PH880 Topics in Physics

Transcription

1 PH880 Topics in Physics Modern Optical Imaging (Fall 2010)

2 Overview of week 4 Monday PSF, OTF Bright field microscopy Resolution/NA Deconvolution Wednesday : holiday

3 Impulse response (PSF) in imaging system x Object Plane Image Plane x Arbitrary Imaging System A point source at the input plane... does not focused into a point image. But into a diffracted pattern δ ( xy, ) h( x, y ) Then, any arbitrary wave, f ( xy, ) will have an output as: f h * For LSI (Linear Shift Invariant) system

4 PSF & ATF in coherent imaging i φ 1 1 f = Ae + Ae i φ 1 1 λ F Fourier Plane before filter x F H Fourier Plane after filter Object Plane Spatial Filter Image Plane f H f h x ATF * PSF

5 PSF & ATF in incoherent imaging I = I + I 1 2 λs ÎI = F F ÎI H Fourier Plane before filter x Fourier Plane after filter Object Plane Spatial Filter Image Plane I 2 = f H I h x OTF * ipsf Optical Transfer function H = H H Incoherent PSF h = h 2

6 Terminology (spatial domain) (spatial frequency domain) h( xy, ) : (coherent) Point Spread Function (PSF) Huv (, ) : Amplitude Modulation Function (AMF) hxy (, ) = hxy (, ) = hh : (incoherent) PSF 2 * H ( uv, ) = H ( uv, ) H ( uv, ) Optical Transfer Function (OTF) Huv (, ) = Huv (, ) Huv (, ) Modulation Transfer Function (MTF)

7 Conjugate planes f f g ( x, y ) g ( x, y ) = 2 f3 f3 Fourier Conjugate planes g 2 ( ', ') g 4 (, ) x x x X f 1 f 1 f f 2 2 f 3 f 3 g 1 ( x, y) g 3 ( x, y ) Imaging forming Conjugate planes f1 f1 g3( x, y ) = g1( x, y) f f 2 2

8 Conjugate plane: example

9 Bright field microscopy

10 Optical trains in bright field microscopy

11 Imaging formation in microscopy Thin lens fomula = a b f 4f imaging syst.

12 Accomodation (focusing) in eyes Imaging object at far plane = z z f Imaging object at near plane ~3cm = 3 cm 3 cm = 25 cm 3 cm 2.68 cm ~25cm ~3cm Comfortable viewing up to 25cm away from the cornea (i.e. focal length of human lens can be varied from ~ cm)

13 Imaging formation in microscopy # = a b f 4f imaging syst.

14 Conjugate planes in bright field microscopy Aperture or illuminating Conjugate planes Imaging forming Conjugate planes

15 Conjugate planes in bright field microscopy

16 Objective lens

17 Objective lens Manufacturer Tube Lens Focal Length (mm) Parfocal Distance (mm) Thread Type Leica M25 Nikon M25 Olympus RMS Zeiss RMS Parfocal distance f 2 f 2 When you have a tube lens with ihcorrect focal llength, M l =f2/f1=60x

18 NA and spatial resolution Low NA High NA Wide PSF Narror PSF

19 NA and spatial resolution max angle g θ max at the obj. plane max spatial freq. nsinθ NA PSF max = λ λ at the image plane at the Fourier plane x x f f 1 f 1 f 2 2 λu x' circ = circ NA x' NAf 1 u= λ f 1 ( ) jinc NAf u 1 x u = λ f NA f 1 = jinc x λ f2 NA x = jinc λ M 2

20 (spatial domain) NA and spatial resolution ipsf NA x = jinc λ M 2 (Fourier domain) R λ λ = = NA nsin θ x ' = x ' OTF circ MTF = circ circ NAf1 NAf 1

21 Immersion oil NA = nsinθ max No immersion oil (n=1) Oil immersion objective lens (n~1.51, why?) * Water immersion (n=1.33) or glycerol immersion (n=1.473) * Solid immersion lens (n~2 or above, see the reading list)

22 Tungsten halogen Light sources Arc Lamps

23 Köhler Illumination

24 3D PSF 2D PSF for various focal plane (i.e. various z position) 3D PSF z x y x

25 Deconvolution Then, can we do deconvolution the image with the known PSF? * z x BioTechniques 31: (November 2001)

26 Aberrations 1. Spherical aberration 2. Comatic Aberration (Coma) 3. Chromatic aberration 4. Field curvature 5. Distortioni 6. Astigmatism

27 Spherical aberration & Coma spherical surfaces are not the ideal shape with which to make a lens parabolic surfaces give perfectcorrectionof correction of spherical aberration when rays pass through the lens at an angle to the axis θ

28 Chromatic aberration caused by the dispersion of the lens material the variation of its refractive index, n, with the wavelength

29 (Petzval) field curvature the image plane is not flat IW Jung et al, APPLIED PHYSICS LETTERS 96, (2010)

30 Distortion Barrel distortion bends the tower and the foundation Barrel distortion Pincushion distortion Mustache distortion

31 Astigmatism When object is away from the optical axis Two perpendicular planes have different foci (T1 and S1)

32 Aberration and MTF Ideal thin lens w/ finite NA Re{ H } realistic thin lens w/ finite NA w/ aberrations 2u max u max nsinθmax = = λ NA λ

33 MTF

34 Cell scope? KAIST PH880 9/27/2010

35 Reading List (wk 4 day 1) 1. Davidson, M. W. and Fellers, T. J. Understanding conjugate planes and Köhler illumination. Nikon MicroscopyUWhitepaper 4 pages (2003). 2. Mansfield, S. M. and Kino, G.S.. Solid immersion microscopy, App. Phys. Lett. 72, 2778 (1998) 3. Agard, D. A. Optical Sectioning Microscopy: cellular architecture in three dimensions. Annual Review of Biophysics and Bioengineering 13: (1984). 4. Sibarita, J. B. Deconvolution microscopy. Advances in Biochemical Engineering and Biotechnology 95: (2005). 5. Carrington, W. A., Lynch, R. M., Moore, E. E. W., Isenberg, G., Fogarty, K. E. and Fay, F.S. Superresolution three dimensional images of fluorescence in cells with minimal light exposure. Science 268: (1995).