1 / 40

Today Imaging with coherent light

Today Imaging with coherent light. • Coherent image formation –space domain description: impulse response –spatial frequency domain description: coherent transfer function. The 4F system. Fourier transform relationship. Fourier transform relationship. The 4F system. Theorem:.

jclemmer
Download Presentation

Today Imaging with coherent light

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


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

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

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

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

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

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

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

  9. Transfer function & impulse response of rectangular aperture Impulse response: Airy function Transfer function: circular aperture 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 output amplitude Impulse response convolution illumi nation Fourier transform Fourier transform transfer function (≡plane wave spectrum multiplication MIT 2.71/2.710 Optics 11/08/04 wk10-a-

  11. Transfer function & impulse response of rectangular aperture 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 output amplitude Impulse response convolution illumi nation Fourier transform Fourier transform transfer function (≡plane wave spectrum multiplication MIT 2.71/2.710 Optics 11/08/04 wk10-a-

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

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

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

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

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

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

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

  24. f1=20cm λ=0.5μm Low–pass filtering the impulse monochromatic coherent on-axis illumination object plane transparency Fourier plane cire-aperture intensity at input plane Fourier filter transitivity Intensity before Fourier Filter (negative contrast) MIT 2.71/2.710 Optics 11/08/04 wk10-a-

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

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

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

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

  29. Weak low–pass filtering Pinhole, radius 2.5mm Filtered with pinhole, radius 2.5mm Fourier filter Intensity @ image plane f1=20cm λ=0.5μm MIT 2.71/2.710 Optics 11/08/04 wk10-a-

  30. Moderate low–pass filtering (aka blurringblurring) Pinhole, radius 1mm Filtered with pinhole, radius 1mm Fourier filter Intensity @ image plane f1=20cm λ=0.5μm MIT 2.71/2.710 Optics 11/08/04 wk10-a-

  31. Strong low–pass filtering Pinhole, radius 0.5mm Filtered with pinhole, radius 0.5mm Fourier filter Intensity @ image plane f1=20cm λ=0.5μm 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 filter Intensity @ image plane f1=20cm λ=0.5μm MIT 2.71/2.710 Optics 11/08/04 wk10-a-

  33. Strong high–pass filtering (aka edge enhancement) Reflective disk, radius 2.5mm Filtered with reflective disk, radius 2.5mm Fourier filter Intensity @ image plane f1=20cm λ=0.5μm MIT 2.71/2.710 Optics 11/08/04 wk10-a-

  34. 1-dimensional blurring Filtered with horizontal slit, width 2mm Horizontal slit, width 2mm Fourier filter Intensity @ image plane f1=20cm λ=0.5μm MIT 2.71/2.710 Optics 11/08/04 wk10-a-

  35. 1-dimensional blurring Filtered with vertical slit, width 2mm vertical slit, width 2mm Fourier filter Intensity @ image plane f1=20cm λ=0.5μm MIT 2.71/2.710 Optics 11/08/04 wk10-a-

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

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

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

  39. Imaging with Zernicke mask phase-shift mask (phase), radii 5mm & 1mm (phase) Filtered with, phase-shift mask, radii 5mm & 1mm Fourier filter Intensity @ image plane f1=20cm λ=0.5μm MIT 2.71/2.710 Optics 11/08/04 wk10-a-

  40. Imaging with Zernicke mask phase-shift mask (phase), radii 5mm & 0.1mm (phase) Filtered with, phase-shift mask, radii 5mm & 0.1mm Fourier filter Intensity @ image plane f1=20cm λ=0.5μm MIT 2.71/2.710 Optics 11/08/04 wk10-a-

More Related