Spatial filtering and optical tomography of edge enhancement of a phase object

Areli Montes Pérez; Cruz Meneses Fabián; Gustavo Rodríguez Zurita

doi:10.1117/12.851102

3 December 2009 Spatial filtering and optical tomography of edge enhancement of a phase object

Areli Montes Pérez, Cruz Meneses Fabián, Gustavo Rodríguez Zurita

Proceedings Volume 7499, Seventh Symposium Optics in Industry; 74990Y (2009) https://doi.org/10.1117/12.851102
Event: Seventh Symposium on Optics in Industry, 2009, Guadalajara, Jalisco, Mexico

Abstract

Using a 4f optical system, the Hilbert transform [1] of the projections of the object slice is implemented to reconstruct its edge enhancement using the parallel projection tomography. The projection going out of the object is considered as the entrance to the 4f optical system, the filter employed in the Fourier plane consisting of a phase step of π radians, in the image plane, as it is well known, the output function is given by the convolution of the impulse response and the input function, then in the image plane the Hilbert transform of the projection is obtained. We show that the reconstruction in this case is the Hilbert transform in vertical direction of the slice function, which is a special case. Also study in detail the synthesis of the filter in order to obtain the reconstruction the edge enhanced in an arbitrary direction, which is general case.

Citation Download Citation

Areli Montes Pérez, Cruz Meneses Fabián, and Gustavo Rodríguez Zurita "Spatial filtering and optical tomography of edge enhancement of a phase object", Proc. SPIE 7499, Seventh Symposium Optics in Industry, 74990Y (3 December 2009); https://doi.org/10.1117/12.851102

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