The width of the function in the space domain ($a$) is inversely proportional to the width of the spectrum in the frequency domain. Section 2: Foundations of Scalar Diffraction Theory (Chapter 3) Problem 3-2 (Topic: Fresnel Diffraction of a Slit) Problem Statement: A slit of width $w$ is illuminated by a unit-amplitude plane wave normal to the aperture. Find the field distribution a distance $z$ away under the Fresnel approximation . The Configuration File Tecdoc New | Loading Data Failed Check
The solution is expressed in terms of the Fresnel Integrals $C(u)$ and $S(u)$: $$ U(x, z) = \frac12 \left( \frac1+j2 \right) \left[ [C(u_2) + jS(u_2)] - [C(u_1) + jS(u_1)] \right] $$ Solution Manual Of Theory Of Machine By Rs Khurmi Gupta 971 Extra Quality
Fresnel diffraction requires numerical evaluation of Fresnel integrals unless the distance $z$ is very large (Fraunhofer regime) or very small (Rayleigh-Sommerfeld regime). Section 3: Fourier Transforming Properties of Lenses (Chapter 5) Problem 5-1 (Topic: Lens as a Fourier Transformer) Problem Statement: A transparency with amplitude transmittance $t_1(x, y)$ is placed immediately in front of a positive lens of focal length $f$. The lens is illuminated by a normally incident plane wave of wavelength $\lambda$. Find the field distribution at the back focal plane.
While this integral cannot be solved in closed form using elementary functions, the standard method involves expanding the term $e^j \frack2z\xi^2$ inside the slit or utilizing the .
For a coherent imaging system, the CTF is the scaled pupil function. The pupil function is: $$ P(x,y) = \textrect\left(\fracxw\right) \textrect\left(\fracyw\right) $$