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 fo objective lens object focused near the focal length  Objective creates image at distance g from fo & magnifies image  Tube length g is distance from fo 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  fo = objective focal length  Eyepiece magnification is (fe in cm) 25 me  fe  Net Microscope Magnification g25 M  mo me  fo fe

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  fo  fe

 Magnification is again  f m  e  o  o fe

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  fo  fe

 Eyepiece now negative fe  Advantage: non-inverting images but harder to make  Erecting: Kepler with lens to create inversion  Early telescope had poor images & lots of chromatic aberration

Reflecting Telescopes  Much easier to make big mirrors then lenses & better images  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 24Dobjective(dia in cm) or 60Dobjective (inches)

Telescopes as Beam Expanders  With lasers telescopes used as beam expanders  Parallel light in, parallel light out  Ratio of incoming beam width W1 to output beam W2

f 2 W2  W1 f1

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 >5o  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  3  5 sin( )      3! 5!  Gaussian Lens formula

n n n  n   s s r  Now Consider adding the 3 to the lens calculations  Then the formula becomes

2 2 n n n  n 2  n 1 1  n  1 1      h          s s r 2s  s r  2s r s 

 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

r  r q  2 1 r2  r1

 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

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 ,