optics - · pdf fileinf 5440 - cmos image sensors ao 10v 6.2 optics and resolution focal...

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AO 6.1

Op

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OPTICS

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AO 6.2

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FoA t m the object enter the lens, is focTh

R i

R1

Ref.: Nakamura

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cal lengthhin lens: A object in ‘infinite’ distance from the lens, such that parallel beams forused in the focal point. e focal length, f, is the distance lens - focal point.

s the radius of curvature, n is the refractive index

- R2

f

1f--- n 1–

R1------------ n 1–

R2------------–=

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AO 6.3

Op

Co

ortened” focal length

reased” focal length

Ref.: Nakamura

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mbinations of lenses1f--- 1

f1---- 1

f2---- d

f1f2---------–+=

d

Retrofocus lens: “Sh

Telephoto lens: “inc

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AO 6.4

Op

Ap

(6.1)

(6.2)

ly with increasing f/#

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erture

F-factor, f/# (definition):

Small angles:

Light opening = : Light intensity decreases quadratical

F 12 θ′sin----------------=

θ′ D 2⁄f

----------- F fD----≈⇒≈sin

π D2----

2 πf2

4F2---------=

θ’DD

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AO 6.5

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Sc

FluIo, obj

ThtheSm

Intewri

Whm2

Typpla

f

AL=s=a

gel

AI

y

Flux

bb-f

yβ

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aling (one dimension)

(6.3)

x through a spheric area is given by the intensity multiplied width the solid angle. Flux from an ect with area Ao becomes proportional with IoAo.

e solid angle is given by spheric area divided by square of radius a of the sphere. all angles: area ~ aperture.

nsity at the image plane, the sensor, can be tten as

ere D is the diameter of the aperture. = Ai / Ao is the ratio image area to the object area.

ically, m << 1 and the illuminance at the image ne can be written as

(6.4)

fa

a - f

radiu

Solid an

AO

x

Io

αα

βm y

x--- b

a--- b f–

f----------- f

a f–----------== = = 1

f---→ 1

a--- 1

b---+=

Ii IoAoAL

a2------- 1

AI------ Io

πD2

4---------- 1

a2m2-------------≈

IoπD2

4 1 m+( )2f2------------------------------= =

Ii IoπD2

4f2----------≈ Io

π

4f2 D2⁄------------------- Io

π

4 F( )2--------------= =

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AO 6.6

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UnTh shape(th

6 8 10

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iformitye light will generally decrease form the centre to the periphery and follow a cos4θis is compensated in some lenses).

-10 -8 -6 -4 -2 0 2 40.94

0.95

0.96

0.97

0.98

0.99

1

θ [°]

Norm

aliz

ed in

tensi

ty

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AO 6.7

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Ci

δ “ as a point when viewed at a dis

To rmat (size of image plate).

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rcle of confusion and scaling with sensor size.

Circle of confusion”: Largest blur circle that will be perceived by the human eye tance of 25 cm.

keep the field of view (θ) constant, the focal length is reduces with the optical fo

θ

δ

δ

1 2

12

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AO 6.8

Op

De

Fro

giv

(6.5)

∆=

(6.6)

δD

f

b

b-f

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pth of Field

m triangles above and equation (6.3), Dh = a, and equation (6.2)

es the “Hyper focal length” :

b-f becomes “Depth of focus”:

Dhf

8

DoF

a

δD---- b f–

b----------- f

Dh f–---------------= =

DhDδ---- f 1 δ

D----+

= Dδ----f≈ f2

Fδ------=

∆ δD----b= δ

f--Ff≈ δF=

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AO 6.9

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Ex

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amples

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AO 6.10

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AO 6.11

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De

Us itten as:

(6.7)

δD f

b

b2

b1

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pth of Field

ing the same technique as above, it can be shown that Depth of Field can be wr

f

DoF

a

a1

a2

a2 a1–

2f2

δF--------a a f–( )

2f2

δF--------

2

a f–( )2–

-----------------------------------------=

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AO 6.12

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DiEvebe

Inteairy

Racritpoi

00%

1.75%

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ffractionn optics without aberrations and smear will

a source of diffraction due to the aperture.

rference around small light points called discs.

dius of the first dark circle is the Rayleigh erion for resolution, the separation of two nts.

(6.8)

1

r 1 22λf #⁄,=

r100%

73.5%

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AO 6.13

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NCTION

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MTFMODULATED TRANSFER FU

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MTconfre(1)

or spares

or res

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F of the optics can have low trast at intermediate spatial

quencies, but still high resolution ,

high contrast at intermediate tial frequencies, but low olution (2),

both high contrast and high olution (3).

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AO 6.17

Op

Ra

) = 9%

Ref.: Nakamura

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(6.9)

Using (6.8), and ,

yleigh limit can be expressed by MTF:

MTF (1/r

MTF ν( ) 2π--- λFν( ) λFν 1 λFν( )2––acos

=

ν 1r--- 1

1 22λF,-------------------= =

MTF 1r---

0 0894,=

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AO 6.18

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PIXEL PITCHARRAY SIZE

ANDRESOLUTION

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AO 6.19

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Op diameter)

Ref.: Nakamura

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tical format• Standard lens sizes are measured in inches, i.g. 2/3”, 1/2”, 1/3”, 1/4” (kind of

• The size has influence on the light sensitivity (responsivity), and cost.

• Sensor diagonal is less than the lens diameter

• Example: The format 1/3” (8.5 mm) need a sensor diagonal of 6.1 mm

Optical Format Sensor diagonal

1/7 inch (=3.63 mm) ~2.3 mm

1/6 inch (=4.23 mm) ~2.7 mm

1/5 inch (=5.08 mm) ~3.2 mm

1/4 inch (=6.35 mm) ~4 mm

1/3 inch (=8.47 mm) ~6 mm

1/2 inch (=12.7 mm) ~8 mm

2/3 inch (=16.9 mm) ~11 mm

1 inch (=25.4 mm) ~20 mm

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AO 6.20

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OpTh at.

7.8 µm5.6 µm3.6 µm

2.8 µm

“1/4 in”

Ref.: Fossum

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tical format (cont.)e figure shows the connection between pixel size, array format, and optical form

1

10

1/7 1/6 1/5 1/4 1/3 1/2 2/3

Lens Format

Pixe

l Siz

e (u

m) CIF

VGA1.3M2.1M3.3M4.1M

OPTICAL FORMATS

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AO 6.21

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Ar

CIF

Q

VG

Q

Q

SV

X

S

1

2

3

4

~1

Covered with blue filter (+metal)Dark reference pixels

ve part.lue filter (+metal)

Ref.: Fossum

ixel Pitch

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ray formats

(Common Intermediate Format): 352H x 288V

CIF (Quarter CIF): 176H x 144V

A (Video Graphics Array): 640H x 489V

VGA (Quarter VGA): 320H x 240V

QVGA: 160H x 120V

GA (Super VGA): 800H x 600V

GA (Extended Graphics Array): 1024H x 768V

XGA: 1280H x 1024V

.3M 1280H x 1024V

.1M 1680H x 1248V

.3M 2088H x 1550V

.1M 2310H x 1732V

2M ~¨4000H x 3000V

Active part

Barrier pixelsaround the actiCovered with b

P

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AO 6.22

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Re

o r

t

N

a m p le d )

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gular pixel array. The image is spatially sampled

s e n so ff r e q u e n c ys p a t ia l1

t a r g eo ff r e q u e n c ys p a t ia l1

==

==

ps

TT

xf

xf

∆

tx

px

Ns ff21

= s ff =

( u n d e r s a m p le d ) ( c o r r e c t ly s

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AO 6.23

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A

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liasing

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Te

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st pattern

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AO 6.25

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Te

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st pattern

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AO 6.26

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Re

ras,

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ferences

Micron ImagingAptina Imaging

Internett steder.

NakamuraImage Sensors and Signal Processing for Digital Still Cameedited by Junich NakamuraTaylor & Francis

FossumSee INF 5440 introductory lecture