Optical Microscopy Lecture 1

Concepts we will discuss in this lecture: Natures of light Mechanism of Optical Imaging system The Use of Lenses and the Problem of Lenses Spatial Resolution

Some Properties of Light Both lasers and white light sources used in microscopy Laser White light Chromatic Polarization Phase Direction

Monochromatic vs white light 450 nm 600 nm White light contains all, or most, of the colors of the visible spectrum. Lasers are Monochromatic (very narrow frequency distribution) Both white light, lasers used in microscopy techniques

Polarization of Light s= horizontal p= vertical for propagation Plane where electric field vector lies, E=Eºcos(ωt) Perpendicular to direction of propagation s= horizontal p= vertical Vertical for propagation Parallel to floor Circular polarization: H,V (s,p) 90 degrees out of phase horizontal This nature used extensively In microscopy: pol microscopy, DIC, SHG elliptical polarization: less than 90 out of phase

Particle (Quantized) Behavior Light interacting with matter: absorption, reflection photon smallest unit- energy corresponds to frequency ()   h=6x10-34 J*s Planks constant ~10-19 J for visible light (=600 nm) best for describing absorption, emission of light Best for describing how detectors work (photomultipliers, Diodes)

Wave Behavior Constructive, destructive interference 0, 180 degrees Limiting cases for complete constructive, Destructive interference, respectively Underlies image formation in almost all forms of microscopy: phase, DIC, polarization, Some advanced forms of confocal

Representations of Light Absorption, lasers Interference, Image formation Good for modeling Light propagation: Ray Tracing Not real form Wave, particle duality physically important Some phenomenon described by both

Hooke made the first optical microscope Robert Hooke

The first image of Hooke and the birth of the term “Cell”

Converging (focusing) Lens The parallel rays converge at the second focal point F‘. The first focal point is at the front. All rays originated at This point become parallel to the axis after the lens.

Diverging (defocusing) Lens Focal length is negative To an eye on the right-hand side, these diverging rays will Appear to be coming from the point F’: the second focal point.

Snell’s Law medium index air (STP) 1.00029 water (20° C) 1.33 where q1 is the angle of incidence, q2 is the angle of refraction medium index air (STP) 1.00029 water (20° C) 1.33 crown glass 1.52 flint glass 1.65                                            

Ray Tracing Rules for locating image Only need 2 rays

Single-lens Imaging system Real image: if rays intersect and unite in image plane and can be projected onto some surface in image plane Two-lens Imaging system Virtual Image: if rays diverge, but backwards extensions converge and intersect behind specimen

Eye is part of optical system of microscope A slightly more complicated imaging system aka old microscope Eye is part of optical system of microscope

Infinity Corrected Microscopes: last 15 Years Infinity optics allows insertion of Filters, analyzers without changing tube length, or final image Infinity=parallel

Basic Formulae in air Lensmakers equation Thin lens formula Object plane Image plane Lensmakers equation  Thin lens formula 

Some Conventions S is distance from the object; S’ is distance from the image Sign conventions: m = positive for inverted image; negative for upright Sign conventions: f = positive for converging lens; negative for diverging lens

Keplerian Telescope

Galilean telescope

Upright Microscope Geometry

Inverted Microscope Geometry

Inverted vs Upright Geometries Move stage for focusing (unless fixed stage) Optical path is simpler Easier for immersion (long working distance) Inverted: Move objective for focusing Better access for live cells in culture Electrophysiology Harder for oil, water immersion.

Refractive Index Depends on the Wavelength This is called dispersion

Dispersion of Air

Dispersion of Glass

How to Calculate? Sellmeier Equations All but quartz Quartz These values are tabulated (e.g. CVI Laser, Melles Griot)

Chromatic Aberration in Photography

Doublet Lens Corrects Aberration Crown Flint

Spherical Aberration could also be caused by the use of the cover glass-slip. A correction collar might be found on the objective to set the thickness of the glass-slip. If no correction collar can be found, the objective is corrected for a 0.17 mm glass-slip.

Astigmatism and coma are caused by imperfection in the lens manufacturing.

Field Curvature

Newer: CF lens – meaning Chromatic aberration Free.

The Main Function of the Microscope is NOT to MAGNIFY

What’s Important for a Microscope? Contrast is necessary to detect detail from background light from an object must either be different in intensity or color (= wavelength) from the background light: Both used in light and fluorescence microscopy Resolution fundamentally limited by diffraction diffraction occurs at the objective lens aperture

Numerical Aperture (N.A.) q specimen Objective lens Image plane From diffraction theory l n sinq d  N.A. = n sinq Minimum spot NA= radius/focal length Abbe` Limit ~250 nm in visible Resolution only determined by NA and wavelength

Electromagnetic Spectrum Visible region used for Light microscopy small Part of EM spectrum Resolution limit : λ/2 ~200 nm: Visible good for Live specimens: Cells, organelles Ideal for micron sized structures EM, X-ray cannot do live imaging

Consider microscope object as simple grating Spacing of Grating and Diffraction Pattern S=3 microns S=12 microns Inverse relationship (transform) of object spacing (or size) and diffraction pattern

Double-slit Experiment Condition for Constructive interference: a sinθ = nλ n = 0, 1, 2,  3 … After focusing: d = f λ / a

Multiple-slit is not Too Different

Abbe’s Diffraction Pattern from White Light

Tube Lens d1 Fringe spacing in the image: d2 = f’ λ / d1 = f’ λ a / f λ = M a Requires at least one of the first order diffraction spot in order to form the image.

Diffracted Spots in back focal plane No specimen diffraction: no image Specimen diffraction: no collection, no image 0th and first order diffraction 0th and first and second order diffraction better resolution Abbe showed need for central and diffracted spot

2 D diffraction of periodic structures: on road to real object

Visualizing objects below the diffraction limit Subresolution beads Appear same size 60 nm 800 nm

Diffraction from self-luminous spot: delta function source Impossible to remove interference rings: Separated exactly by n Absence of light between Rings is due to destructive interference Light from each point of the object is spread out in the microscope because light diffracts at the edges of the lens Central spot is 0th order diffraction or Airy disk Contains 84% of power

Aperture size, Interference, and Resolution Con inter at P’ Destr at P’’ Full aperture Interference in image plane P’-P’’ distance Smaller for full aperture Reduced aperture Always fill Lens aperture For highest resolution Maxima larger, max, min further apart: Covers more cone cells or camera pixels: less resolution

MORE IMPORTANT THAN MAGNIFICATION !! RESOLUTION The resolution of a microscope is the shortest distance two points can be separated and still be observed as 2 points. Not resolved Well resolved just resolved MORE IMPORTANT THAN MAGNIFICATION !!

Limits on NA and Resolution? High NA Low NA Limits on NA and Resolution? Air: NA= 0.95 for a =70 degrees Immersion increase n: NA= 1.4 a =67 degrees (oil) n~1.5 1.2 (water) n=1.33 Higher index materials for greater resolution? Some exist: methyl iodide, smelly, toxic Also need higher index coverslips, slides

Useful Magnification (total) = 500 to 1000 • NA (Objective) More mag does not help, and decreases image quality through artifacts, diffraction Limit comes from rod separation in the eye

Depth of Field: Axial resolving power Defined only by NA2 Small Depth of Field at high NA Focusing critical at high NA

Gromit captured at f/22 (left) and at f/4 (right). f = image distance / effective diameter of the lens