Fraccional Fourier transform in the case of an inclined image plane
Main Article Content
Keywords
Fresnel diffraction, inclined image plane, fractional Fourier transform.
Abstract
The well-known Fresnel integral relates a known complex wave defined in the object plane (the input wave field) to the observable complex wave (the output wave field) defined in the image plane after free-space propagation; this means that if the object and image plane are parallel to each other, corresponding imaging system is said to be linear-shift-invariant (LSI). This advantageous property was essential for the development of phase sensitive imaging techniques; however, if the image plane is inclined with respect to the incident beam, the effective propagation distance will vary over the image plane, consequently, the imaging system is not shiftinvariant. In this paper an extension of the theoretical formalism of Fresnel diffraction to the case of an inclined image plane is proposed using the fractional Fourier transform.
MSC: 33D15, 33D90, 33D60, 34M03, 62E15
Downloads
References
[2] P. J. Chandley. Surface roughness measurements from coherent light scattering. Optical and Quantum Electronics, ISSN 0306–8919, 8(4), 323–327 (1976).
[3] H. M. Pedersen. Object–roughness dependence of partially developed speckle patterns in coherent light . Optics Communications, ISSN 0030–4018, 16(1), 63–67 (1976).
[4] H. Fuji, T. Asakura and Y. Shindo. Measurement of surface roughness properties by means of laser speckle techniques. Optics Communications, ISSN 0030–4018,16(1), 68–72 (1976).
[5] Hitoshi Fujii and Toshimitsu Asakura. Roughness measurements of metal surfaces using laser speckle. Journal of the Optical Society of America B, ISSN 0740–3224, 67(9), 1171–1176 (1977).
[6] Ulf Persson. Real time measurement of surface roughness on ground surfaces using speckle–contrast technique. Optics and Lasers in Engineering, ISSN 0143–8166, 17(2), 61–67 (1992).
[7] Lisa C. Leonard and Vincent Toal. Roughness measurement of metallic surfaces based on the laser speckle contrast method. Optics and Lasers in Engineering, ISSN 0143–8166, 30(5), 433–440 (1998).
[8] S. L. Toh, H. M. Shang and C. J. Tay. Surface–roughness study using laser speckle method. Optics and Lasers in Engineering, ISSN 0143–8166, 29(2–3), 217–225 (1998).