SLIDE 1
Ivo Ihrke / Summer 2011
Ivo Ihrke / Summer 2011
Aperture: Stops and Pupils
- Principal effect: changes exposure
- Side effect: depth of field
Optics II Ivo Ihrke / Summer 2011 Aperture: Stops and Pupils - - PowerPoint PPT Presentation
Optics II Ivo Ihrke / Summer 2011 Aperture: Stops and Pupils - - PowerPoint PPT Presentation
Optics II Ivo Ihrke / Summer 2011 Aperture: Stops and Pupils Principal effect: changes exposure Side effect: depth of field Ivo Ihrke / Summer 2011 Aperture Irradiance on sensor is proportional to square of aperture diameter A
SLIDE 2
SLIDE 3
Ivo Ihrke / Summer 2011
Aperture
Irradiance on sensor is proportional to
square of aperture diameter A inverse square of sensor distance (~ focal length)
Aperture N therefore specified relative to focal length
A f f = /#
f-number
SLIDE 4
Ivo Ihrke / Summer 2011
Aperture
How to read the f/#:
numbers like “f/1.4” – for 50mm lens, aperture is
~35mm
exposure proportional to square of F-number, and
independent of actual focal length of lens!
Doubling series is traditional for exposure
therefore the familiar (rounded) sqrt(2) series 1.4, 2.0, 2.8, 4.0, 5.6, 8.0, 11, 16, 22, 32, …
SLIDE 5
Ivo Ihrke / Summer 2011
How low can N be?
Principal planes are the paraxial approximation
- f a spherical “equivalent refracting surface”
Lowest N (in air) is f/0.5 Lowest N in SLR lenses is f/1.0
image: Kingslake 1992
' sin 2 1 /# θ = f
SLIDE 6
Ivo Ihrke / Summer 2011
Depth of Field
images: London and Upton
SLIDE 7
Ivo Ihrke / Summer 2011
Depth of focus
(in image space)
tolerance for placing the focus plane Note that distance from (in-focus) film plane to front versus back of depth of focus differ
image: Kingslake 1992 C’ - circle of confusion
SLIDE 8
Ivo Ihrke / Summer 2011
Depth of Field
(in object space)
the range of depths where the object will be in focus
www.cambridgeincolour.com
SLIDE 9
Ivo Ihrke / Summer 2011
Depth of field
(in object space)
total depth of field (i.e. both sides of in-focus plane) where
f/# = F-number of lens C = size of circle of confusion (on image) U = distance to focused plane (in object space) f = focal length of lens
hyperfocal distance
back focal depth becomes infinite when U = f 2 / C f/#
2 2
/# 2 f U C f Dtot =
(from Goldberg)
SLIDE 10
Ivo Ihrke / Summer 2011
Numerical Aperture
The size of the finest detail that can be resolved is
proportional to λ/NA.
larger numerical aperture resolve finer detail
θ sin n NA =
SLIDE 11
Ivo Ihrke / Summer 2011
Numerical Aperture vs. F-Number
low magnification working f-number: distance-related magnification: m relevant for systems with high magnification (microscopes or macro lenses)
NA f 2 1 /#≈ /# ) 1 ( 2 1 /# f m NA f
w
+ ≈ =
w
f /#
SLIDE 12
Ivo Ihrke / Summer 2011
Examples
f/# = f/4, C = 8, U = 1m, f = 50mm
Dtot = 80mm
f/# = f/16, C = 8, U = 9mm, f = 65mm
Canon MP-E at 5:1 (macro lens) use at short distances
(M=5 here)
Dtot = 0.075mm !
2 2
/# 2 f U C f Dtot =
image: Charles Chien
SLIDE 13
Ivo Ihrke / Summer 2011
Tilt and Shift Lens
Lens shift simply moves the optical axis with regard to the film.
change of perspective (sheared perspective)
Tilt allows for applying Scheimpflug principle
all points on a tilted plane in focus
image: wikipedia
SLIDE 14
Ivo Ihrke / Summer 2011
Diffraction Limit
Diameter d of 70% radius of the Airy disc
A f N d λ λ 22 . 1 22 . 1 = =
single spot barely resolved no longer resolved
SLIDE 15
Ivo Ihrke / Summer 2011
Resolution
Ernst Abbe (1840-1905)
image of a lens focusing as a wave optical picture
SLIDE 16
Ivo Ihrke / Summer 2011
Describing Sharpness
Point spread function (PSF)
image: Smith 2000
SLIDE 17
Ivo Ihrke / Summer 2011
Describing Sharpness
Modulation transfer function (MTF)
Modulus of Fourier transform of PSF
image: Smith 2000
SLIDE 18
Ivo Ihrke / Summer 2011
Camera Exposure
- Exposure can be varied in two ways:
Aperture: f-stop - 1 stop doubles H
Interaction with depth of field
Shutter: Doubling the effective time doubles H
Interaction with motion blur
H E T = ×
SLIDE 19
Ivo Ihrke / Summer 2011
Aperture vs Shutter
f/16 1/8s f/4 1/125s f/2 1/500s images: London and Upton
SLIDE 20
Ivo Ihrke / Summer 2011
Imperfections in Imaging
SLIDE 21
Ivo Ihrke / Summer 2011
Lens Aberrations
Spherical aberration Coma Astigmatism Curvature of field Distortion
SLIDE 22
Ivo Ihrke / Summer 2011
Sharpness Related Aberrations
SLIDE 23
Ivo Ihrke / Summer 2011
Chromatic Aberration
Index of refraction varies with wavelength For convex lens, blue focal length is shorter Can correct using a two-element “achromatic doublet”, with a different glass (different n’) for the second lens Achromatic doublets only correct at two wavelengths… Why don’t humans see chromatic aberration?
SLIDE 24
Ivo Ihrke / Summer 2011
Chromatic Aberrations
Longitudinal chromatic aberration (change in focus with wavelength)
image: Smith 2000
SLIDE 25
Ivo Ihrke / Summer 2011
Chromatic Aberrations
Lateral color (change in magnification with wavelength)
image: Smith 2000
SLIDE 26
Ivo Ihrke / Summer 2011
Spherical Aberration
Focus varies with position on lens.
images: Forsyth&Ponce and Hecht 1987
- Depends on shape of lens
- Can correct using an aspherical lens
- Can correct for this and chromatic aberration by combining
with a concave lens of a different n’
SLIDE 27
Ivo Ihrke / Summer 2011
Oblique Aberrations
Spherical and chromatic aberrations occur on the lens axis. They appear everywhere on image. Oblique aberrations do not appear in center of field and get worse with increasing distance from axis.
SLIDE 28
Ivo Ihrke / Summer 2011
Aberrations
Coma
- ff-axis will focus to different locations depending on
lens region
(magnification varies with ray height)
images: Smith 2000 and Hecht 1987
SLIDE 29
Ivo Ihrke / Summer 2011
Coma
SLIDE 30
Ivo Ihrke / Summer 2011
Astigmatism
The shape of the lens for an of center point might look distorted, e.g. elliptical
different focus for tangential and sagittal rays
image: Smith 2000 Hardy&Perrin
SLIDE 31
Ivo Ihrke / Summer 2011
Astigmatism
(Video)
SLIDE 32
Ivo Ihrke / Summer 2011
Astigmatism
red - unsharp
SLIDE 33
Ivo Ihrke / Summer 2011
Curvature of Field
focus “plane” is actually curved
Object Image
SLIDE 34
Ivo Ihrke / Summer 2011
Field Curvature
SLIDE 35
Ivo Ihrke / Summer 2011
Field Curvature
different image distance
SLIDE 36
Ivo Ihrke / Summer 2011
Bad Optics
curvature of field, coma, chromatic aberration
SLIDE 37
Ivo Ihrke / Summer 2011
Distortion
SLIDE 38
Ivo Ihrke / Summer 2011
Distortion
Ratios of lengths are no longer preserved.
Object Image
SLIDE 39
Ivo Ihrke / Summer 2011
Geometric distortion
Change in magnification with image position
image: Smith 2000
SLIDE 40
Ivo Ihrke / Summer 2011
Radial Distortion
image: Kingslake
SLIDE 41
Ivo Ihrke / Summer 2011
Contrast Issues
SLIDE 42
Ivo Ihrke / Summer 2011
Radial Falloff
Vignetting – your lens is basically a long tube. Cos^4 falloff – “rule of thumb”.
At an angle, area of aperture reduced by cos(a) 1/r^2: Falls off as 1/cos(a)^2 (due to increased
distance to lens)
Light falls on film plane at an angle, another cos(a)
reduction.
SLIDE 43
Ivo Ihrke / Summer 2011
Vignetting - Example
a white diffuse target actual photograph
SLIDE 44
Ivo Ihrke / Summer 2011
Flare
Artifacts and contrast reduction caused by stray reflections
image: Curless notes
SLIDE 45
Ivo Ihrke / Summer 2011
Flare
Artifacts and contrast reduction caused by stray reflections Can be reduced by antireflection coating (now universal)
images: Curless notes
SLIDE 46
Ivo Ihrke / Summer 2011
Ghost Images
Minimize artifacts, maximize flexibility Artifacts
Spherical Aberration Chromatic Aberration Distortions Lens Flare
image: Kingslake 1992
SLIDE 47
Ivo Ihrke / Summer 2011
Ghost Images
image: Kingslake 1992
SLIDE 48
Ivo Ihrke / Summer 2011
Lens Flare – Effect of Coating
coating
SLIDE 49
Ivo Ihrke / Summer 2011
Other Optical Elements
SLIDE 50
Ivo Ihrke / Summer 2011
Beam Splitters
splits ray into two can be polarizing or not 50/50 most common
- ther ratios available e.g. 90/10
two types
beam splitter cube – no ray offset semi-transparent mirror – ray offsets
[Zetterling/KTH] incoming ray cause of ray offsets
SLIDE 51
Ivo Ihrke / Summer 2011
Polarizers
SLIDE 52
Ivo Ihrke / Summer 2011
[victorvonsalza/Flickr] unpolarized with polarizing filter
SLIDE 53
Ivo Ihrke / Summer 2011
Neutral Density Filters
pieces of dark glass
─ flat spectral response
Use: generate different exposure at same lens settings and exposure time
─ i.e. preserve motion blur and depth-of-field
characteristics of photograph while making it darker
graduated versions exist
SLIDE 54
Ivo Ihrke / Summer 2011
Neutral Density Filter
SLIDE 55
Ivo Ihrke / Summer 2011
Spectral Filters
are attenuating different wavelengths differently attenuation in mathematical terms: multiplication
spectrum filter response filtered spectrum
SLIDE 56
Ivo Ihrke / Summer 2011
Variable Spectral Filters
interference-based filters can be designed almost arbitrarily for specific incidence angle
SLIDE 57
Ivo Ihrke / Summer 2011
Prisms
several types of prisms exist
dispersing ─ e.g. spectroscope reflecting ─ e.g. SLR, binoculars polarizing
SLIDE 58
Ivo Ihrke / Summer 2011
Diffraction grating
laser ray is diffracted into multiple individual rays
diffraction grating
SLIDE 59
Ivo Ihrke / Summer 2011
Diffraction Gratings
transmissive / reflective types example: compact disc
large reflective grating
SLIDE 60
Ivo Ihrke / Summer 2011
Grating Formulas – Position of Maxima
SLIDE 61
Ivo Ihrke / Summer 2011
Grating Formulas – Intensity of Maxima
radiance from superposition of spherical waves (interference) – solid line modulated (multiplied) by single slit diffraction pattern (Airy pattern) – dashed line
SLIDE 62
Ivo Ihrke / Summer 2011
Summary
Optics Depth of Field Point-Spread-Function Numerical Aperture and resolution limits Lens Aberrations
- ther optical elements
SLIDE 63
Ivo Ihrke / Summer 2011
Next Lecture
Sensor Technology
SLIDE 64
Ivo Ihrke / Summer 2011
Bibliography
Hecht, Optics. 2nd edition, Addison-Wesley, 1987. Smith, W. J. Modern Optical Engineering. McGraw-
Hill, 2000.
Kingslake, R. A History of the Photographic
- Lens. Academic Press, 1989.