Optical Tomography Of Phase Objects 6ith Phase-Shifting Interferometry And Stepping 6ise Shifted Ronchi Ruling Cruz Meneses-Fabian 1 , Gustavo Rodriguez-Gurita 1 , and VIctor ArrizJn 2 1 Benemerita Universidad Autonoma de Puebla, Facultad de Ciencias Fisico-Matematicas Apartado Postal 1152, Puebla PUE 72000, México. 2 Instituto Nacional de Astrofísica, Optica y Electrónica, Apartado Postal 51 y 216, Puebla PUE 72000, México ABSTRACT An experimental setup for tomographic inspection of phase objects is presented. The system is based on an interferometer which uses two windows in the input plane and a translating grating as its pupil. In the output, interference of the fields associated with replicated windows can be achieved by a proper choice of the spacing between windows with respect to the grating period. Placing a rotating object in one window and with a reference crossing through the second one, the phase of projections results encoded in a composite interference pattern over the plane of the traditional sinogram. Phase stepping of such composite interferograms can be achieved by lateral translation of the grating to obtain the unwrapped phase distribution as the corresponding sinogram of the object slide under inspection. The sinogram allows tomographic reconstruction of slices by standard procedures. Composite interferograms and preliminary reconstructions for some transparent samples are shown. Meywords: Tomographic, Interferometry, spatial filter, Fourier Optics. 1. INTRODUCCION It has been recently presented a Fourier theory describing the image-formation process of a common-path interferometer consisting of two windows in the object plane and a grating as a spatial filter 1 . By proper choice of the spacing between windows with respect to the grating period, interference patterns between the fields of each window can be achieved. In addition, the patterns can be shifted through the phase introduced by grating displacements 1 . The common-path interferometer has thus resemblance with well-known phase-shifting methods which employ gratings driven by actuators 2-4 . Because this interferometer shows practical advantages as good stability and a relative easiness for introducing phase steps, it might be worthwhile to adapt it in an optical tomographic system for imaging distributions of phase-objects slices. In optical tomography, the phase variations which an optical beam accumulates along its path across an object has to be measured in order to obtain the phase distribution of a given object slice by reconstruction techniques 5 . For example, parallel projections tomographic techniques can be applied to phase objects in the visible range immersing them in a liquid gate 6 . So, backprojection algorithms can be employed for the slice reconstruction 7 . In this communication, we report experimental data projections and their corresponding tomographic reconstructions belonging to transparent samples as they result from a tomographic system equipped with an amplitude Ronchi ruling in a modified common-path interferometer 1 . 2. COMMON PATH INTERFEROMETER. Fig.1 shows the experimental tomographic set-up, which is a double Fourier-transform spatial filtering imaging system. A transparent object O is placed before the x-y object plane. As the light source, a collimated He-Ne laser is used. The x- y plane comprises two identical rectangular windows, each of sides a and b, with a separation of 0 x between their respective centers. One of the windows allows the light emerging from the object to enter into the system, while the second window transmits light that has not traveled through the object, therefore acting as a reference. The object remains immersed within a liquid gate filled with immersion oil, but it is vertically attached to the axis of a stepping motor in order to rotate. The refractive index of the object boundaries is matched with that of the surrounding medium, thus approaching the refractionless condition. Then, parallel projection tomographic techniques for slice reconstruction Eighth International Symposium on Laser Metrology, edited by R. Rodriguez-Vera, F. Mendoza-Santoyo, Proc. of SPIE Vol. 5776 (SPIE, Bellingham, WA, 2005) 0277-786X/05/$15 · doi: 10.1117/12.611838 613 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 04/12/2013 Terms of Use: http://spiedl.org/terms