Zoom Lenses
• Many camera lenses now Zoom Lenses
• Idea is to have a single lens with many focal lengths
• Eg. standard 35 mm/DSLR lens is 50 mm
• Smaller f is wide angle, larger telephoto
• Typical Zoom cover 24-70 mm,70-300mm or 28-200 mm
• Lens lengthens as zoom
Nikkor 28-200 mm zoom
200 mm
28 mm
Variable Power (Zoom) Concept
• Any single with unit power can be zoom lens
• Magnification depends on position of the lens
• If move lens towards object image larger, and s’ increases
• If move lens away from object image smaller, and s’ decreases
• Conjagate pairs where object to image is constant
• But magnification is reciprocal of distances
• Problem is to do this without significant changes
• Need an afocal zoom
Zoom Lenses Structure
• Zoom lens consists of an afocal zoom system + focussing lens
• Afocal zoom takes in parallel light and changes diameter
• Acts as a variable beam expander
• Consists of L1 positive, L2 negative, L3 positive
• Need L1=L3, L2<-f1/2
• Focusing lens creates the actual image
Zoom Lens Operation
• As L1 and L2 moves between changes amount of zoom
• L2 close to L1 and far from L3, max magnification
• L2 close to L3 and shortest separation, min magnification
• L1 moves forward as L2 moves to L3
• At the two extreme and center is afocal (parallel)
• Inbetween slight modification
Zoom Lens Movement
• Zoom requires a complicated gear/movement system to work
• Called mechanical compensation
• In practice change two of the lens
• Create cams: L2 moves in on path will L1 follows the curve
• Complicated formulas to get this
• Top lenses use computer controlled servo motors now
Zoom Limitation
• Focusing lens brings the parallel light into focus
• Parfocal lens: stays in focus as zooms
• Important for video/movie cameras & still
• Varifocal allows focus to change – possible now with autofocus
• To make parfocal the fixed lens designed to focus at 3 points
• Adding additional negative makes more parfocal
• As change zoom change aberrations
• Hard to compensate for chromatic and field curvature
• Often requires additional lenses
• Min f# often decreases as zoom increases
• Microscopes and telescopes use eyepieces for magnification
• Aperture stop is actually the iris of the eye for these
• Design to trace rays from the eye/iris aperture stop to image plane
• Problem is at outer edges get
astigmatism, lateral color coma, & distortion
• Many different designs used to compensate
• Lower magnification, less problems
• Typically 5x to 20x used
Classic Eyepieces: Huygenian
• Invented by Christiaan Huygens in the 17th century
• Huygenian: 2 plano convex with plane to the eye
• Use low index glass
• Probably the most common type used
• Correct lateral colour by spacing
• Spacing for chromatic aberration of one lens balances other
• Coma is corrected for a given objective distance
• Field stop is in “natural” position between lenses
• Image plane internal to lens – eye does most of magnification
• Field of view up to ~30-35o
• Tends to strain eyes
• Due to eye relief the distance the eye must be from eyepiece
• Small distance hard to keep in focus
• Typically 2 mm – 20 mm for many eyepieces
Ramsden Eyepiece
• Created by Jesse Ramsden in the 18th century
• Ramsden reduces distance between lenses
• Now planer sides on ends
• Field stop is at back of objective
• Image plane is external to lens
• Lateral colour not corrected
• but chromatic aberrations generally smaller
• Reduces spherical aberrations and distortion
• Coma adjusted by ratio of lens powers
• Can place a reticle (cross hair) at back flat surface
• Very good for monochromatic light
Kellner Eyepiece
• Carl Kellner created an achromatic eyepiece in 1850
• Ramsden with achromat added as first lens
• Often departs from plano-convex lenses
• Achromat reduces chromatic aberrations significantly
• Also space in achromat adds additional design freedom
• Field of view also larger
Comparing Eyepieces
• Improve as goes from Hygens to Kellner
• Kellner very good in chromatic & distortion
• Better eye relief also
Criteria for Optical Systems: Optical Path Difference
• Optical Path Difference from different part of lens sets quality
• Called OPD
• Related to the Airy disk creation
Point Sources and OPD
• Simplest analysis: what happens to a point source
• As add OPD delay get distortion
• Little effect at λ/4
• By OPD λ/2 get definite distortion
• λ OPD point is really distorted
Point Spread Function
• Point Spread Function (PSF) is distribution of point
• Often calculate for a system
• Distorted by Optical path differences in the system
Wave Front Error
• Measure peak to valley (P-V) OPD
• Measures difference in wave front closest to image
• and furthest (lagging behind) at image
• Eg. in mirror system a P-V <0.125 to meet Rayleigh criteria
• Because P-V is doubled by the reflection
• Reason this is doubled
• Also measure RMS wavefront error
• Difference from best fit of perfect spherical wavefront
Depth of Focus
• Depth of focus: how much change in position is allowed
• With perfect optical system <λ/4 wavefront difference needed
• Set by the angle θ of ray from edge of lens
• This sets depth of focus δ for this OPD <λ/4
δ =±
(2 n sin θ )
= ±2λ ( f # )
• Thus f# controls depth of focus
• f#:4 has 16 micron depth
• f#:2 only 2 micron
• Note Depth of Field is used in photography
• Depth that objects appear in focus at fixed plan
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