Part 4: Filed and Aperture, Stop, Pupil, Vignetting Herbert Gross

Optical Engineering

Part 4: Filed and aperture, stop, pupil, vignetting Herbert Gross

Summer term 2020 www.iap.uni-jena.de 2 Contents

. Definition of field and aperture . Numerical aperture and F-number . Stop and pupil . Vignetting Optical system stop

. Pupil stop defines: 1. chief ray angle w 2. aperture cone angle u . The chief ray gives the center line of the oblique ray cone of an off-axis object point . The coma rays limit the off-axis ray cone . The marginal rays limit the axial ray cone

stop pupil

coma ray marginal ray y field angle image w u object aperture angle y'

chief ray 4 Definition of Aperture and Field

. Imaging on axis: circular / rotational symmetry Only spherical aberration and chromatical aberrations

. Finite field size, object point off-axis:

- chief ray as reference

- skew ray bundels: y y' coma and distortion y p y'p

- Vignetting, cone of ray bundle not circular O' field of marginal/rim symmetric view ray RAP' chief ray - to distinguish: u w' u' w tangential and sagittal chief ray plane O entrance object exit image pupil plane pupil plane 5 Numerical Aperture and F-number

image . Classical measure for the opening: plane numerical aperture (half cone angle) object in infinity

NA' nsinu' DEnP/2 u'

. In particular for camera lenses with object at infinity: F-number f f F# DEnP

. Numerical aperture and F-number are to system properties, they are related to a conjugate object/image location 1 . Paraxial relation F  # 2n'tanu'

. Special case for small angles or sine-condition corrected systems 1 F  # 2NA' 6 Generalized F-Number

. More general definition infinity

of the F-number for systems finite with finite object location object DExP u' u'o

. Effective or working F-number with f' s' f '1 m s' and D D m D sinu' ExP  ExP  p EnP 2s' 2 f '(1 m) 2n' f (1 m)

we get as a relation with the object-in-infinity-case

eff 1 1 m F#   F#  2n'sinu' mp

m is the system magnification, mp is the pupil magnification Properties of the pupil

Relevance of the system pupil :

. Brightness of the image Transfer of energy

. Resolution of details Information transfer

. Image quality Aberrations due to aperture

. Image perspective Perception of depth

. Compound systems: matching of pupils is necessary, location and size Entrance and exit pupil

field point of image upper object marginal ray point U on axis U' W on axis lower marginal chief point of ray ray image upper coma ray

lower coma ray stop outer field point of object exit entrance pupil pupil 9 Pupil Mismatch

. Telescopic observation with different f-numbers . Bad match of pupil location: key hole effect

F# = 2.8 F# = 8 F# = 22 a) pupil adapted

b) pupil location mismatch

Ref: H. Schlemmer Vignetting

. 3D-effects due to vignetting

. Truncation of the at different surfaces for the upper and the lower part of the cone

object lens 1 aperture lens 2 image stop upper truncation chief ray

lower sagittal coma truncation trauncation rays 11 Vignetting

field . Artificial vignetting: stop truncation Truncation of the free area of the aperture light cone

axis 0.8 D

truncation

AExp . Natural Vignetting: Decrease of brightness according to cos w 4 due to oblique projection of areas and changed photometric distances field angle w imaging with imaging without vignetting imaging with vignetting vignetting

complete field of view 12 Vignetting

. Illumination fall off in the image due to vignetting at the field boundary