Survey
* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project
Download document 8540151
Document related concepts
no text concepts found
Transcript
The convolution theorem multiplication MIT 2.71/2.710 04/08/09 wk9-b-18 convolution The convolution theorem multiplication MIT 2.71/2.710 04/08/09 wk9-b-19 convolution Fraunhofer diffraction patterns MIT 2.71/2.710 04/08/09 wk9-b-20 ∞ → z ∞ → z ∞ z→ ∞ z→ Spatial filtering space domain 3 sinusoids MIT 2.71/2.710 04/08/09 wk9-b-21 Fourier domain Spatial filtering space domain 2 sinusoids (one removed) MIT 2.71/2.710 04/08/09 wk9-b-22 Fourier domain Spatial filtering of a scene Unfiltered: all spatial frequencies present 0 MIT 2.71/2.710 04/08/09 wk9-b-23 Spatial filtering of a scene Low-pass filtered: high spatial frequencies removed 0 MIT 2.71/2.710 04/08/09 wk9-b-24 Spatial filtering of a scene Band-pass filtered: high & low spatial frequencies removed 0 MIT 2.71/2.710 04/08/09 wk9-b-25 The transfer function of Fresnel propagation Fresnel (free space) propagation may be expressed as a convolution integral MIT 2.71/2.710 04/08/09 wk9-b-26 Today • Fourier transforming properties of lenses • Spherical - plane wave duality • The telescope (4F system) revisited – imaging as a cascade of Fourier transforms – spatial filtering by a pupil plane transparency Wednesday • Spatial filtering in the 4F system • Point-Spread Function (PSF) and Amplitude Transfer Function (ATF) MIT 2.71/2.710 04/13/09 wk10-a- 1 Reminder: thin lens (geometrical optics) f (focal length) object at ∞ (plane wave) image at back focal plane f (focal length) object at front focal plane image at ∞ (plane wave) amount of ray bending is proportional to the distance from the optical axis point object at finite distance (spherical wave) point image at finite distance (spherical wave) so MIT 2.71/2.710 04/13/09 wk10-a- 2 si Thin lens complex transmittance Δ(x,y) Δ0 Δ(x,y): glass thickness at coordinate (x,y) n: index of refraction R1, R2: radii of curvature MIT 2.71/2.710 04/13/09 wk10-a- 3 Plane wave incident on a lens back focal plane θ0 f = spherical wave converging to u0λf f MIT 2.71/2.710 04/13/09 wk10-a- 4 Spherical wave incident on a lens front focal plane spherical wave, diverging off–axis MIT 2.71/2.710 04/13/09 wk10-a- 5 plane wave plane wave converging to u0λf Fourier transforming property of lenses MIT 2.71/2.710 04/13/09 wk10-a- 6 MIT OpenCourseWare http://ocw.mit.edu 2.71 / 2.710 Optics Spring 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.
Related documents