Download presentation

Presentation is loading. Please wait.

Published byAdam Rogers Modified over 3 years ago

1
MIT 2.71/2.710 Optics 11/08/04 wk10-a- 1 Today Imaging with coherent light Coherent image formation –space domain description: impulse response –spatial frequency domain description: coherent transfer function

2
MIT 2.71/2.710 Optics 11/08/04 wk10-a- 2 The 4F system Fourier transform relationship Fourier transform relationship

3
MIT 2.71/2.710 Optics 11/08/04 wk10-a- 3 The 4F system Theorem:

4
MIT 2.71/2.710 Optics 11/08/04 wk10-a- 4 The 4F system object plane Fourier plane Image plane

5
MIT 2.71/2.710 Optics 11/08/04 wk10-a- 5 The 4F system object plane Fourier plane Image plane

6
MIT 2.71/2.710 Optics 11/08/04 wk10-a- 6 The 4F system with FP aperture object planeFourier plane : aperture-limited Image plane: blurred i. e. low-pass filtered

7
MIT 2.71/2.710 Optics 11/08/04 wk10-a- 7 Impulse response & transfer function A point source at the input plane...... results not in a point image but in a diffraction pattern h(x,y ) Point source at the origin delta function δ (x,y) h(x,y ) is the inpulse response of the system More commonly, h(x,y ) is called the Coherent Point Spread Function (Coherent PSF)

8
MIT 2.71/2.710 Optics 11/08/04 wk10-a- 8 Coherent imaging as a linear, shift-invariant system transfer function H(u,v): akapupil function Thin transparency output amplitude impulse response convolution Fourier transform illumi nation (plane wave spectrum transfer function multiplication

9
MIT 2.71/2.710 Optics 11/08/04 wk10-a- 9 Transfer function & impulse response of rectangular aperture Transfer function: circular aperture Impulse response: Airy function

10
MIT 2.71/2.710 Optics 11/08/04 wk10-a- 10 Coherent imaging as a linear, shift-invariant system Example: 4F system with circular aperture @ Fourier plane Thin transparency illumi nation Impulse response output amplitude Fourier transform Fourier transform transfer function multiplication convolution (plane wave spectrum

11
MIT 2.71/2.710 Optics 11/08/04 wk10-a- 11 Transfer function & impulse response of rectangular aperture

12
MIT 2.71/2.710 Optics 11/08/04 wk10-a- 12 Coherent imaging as a linear, shift-invariant system Example: 4F system with circular aperture @ Fourier plane Thin transparency illumi nation Impulse response output amplitude Fourier transform Fourier transform transfer function multiplication convolution (plane wave spectrum

13
MIT 2.71/2.710 Optics 11/08/04 wk10-a- 13 Aperture–limited spatial filtering object plane: grating generates one spatial frequency Fourier plane: aperture unlimited Image plane: grating is imaged with lateral de-magnification (all orders pass)

14
MIT 2.71/2.710 Optics 11/08/04 wk10-a- 14 Aperture–limited spatial filtering object plane: grating generates one spatial frequency Fourier plane: aperture limited Image plane: grating is not imaged only 0 th order (DC component) surviving (some orders cut off)

15
MIT 2.71/2.710 Optics 11/08/04 wk10-a- 15 Spatial frequency clipping field after input transparency field before filter field after filter field at output (image plane)

16
MIT 2.71/2.710 Optics 11/08/04 wk10-a- 16 Effect of spatial filtering Fourier plane filter with circ-aperture Original object (sinusoidal spatial variation, i.e. grating) Frequency-filtered image (spatial variation blurred out, only average survives)

17
MIT 2.71/2.710 Optics 11/08/04 wk10-a- 17 Spatial frequency clipping f1=20cm λ =0.5 μ m monochromatic coherent on-axis illumination object plane Transparency intensity at input plane Intensity before Fourier Filter (negative contrast) Fourier plane cire-aperture Fourier filter transitivity

18
MIT 2.71/2.710 Optics 11/08/04 wk10-a- 18 Space-Fourier coordinate transformations :pixel size :frequency resolution spare domain Spatial Frequency domain Nyquist relationships.

19
MIT 2.71/2.710 Optics 11/08/04 wk10-a- 19 4F coordinate transformations :pixel size Nyquist relationships. spare domain Fourier plane

20
MIT 2.71/2.710 Optics 11/08/04 wk10-a- 20 Spatial frequency clipping f 1 =20cm λ =0.5 μ m monochromatic coherent on-axis illumination object plane transparency intensity at input plane Intensity before Fourier Filter (negative contrast) Fourier plane cire-aperture Fourier filter transitivity Image plane observed field

21
MIT 2.71/2.710 Optics 11/08/04 wk10-a- 21 Formation of the impulse response object plane: pinhole generates spherical wave Fourier plane: circ-aperture limited Image plane: Fourier transform of aperture, Airy pattern (plane wave is clipped)

22
MIT 2.71/2.710 Optics 11/08/04 wk10-a- 22 field after input transparency field before filter field after filter field at output (image plane) Low–pass filtering (Airy pattern)

23
MIT 2.71/2.710 Optics 11/08/04 wk10-a- 23 Effect of spatial filtering Fourier plane filter with circ-aperture Original object (small pinhole impulse, generating spherical wave past the transparency) Impulse reponse (aka point point-spread function, original point has blurred to an Airy pattern, or jinc)

24
MIT 2.71/2.710 Optics 11/08/04 wk10-a- 24 Low–pass filtering the impulse f 1 =20cm λ =0.5 μ m monochromatic coherent on-axis illumination object plane transparency intensity at input plane Intensity before Fourier Filter (negative contrast) Fourier plane cire-aperture Fourier filter transitivity

25
MIT 2.71/2.710 Optics 11/08/04 wk10-a- 25 Spatial frequency clipping monochromatic coherent on-axis illumination object plane transparency intensity at input plane Intensity after Fourier filter Fourier plane cire-aperture Intensity at output plane Image plane observed field note: pseudo-accentuated sidelobes

26
MIT 2.71/2.710 Optics 11/08/04 wk10-a- 26 Low-pass filtering with the 4F system monochromatic coherent on-axis illumination object plane transparency Fourier plane cire-aperture Image plane observed field field arriving At Fourier plane field arriving from Fourier plane Fourier transform

27
MIT 2.71/2.710 Optics 11/08/04 wk10-a- 27 monochromatic coherent on-axis illumination object plane transparency Fourier plane cire-aperture Image plane observed field Spatial filtering with the 4F system field arriving At Fourier plane field arriving from Fourier plane Fourier transform Fourier transform

28
MIT 2.71/2.710 Optics 11/08/04 wk10-a- 28 Examples: the amplitude MIT pattern Original MIT pattern

29
MIT 2.71/2.710 Optics 11/08/04 wk10-a- 29 Weak low–pass filtering Pinhole, radius 2.5mmFiltered with pinhole, radius 2.5mm Fourier filterIntensity @ image plane f 1 =20cm λ =0.5 μ m

30
MIT 2.71/2.710 Optics 11/08/04 wk10-a- 30 Moderate low–pass filtering (aka blurringblurring) Fourier filterIntensity @ image plane Pinhole, radius 1mmFiltered with pinhole, radius 1mm f 1 =20cm λ =0.5 μ m

31
MIT 2.71/2.710 Optics 11/08/04 wk10-a- 31 Strong low–pass filtering Pinhole, radius 0.5mmFiltered with pinhole, radius 0.5mm Fourier filterIntensity @ image plane f 1 =20cm λ =0.5 μ m

32
MIT 2.71/2.710 Optics 11/08/04 wk10-a- 32 Moderate high–pass filtering Reflective disk, radius 0.5mm Filtered with reflective disk, radius 0.5mm Fourier filterIntensity @ image plane f 1 =20cm λ =0.5 μ m

33
MIT 2.71/2.710 Optics 11/08/04 wk10-a- 33 Strong high–pass filtering Reflective disk, radius 2.5mmFiltered with reflective disk, radius 2.5mm Fourier filterIntensity @ image plane f 1 =20cm λ =0.5 μ m (aka edge enhancement)

34
MIT 2.71/2.710 Optics 11/08/04 wk10-a- 34 1-dimensional blurring Horizontal slit, width 2mm Filtered with horizontal slit, width 2mm Fourier filterIntensity @ image plane f 1 =20cm λ =0.5 μ m

35
MIT 2.71/2.710 Optics 11/08/04 wk10-a- 35 1-dimensional blurring vertical slit, width 2mm Filtered with vertical slit, width 2mm Fourier filterIntensity @ image plane f 1 =20cm λ =0.5 μ m

36
MIT 2.71/2.710 Optics 11/08/04 wk10-a- 36 Phase objects glass plate (transparent) thickness protruding part phase-shifts coherent illumination by amount φ =2 π (n-1)t/ λ Often useful in imaging biological objects (cells, etc.)

37
MIT 2.71/2.710 Optics 11/08/04 wk10-a- 37 Viewing phase objects Intensity (object is invisible) Amplitude (need interferometer) Original phase MIT pattern (intensity) Original 0.1 rad phase MIT pattern (phase)

38
MIT 2.71/2.710 Optics 11/08/04 wk10-a- 38 Zernicke phase-shift mask phase-shift mask (magnitude), radii 5mm & 1mm phase-shift mask (phase), radii 5mm & 1mm (phase)

39
MIT 2.71/2.710 Optics 11/08/04 wk10-a- 39 Imaging with Zernicke mask Fourier filterIntensity @ image plane f 1 =20cm λ =0.5 μ m phase-shift mask (phase), radii 5mm & 1mm (phase) phase-shift mask, radii 5mm & 1mm Filtered with,

40
MIT 2.71/2.710 Optics 11/08/04 wk10-a- 40 Imaging with Zernicke mask Fourier filterIntensity @ image plane f 1 =20cm λ =0.5 μ m phase-shift mask (phase), radii 5mm & 0.1mm (phase) phase-shift mask, radii 5mm & 0.1mm Filtered with,

Similar presentations

Presentation is loading. Please wait....

OK

PP Test Review Sections 6-1 to 6-6

PP Test Review Sections 6-1 to 6-6

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on financial markets and institutions Ppt on ideal gas laws Ppt on poet robert frost Ppt on liquid crystal display Ppt on abo blood grouping test Constitution day for kids ppt on batteries Ppt on minimum wages act 2014 Ppt on job rotation articles Liquid vapour display ppt online Ppt on cross-sectional study definition