What is depth of focus of camera lens? • Depth of focus – Range of lens-to-cameraback distances for which one image is tolerably sharp (reasonably in focus) • Infinite for pinhole camera • image is always in focus • ≈ one ray connects each object pt to image pt – For lens-camera depth of focus depends on • lens diameter, • focal length and • object distance – Circle of confusion • locus of rays that focus to pt elsewhere • If diameter of circle of confusion is small enough blur is tolerable – Lens with smaller diameter has larger depth of focus • More like a pinhole (image is dimmer) f f circles of confusion image blurry here but tolerable depth of focus smaller circle of confusion missing ray 1
Transcript
What is depth of focus of camera lens?• Depth of focus
– Range of lens-to-cameraback distances for which one image is tolerably sharp (reasonably in focus)
• Infinite for pinhole camera • image is always in focus • ≈ one ray connects each object pt to
image pt– For lens-camera depth of focus
depends on • lens diameter, • focal length and • object distance
– Circle of confusion • locus of rays that focus to pt elsewhere• If diameter of circle of confusion is
small enough blur is tolerable– Lens with smaller diameter has
larger depth of focus• More like a pinhole (image is dimmer)
f
fcircles of�confusion
image�blurry here�
but �tolerable
depth of focus
smaller�circle of�
confusion
missing ray
1
What is depth of field of a lens?
• Depth of field – related to depth of focus– maximum separation distance
(along axis) between two objects such that both objects are tolerably sharp (in reasonably good focus)
– Deep focus: term for large depth of field in movie-making
– Pinhole camera depth of field is ∞ • all objects in focus at all lens-to-
camera-back distances.
• Smaller lens opening (aperture) ⇒ – larger depth of field but– dimmer image
• Wide angle lenses generally have more depth of field than telephotos
Depth of�field
diameter ofcircle of confusion�
(maximum tolerable blur)
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Circles of confusion
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A camera is focused by changing the distance between the lens and the film or CCD at the back of the camera
• xi in lens eqn is distance between lens and back of the camera (where image is recorded) • 1/f = 1/xo + 1/xi
• Suppose you take a picture of your friend using a camera with a lens of focal length f = 1 cm • The friend is a distance xo = 100cm
from the camera lens• For what value of xi is the image at
the back of the camera in focus?a) The value obtained by solving
the lens eqn for xib) 100 cmc) Roughly the same as the focal
length, f
• Given: f = 1 cm, xo = 100 cm• Find: image distance, xi• 1/f = 1/xo + 1/xi• 1/1 = 1/100 + 1/xi• 1 - 0.01 = 1/xi• 0.99 = 1/xi• xi = 1/0.99 = 1.01 cm– Both (a) and (c) are both correct
• When take picture of object a distance xo away from camera which is much larger than the focal length, f, the image distance, xi, will always be a number very close to f• This is because rays from distant
object are almost parallel and therefore go through the focal point!!
• Can also see from lens equation4
What are apertures, f-numbers and stops?
• Diameter of lens aperture can be reduced by using diaphragm.– Largest aperture is full diameter of
lens– Smaller apertures are called stops
• Aperture is measured by f-number: focal length of lens divided by diameter of aperture:– f-number (or f-stop) = f/d– Large f-number means small lens
diameter
• What is f-number (f-stop) of same lens when diaphragm reduces dia-meter of lens from 10 mm to 5 mm?
40 mm focal�length lens
at full aperture�of diameter d = 10 mm
40 mm focal�length lens
with aperture�of diameter�d = 5 mm
10f-number = -
f = 4 ( = f/4)
a) f/2, b) f/4, c) f/6, d) f/8, e) f/10
10 5
5
Camera exposure is related to Poynting flux carried by light wave.
• Wave energy density and flux of wave energy density ∝ E2
– Flux of energy density =• Poynting flux
[velocity×energy-density – �(m/s)×J/m3]
• Intensity �[power/m2 - watts/m]
• When brighter (more intense) light enters your eye– Electric force field of light is
stronger (more photons)– More absorption in your retina
(back of eye)
rays converge here
electric force fields add here
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Lens with larger aperture lets more light energy reach image pts. at back of camera �
(where CCD records image)• Larger aperture lens brings
more rays from each object pt. to corresponding image pt.
• Pinhole only lets "one" ray from real nose converge at image nose. – Image is dim (not intense)
• Small aperture lens lets a few more rays from nose converge to image nose. – Brighter image
• Large aperture lens allows more rays from nose to con-verge to image nose. – Image even brighter– Why do we squint in bright light?
Pinhole
Small aperture lens
Large aperture lenswith same focal lengthas smaller aperture lens
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Light is more intense when there is more energy per unit area.
• Intensity of light (Poynting flux) = energy per second per unit area
• Power = energy per second (watts)
• Intensity = power divided by area– Power from 60 watt light bulb same as
move away but intensity decreases– Alex sees intensity (power reaching his
eye = intensity times his eye area) • Intensity ∝ 1/r2
– r = distance from center of light bulb to your eye
– Intensity falls off as square of the distance
– Star seems dim!– Camera flash sometimes can't supply
enough light?
Lightbulb
Draw imaginary sphere whose radius, r = distance from your eye to center of light bulb
r
• Intensity of light is same everywhere on sphere = power divided by area of sphere
Area of sphere ∝ r2 so intensity ∝ r-28
Light energy reaching film each second is proportional to the AREA of lens
• Light energy/s ∝ lens area, A• A ∝ d2
• d ∝ √A
• If A is doubled by what factor does d increase?a) √2b) 2c) 4
Lens
diameter of lens = dd
Area of lens = A = π(d/2)2
Camera
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More light energy reaches ccd when lens f-stop is lower number (lower number means larger area)
• f-stop = (focal length)/d– f-stop at right has diameter d = 5 so f-
stop is 40/5 = 8
• Double diameter, d from 5 to 10 mm– New f-stop is 40/2d = 4– New area of aperture, A, increases by
factor 4– Lets in 4 times amount of �
light energy/s (since energy ∝ Area)
• To double energy reaching CCD: – Multiply old diameter, d, by √2– New area is doubled because √22 = 2– New f-stop ∝1/(√2d) decreased by
factor of 1/√2 from f/8 to f/5.6
40 mm lensat full aperture�2d = 10 mm
10
f = 40 mm lenswith aperture�
d = 5 mm
5
40/d = f/8 40/(2d)�= f/4
Area�= π ·(d/2)2 �
= 6.25 mm2
Area�= π·(2d/2)2�= 25 mm2 �
(4x energy �as at f/8)
40/(√2·d) �= f/5.6
Area = �π ·(√2·d/2)2 �= 12.5 mm2�
(2x energy�as at f/8)
new diameter �= √2·d mm= 7.1 mm
5·√2
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Sequence of f-stops which each let in twice the light energy per sec
Exposure time 1/250 sec 1/125 sec 1/60 sec 1/30 sec
f-number f/5.6 f/8 f/11 f/16
Diameter of 28mm lens
5 mm 3.5mm 2.5mm 1.75mm
Area of aperture of 28 mm lens
20 mm2 10 mm2 5 mm2 2.5 mm2
Light intensity reaching film (arb units)
500 250 120 60
Exposure (arb. units) 2 2 2 2
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How we can understand the concept of intensity in terms of the images from pinhole cameras.
• Intensity of light is energy/second per unit area (e.g., watts per m2)– Light is more intense when there
is more energy delivered to each unit area each second
• How does the intensity change when the image is larger? Is the intensity of light on the film of the telephoto cameraa) higher, b) lower, c) the same
• The same light energy is spread over a larger area so the intensity goes down
• To compensate for this lower intensity cameras use a lens to let in more light than a pinhole can.
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Qualitative argument why f-number is defined as f/d. �(focal length divided by lens aperture diameter)
• Consider two lenses with different focal length but same f-number, say, f/2– f/2 lens with longer focal length, f, must
have larger diameter, d, by definition �f-number = f/d
– Larger d brings more rays to each image point
• If d were not larger, image would be less intense (dimmer, as in pinhole camera)
• Definition f-number = f/d – guarantees that every f/2 lens gives same
exposure for the same shutter speed– regardless of whether focal length, f, is small
(wide-angle lens) or large (telephoto lens).• Quantitative proof on next slide
fnew = 60 mm
f/2 lens with focal length 40 mm means �2= 40/d, so lens has diameter d = 20 mm
f/2 lens with focal length 60 mm means �2= 60/d, so lens has diameter d = 30 mm
f = 40 mm
20 mm
30 mm
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Quantitative argument why two lenses with same f-numbers give image of Alex with same intensity
• If fnew= 60 mm lens did not have larger diameter than f = 40 mm lens, the intensity, Iimage of its image would
– be lower by 1/xi2, where xi is distance from
center of lens to Alex's image– Object is usually far from lens so rays enter
lens almost parallel and xi ≈ f • For same d, Iimage decreases as 1/fnew
2
– Doubling f2 decreases Iimage by factor 2• For same f, Iimage increases as d2
– Doubling d2 increases Iimage by factor 2• Different focal length lenses only have
same Iimage if d2/f2 is same for both.• Ratio d2/f2 = 1/(f-number)2
– If both lenses have same f-number there is no change in image intensity
f = 40 mm
fnew = 60 mm
f/2 lens with f = 40 mm�must have d = 20 mm
f/2 lens with f = 60 mm�must have d = 30 mm
20 mm
30 mm
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Common focal lengths, f, of f/2.8 lenses and required diameters for each
Lens focal length, f
35mm 50mm 80mm 105mm 135mm
Max f/stop f/2.8 f/2.8 f/2.8 f/2.8 f/2.8
d = lens diameter = f/(f/stop)
12.5mm 17.9mm 28.6mm 37.5mm 48.2mm
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Wide angle and telephoto effects in the pinhole camera only depend on distance from pinhole to film
• As distance between pinhole and cam-era back increases, image gets larger
– First camera gives wide-angle effect• camera back is covered by image that
includes more than Alex– Longer camera gives telephoto effect
• Alex's image covers entire camera back – Angle between crossed yellow lines smaller in longer camera
– Image alwayss in focus (sharp)
• Wide angle and telephoto lenses have some similarities to pinhole camera
– Telephoto lenses are long and wide angle lenses are short
• There are also differences– Lens lets in more light ⇒ brighter image – f must be different for different image sizes to maintain focus
smaller�angle
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Digital and 35 mm camera lenses compared (lens may be a zoom lens)
Focal Length of digital
camera lens
Equivalent focal length of 35mm film camera lens
Image appearance
Typical Uses
5.4 mm 35 mm Object looks smaller and farther away.
Wide-angle shots, landscapes, large
buildings, groups of people
7.7 mm 50 mm Object looks about same as what eye sees.
"Normal" shots of people and objects
16.2 mm 105 mm Object is magnified and
appears closer.
Telephoto shots, close-ups
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Meaning of ISO on digital cameras• ISO measures sensitivity of CCD at
image plane– Formerly a measure of film sensitivity
(film "speed")
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• High ISO number means• high sensitivity of CCD• take pictures with less light• or at smaller f/numbers with greater
depth of field• However pictures taken at high ISO
have less resolution• They are pixelated or grainy
