Optical Systems: Pinhole Camera Pinhole camera: simple hole in a box: Called Camera Obscura Aristotle discussed, Al-Hazen analyzed in Book of Optics 1011CE Restricts rays: acts as a single lens: inverts images Best about 0.5-0.35 mm hole at 25 cm distance Diffraction from pinole edges blurs image below that Advantages: simple, always in focus Disadvantages: very low f# ~500 so slow exposure
Classical Compound Microscope 2 lens optical systems were the first: microscope & telescope ~1590 eyeglass maker Janssen assembly 2 lenses into telescope 1667 Robert Hook uses first microscope to image material Classical system has short f o objective lens object focused near the focal length Objective creates image at distance g from f o & magnifies image Tube length g is distance from f o to where eyepiece is focused Objective working distance typically small (20-1 mm) Eyepiece is simple magnifier of that image at g Magnification of Objective g mo fo where g = Optical tube length f o = objective focal length Eyepiece magnification is (f e in cm) 25 me fe Net Microscope Magnification g25 M mome f f o e First Telescope
Classic Microscope To change magnification change objective or eyepiece f s Typical max is eyepiece 10x to 20x and objective 100x Total optical magnification ~ 1000
Infinite Corrected Microscopes Classical Compound Microscope has limited tube length New microscope "Infinite Corrected" Objective lens creates parallel image Tube lens creates converging image Magnification now not dependent on distance to tube lens: thus can make any distance between objective/eyepiece Good for putting optics in microscope Laser beam focused at microscope focus
Telescope Increases magnification by increasing angular size Eyepiece magnifies angle from objective lens Earliest used convex objective and concave eyepiece 1609 Galileo makes this telescope into useful distance imager Simplest "Astronomical Telescope" or Kepler Telescope two convex lenses focused at the same point Distance between lenses: d f o f e Magnification is again m e o f f o e
Different Types of Refracting Telescopes Refracting earliest telescopes comes from lens Keplerean Telescope: 2 positive lenses Problem: inverts the image Galilean: concave lens at focus of convex d f o f e Eyepiece now negative f e Advantage: non-inverting images but harder to make Erecting: Kepler with lens to create inversion
Reflecting Telescopes Much easier to make big mirrors then lenses Invented by James Gregory (Scotland) in 1661 Many designs: Hale (on axis observer) & Herschel (off axis) first Newtonian: flat secondary mirror reflects to side: first practical Gregorian adds concave ellipsoid reflector through back Cassegrainian uses hyperboloid convex through back Newtonian & Cassagranian most common Practical max mag 24D objective (dia in cm) or 60D objective (inches)
Telescopes as Beam Expanders With lasers telescopes used as beam expanders Parallel light in, parallel light out Ratio of incoming beam width W 1 to output beam W 2 W 2 2 W1 1 f f
Telescopes as Beam Expanders Can be used either to expand or shrink beam Kepler type focuses beam within telescope: Advantages: can filter beam Disadvantages: high power point in system Galilean: no focus of beam in lens Advantages: no high power focused beam more compact less corrections in lenses Disadvantages: Diverging lens setup harder to arrange
Aberrations in Lens & Mirrors (Hecht 6.3) Aberrations are failures to focus to a "point" Both mirrors and lens suffer from these Some are failures of paraxial assumption 3 5 sin( ) 3! 5! Paraxial assumption: uses only the first term Recall that errors strongly occurs for angles >5 o Error results in focused points having halos around them For a image all these rings add up to make the image fuzzy
Spherical Aberrations from Paraxial Assumption Formalism developed by Seidel: terms of the sin expansion!! ) sin( 5 3 5 3 Gaussian Lens formula r n n s n s n Now Consider adding the 3 to the lens calculations Then the formula becomes 2 2 2 1 1 2 1 1 2 s r s n r s s n h r n n s n s n Higher order terms add more Now light focus point depends on h (distance from optic axis)
Types of Spherical Aberration Formalism developed by Seidel: terms of the sin expansion First aberrations from not adding the 3 to the lens calculations Longitudinal Spherical Aberration along axis Transverse Spherical Aberration across axis These create a circle of least confusion at focus Area over which different parts of image come into focus Lenses also have aberrations due to index of refraction issues
Mirrors and Spherical Aberrations For mirrors the shape of the mirror controls the aberrations Reason reflectors generally no have wavelength effects Corrected by changing the mirror to parabola If y is optical axis and x, y 0 starts at vertex then 4 Where f = focal length Mirrors usually have short f compared to radius f4-f10 Hence almost all mirror systems use parabolic mirrors
Hubble Telescope Example of Design Error Hubble mirror was not ground to proper parabola too flat Not found until it was in orbit Images were terribly out of focus But they knew exactly what the errors Space walk added a lens (called costar) to correct this
Spherical Aberration: Off axis rays Off axis rays are not focused at the same plane as the on axis rays Called "skew rays" Principal ray, from object through optical axis to focused object Tangental rays (horizontal) focused closer Sagittal rays (vertical) further away Corrected using multiple surfaces Problem is worse furthest from optical axis (low F# systems) Eyes have curved retina so do not have this problem Researchers building sensors with curved surfaces now
Coma Aberration Comes from third order sin correction Off axis distortion Results in different magnifications at different points Single point becomes a comet like flare Coma increase with NA Corrected with multiple surfaces
Field Curvature Aberration All lenses focus better on curved surfaces Called Field Curvature Positive lens, inward curves Negative lens, outward (convex) curves Reduced by combining positive & negative lenses
Distortion Aberration Distortion means image not at par-axial points Grid used as common means of projected image Pincushion: pulled to corners Barrel: Pulled to sides
Lens Shape Different lens shapes is the amount of aberration Coddington Shape Factor measures shape q r r 2 2 r1 r Plano convex has q of +1 if curve to object, -1 if flat to object Biconvex has q = 0 Chart shows how aberrations change with shape The higher the n of the lens the smaller the spherical aberration 1
Index of Refraction & Wavelength: Chromatic Aberration Different wavelengths have different index of refraction Often list wavelength by spectral colour lines (letters) Index change is what makes prism colour spread Typical changes 1-2% over visible range Generally higher index at shorter wavelengths
Chromatic Aberration Chromatic Aberrations different wavelength focus to different points Due to index of refraction change with wavelength Hence each wavelength focuses rays at different points Generally blue closer (higher n) Red further away (lower index) Important for multiline lasers Achromatic lenses: combine different n materials whose index changes at different rates Compensate each other
Lateral Colour Aberration Blue rays refracted more typically than red Blue image focused at different height than red image Results in colour blur around objects at outer edge of lens
Singlet vs Achromat Lens Combining two lens significantly reduces distortion Each lens has different glass index of refraction Also change of n with wavelength different Positive crown glass (n~1.52) Negative meniscus flint glass (n~1.6) Give chromatic correction as well
Combined lens: Unit Conjugation Biconvex most distortion Two planocovex significant improvement Two Achromats reversed best This is why high quality lenses are so expensive
Materials for Lasers Lenses/Windows Standard visible BK 7 Boro Silicate glass, pyrex For UV want quartz, Lithium Fluroide For IR different Silicon, Germanium CaF2 (Calcium Fluoride), BaF2 (Barium Fluoride), LiF (Lithium Fluoride), Si (Silicon), Ge (Germanium), Optical Glass, Fused Silica UV,