor, 1948, 1949), thus it exhibits 3D characteristics like depth of field or parallax. Holographic interferometry (Powell & Stetson, 1965) is a very effective non-destructive, contactless tool to measure shape, deformation or

In 1994 the modern digital holography was introduced (Schnars, 1994; Schnars, & Jüptner, 1994a; Schnars, & Jüptner, 1994b; Schnars et al., 1995; Schnars, & Jüptner, 2005). The digital holography can be defined as digital recording of the holograms and the numerical reconstruction of the wave fields in a computer, where, the charge coupled devices (CCDs) are the most frequently used devices to record the holograms. The digital holography in the last ten years was involved in a lot of applications due to the development of powerful

The phase shifting interferometric (PSI) technique was introduced by Hariharan et al. into the field of holography as an accurate method for real time fringe measurement (Hariharan et al., 1982). Furthermore, PSI combined with digital holography (Skarman et al., 1996). Yamaguchi and Zhang 1997 improved phase shifting digital holography (PSDH) (Yamaguchi & Zhang, 1997). The phase difference using PSDH is measured with an

For a long time, the determination of refractive index distributions in fibres, optical waveguides or other transparent solids was performed by interferometric methods. Twobeam and multiple beam based interferometers were used as a non-destructive tool to determine the optical parameters of fibres (Faust, 1952, 1954; Marhic et al., 1975). While, the mathematics used in (Marhic et al., 1975; Saunder & Gardner, 1977; Barakat et al., 1985) neglect the non-straightforward refraction of the light beam inside the fibres. Hamza et al. (Hamza et al., 1994, 1995) constructed an accurate mathematical model (multilayer model) which considered the exact local refraction of the incident beam on its way through the graded index optical fibre, which is divided into a large number of thin concentric layers of constant refractive index. This model was verified with two-beam and multiple-beam interferometers. The consideration of incident beam refraction gave a better accuracy in the

computers, ultra large memories and smaller pixel size CCD targets (Kreis, 2005).

**1. Introduction** 

refractive index distributions (Kreis, 1996).

accuracy of 2/200 (Hariharan, 2002).

URL: *http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?dispmax=50&DB=pubmed&term= Surface+shape+measurement+by+phase-shifting+digital+holography*

Yamaguchi, I., Matsumura, T. & Kato, J.-i. (2002). Phase-shifting color digital holography, *Optics Letters* **27**(13): 1108.

URL: *http://ol.osa.org/abstract.cfm?URI=ol-27-13-1108*

