Introduction to linear vector spaces, bases and dimension, inner product, orthogonality, Fourier series,orthogonal polynomials, Cauchy Schwartz inequality, eigenvalues, eigenvectors, Hermitian operators,unitary operators, discrete Fourier transform.

Linear system theory and Fourier transformation. Properties of Fourier transform,Fourier transform theorems, some useful Fourier transform pairs, the delta function, circular symmetryand Fourier-Bessel transforms. General aspects of linear systems, Fourier transformation and spatial frequency spectrum, Linear space invariant and space variant systems. Sampling theory–Shannon-Whittaker sampling theorem.

Introduction to diffraction–general aspects. Fraunhofer and Fresnel diffraction. Scalar diffraction theory,Helmholtz equation and Greens theorem approach to Fresnel and Fraunhofer diffraction, the Huygens principle. Fourier transform in Fraunhofer diffraction. Examples of Fraunhofer diffraction such as Rectangular aperture, Circular aperture, Sinusoidal phase grating, sinusoidal amplitude grating, etc.

Fresnel transform, Fresnel diffraction such as square aperture, sinusoidal amplitude grating, etc. Fresnel propagation of a laser beam. Self imaging, Lau and Talbot effects, Fractional Fourier transform.

Wave optics analysis of coherent optical systems. Thin lens as a phase transformation,the paraxial approximation, Fourier transform properties of lenses. Image formation in monochromatic illumination.Diffraction–limited coherent imaging. Fresnel zone plate. Operator approach to optical systems.Frequency response of diffraction-limited coherent imaging – the amplitude transfer function (ATF).

Optical Transfer Function (OTF), frequency response of a diffraction-limited incoherent imaging.Aberrations and their effects on frequency response. Comparison of coherent and incoherent imaging.Resolution beyond the diffraction limit.

Same as Reference

1. Mathematical methods for physicists, Arfken and Weber, Academic Press, Sixth edition, 2005.(For unit 1)
2. Introduction to Fourier Optics, J. W. Goodman, McGraw-Hill. Third Edition, 2004 (For units 2, 3, 4, and 5)
3. Statistical Optics, J. W. Goodman, Wiley Inter-science, 2000. (Ref. for unit 5)
4. Fundamentals of photonics, Saleh and Teich, Wiley Interscience, 2007. (For unit 3)