2. Camera, Optics - Yonsei Universityweb.yonsei.ac.kr/hgjung/Lectures/AUE859/2. Camera, Optics... · 2014-12-29 · E-mail: [email protected] Virtual image, perspective projection

E-mail: [email protected]://web.yonsei.ac.kr/hgjung

2. Camera, Optics2. Camera, Optics


2.1. Camera2.1. Camera


Virtual image, perspective projection [1]Virtual image, perspective projection [1]


How large a pinhole? [1]How large a pinhole? [1]


Shrinking the aperture [2]Shrinking the aperture [2]


Shrinking the aperture [2]Shrinking the aperture [2]


Same function with large pinhole: Lens [1]Same function with large pinhole: Lens [1]


광전효과광전효과(Photoelectric Effect)(Photoelectric Effect)

In the photoelectric effect, electrons are emitted from matter (metals and non-metallic solids, liquids or gases) as a consequence of their absorption of energy from electromagnetic radiationof very short wavelength, such as visible or ultraviolet light. Electrons emitted in this manner may be referred to as "photoelectrons".

Light-matter interaction

http://en.wikipedia.org/wiki/Photoelectric

Symbol for photodiode.


Image SensorImage Sensor

http://www.rocketroberts.com/astro/ccd_fundamentals.htm


Image SensorImage Sensor

An image sensor is a device that converts an optical image to an electric signal. It is used mostly in digital cameras and other imaging devices. Early sensors were video camera tubesbut a modern one is typically a charge-coupled device (CCD) or a complementary metal–oxide–semiconductor (CMOS) active pixel sensor.

A CCD image sensor on a flexible circuit board

http://en.wikipedia.org/wiki/Image_sensor


Image Sensor: CCDImage Sensor: CCD

A charge-coupled device (CCD) is a device for the movement of electrical charge, usually from within the device to an area where the charge can be manipulated, for example conversion into a digital value. This is achieved by "shifting" the signals between stages within the device one at a time. CCDs move charge between capacitive bins in the device, with the shift allowing for the transfer of charge between bins.

Often the device is integrated with an image sensor, such as a photoelectric device to produce the charge that is being read, thus making the CCD a major technology for digital imaging.

http://en.wikipedia.org/wiki/Charge-coupled_device

The charge packets (electrons, blue) are collected in potential wells (yellow) created by applying positive voltage at the gate electrodes (G). Applying positive voltage to the gate electrode in the correct sequence transfers the charge packets.


Image Sensor: CCDImage Sensor: CCD

http://en.wikipedia.org/wiki/Charge-coupled_device

Vertical smear.


Image Sensor: CMOS, APS (Active Pixel Senor)Image Sensor: CMOS, APS (Active Pixel Senor)

An active-pixel sensor (APS), also commonly written active pixel sensor, is an image sensorconsisting of an integrated circuit containing an array of pixel sensors, each pixel containing a photodetector and an active amplifier. There are many types of active pixel sensors including the CMOS APS used most commonly in cell phone cameras, web cameras and in some DSLRs. Such an image sensor is produced by a CMOS process (and is hence also known as a CMOS sensor), and has emerged as an alternative to charge-coupled device (CCD) imager sensors.

http://en.wikipedia.org/wiki/Active_pixel_sensor

A three-transistor active pixel sensor.


Image Sensor: CMOS, APS (Active Pixel Senor)Image Sensor: CMOS, APS (Active Pixel Senor)

강문식, 신경욱, “IT CookBook, 전자회로: 핵심 개념부터 응용까지,” 한빛미디어.


Interlaced .vs. Progressive ScanInterlaced .vs. Progressive Scan

With progressive scan, an image is captured, transmitted, and displayed in a path similar to text on a page: line by line, from top to bottom. The interlaced scan pattern in a CRT (cathode ray tube) display completes such a scan too, but only for every second line. This is carried out from the top left corner to the bottom right corner of a CRT display. This process is repeated again, only this time starting at the second row, in order to fill in those particular gaps left behind while performing the first progressive scan on alternate rows only.

When interlaced video is watched on a progressive monitor with very poor deinterlacing, it exhibits combing when there is movement between two fields of one frame.

http://en.wikipedia.org/wiki/Interlaced_video


ShutteringShuttering

http://www.vision-systems.com/articles/print/volume-10/issue-5/features/component-integration/auto-cameras-benefit-from-cmos-imagers.html

- Image sensor의 sensitivity좋아야 Shuttering speed 높일 수 있고motion blur 줄일수 있음.

- Rolling shutter .vs. global shuttering 노출의 동기화 global shuttering 선호



In photography, shutter speed is a common term used to discuss exposure time, the effective length of time a camera's shutter is open. The total exposure is proportional to this exposure time, or duration of light reaching the film or image sensor.

http://en.wikipedia.org/wiki/Shutter_speedA demonstration of the effect of exposure in night photography. Longer shutter speeds result in increased exposure.

Shutter speed can have a dramatic impact on the appearance of moving objects. Changes in background blurring are apparent from the need to adjust the aperture size to achieve proper exposure.

A pinwheel photographed at three different shutter speeds

짧은 shuttering 선호

화면이 어두워질 수 있음 Sensitivity 좋은 소자 필요



Rolling shutter (also known as line scan) is a method of image acquisition in which each frame is recorded not from a snapshot of a single point in time, but rather by scanning across the frame either vertically or horizontally. In other words, not all parts of the image are recorded at exactly the same time, even though the whole frame is displayed at the same time during playback. This in contrast with global shutter in which the entire frame is exposed for the same time window. This produces predictable distortions of fast-moving objects or when the sensor captures rapid flashes of light.

Rolling Shutter Frame (Global) Shutterhttp://www.ptgrey.com/support/kb/index.asp?a=4&q=115



http://en.wikipedia.org/wiki/Global_shutter

고속으로 움직이면서 촬영하는 자동차응용의 경우, global shuttering 필요


Shuttering: stoboscopic effectShuttering: stoboscopic effect

Extraordinary stroboscopic effect

http://youtu.be/rVSh-au_9aM

Stroboscope: Grinder

http://youtu.be/8mQaXaRVUoM


HDRC(HighHDRC(High Dynamic Range CMOS) Dynamic Range CMOS) 카메라카메라

http://www.vision-systems.com/articles/print/volume-10/issue-5/features/component-integration/auto-cameras-benefit-from-cmos-imagers.html


원적외선원적외선(FIR: Far (FIR: Far InfraRedInfraRed) ) 카메라카메라

http://en.wikipedia.org/wiki/Electromagnetic_wave



Flir Systems - "Path Finder" Automotive Infrared Camera

http://youtu.be/PM9OcBpZaPo


근적외선근적외선(NIR: Near (NIR: Near InfraRedInfraRed) ) 카메라카메라

http://en.wikipedia.org/wiki/Infrared

Active-infrared night vision : the camera illuminates the scene at infrared wavelengths invisible to the human eye. Despite a dark back-lit scene, active-infrared night vision delivers identifying details, as seen on the display monitor.


근적외선근적외선(NIR: Near (NIR: Near InfraRedInfraRed) ) 카메라카메라


Color: Bayer FilterColor: Bayer Filter

어떻게 color 영상을 획득하나?

http://en.wikipedia.org/wiki/Bayer_filter



Bayer Demosaicing

http://en.wikipedia.org/wiki/Demosaicing



Bayer Demosaicing

http://www.sharplabs.com/2pfc/Demosaicing%20One.html


Color: ThreeColor: Three--CCD CameraCCD Camera

http://en.wikipedia.org/wiki/Three-CCD_camera



열화상은 어떻게 온도를 측정하는가?

http://globale-solutions.blogspot.kr/2012/11/thermographic-

camera-thermal-imaging.html

http://logicalmystery.blogspot.kr/2012/09/thermal-camerasreally-why-updated.html



The radiant energy in the entire wavelength range (area beneath each curve) increases to the power of 4

of the temperature. These relationships were recognized by Stefan and Boltzmann in 1879 and illustrate

that an unambiguous temperature can be measured from the radiation signal.

http://support.fluke.com/raytek-sales/Download/Asset/IR_THEORY_55514_ENG_REVB_LR.PDF


Modeling Projection [2]Modeling Projection [2]


Modeling Projection [2]Modeling Projection [2]

-dz

yydz


Homogeneous Coordinates [2]Homogeneous Coordinates [2]


Homogeneous Coordinates: Geometric intuition [2]Homogeneous Coordinates: Geometric intuition [2]


Lines in 2D Homogeneous Coordinates [3]Lines in 2D Homogeneous Coordinates [3]


Lines and Points in 2D Homogeneous Coordinates [3]Lines and Points in 2D Homogeneous Coordinates [3]


Pinhole Camera Model in Homogeneous Coordinates [3]Pinhole Camera Model in Homogeneous Coordinates [3]

숨겨진숨겨진 가정은가정은? ? focal length ffocal length f에에 초점이초점이 맞는맞는 영상이영상이 생긴다생긴다..

물체까지의물체까지의 거리가거리가 초점거리초점거리 ff에에 비하여비하여 월등히월등히 크다크다..


Principal Point [3]Principal Point [3]


Considering Imaging Element [3]Considering Imaging Element [3]


Effects of Perspective Transformation [2]Effects of Perspective Transformation [2]


Perspective ControlPerspective Control

(a) Keeping the camera level, with an ordinary lens, captures only the bottom portion of the building.

(b) Tilting the camera upwards results in vertical perspective.

(c) Shifting the lens upwards results in a picture of the entire subject.

http://en.wikipedia.org/wiki/Perspective_control_lens

Perspective transformPerspective transform의의 ZZ는는 image planeimage plane으로부터의으로부터의 수직거리이다수직거리이다!!!!!!

(Optical center(Optical center로부터의로부터의 거리가거리가 아니다아니다.).)



The 1961 35 mm f/3.5 PC-Nikkorlens—the first perspective control lens for a 35 mm camera http://staticmixers.net/jq/?uid=Using-a-

perspective-control-lens



Picture taken with a 50mm lenson a normal 35mm Camera

Same picture taken with a 50mm lenswith Perspective Control

http://www.danheller.com/tech-persp.html



http://en.wikipedia.org/wiki/Perspective_control


Vanishing Points [2]Vanishing Points [2]


Vanishing Points [2]Vanishing Points [2]


More than One Vanishing Point [2]More than One Vanishing Point [2]


Weak Perspective [4]Weak Perspective [4]

• Issue– perspective effects, but not over the scale of individual objects– collect points into a group at about the same depth, then divide each point

by the depth of its group– Adv: easy– Disadv: wrong



f

Z

O -x

ZZ

XconstZfXx

Z

),(),,( yxszyx • s is constant for all points.

• Parallel lines no longer converge, they remain parallel.



Weak perspective Perspective


Orthographical Projection [4]Orthographical Projection [4]

yYxX When the camera is at a

(roughly constant) distancefrom the scene, take m=1.


Affine Camera [4]Affine Camera [4]


Constant object size [5]Constant object size [5]


Dolly zoom [6]Dolly zoom [6]

Dolly zoom in movieshttp://www.youtube.com/watch?v=Y48R6-iIYHs


Depth of field [2]Depth of field [2]


ScheimpflugScheimpflug PrinciplePrinciple

If the subject plane is not parallel to the image plane, it will be in focus only along a line where it intersects the PoF(Plane of Focus), as illustrated in Figure 1.

Figure 1. With a normal camera, when the subject is not parallel to the image plane, only a small region is in focus.

http://en.wikipedia.org/wiki/Scheimpflug_principle



When an oblique tangent is extended from the image plane, and another is extended from the lens plane, they meet at a line through which the PoF also passes, as illustrated in Figure 2 . With this condition, a planar subject that is not parallel to the image plane can be completely in focus.

http://en.wikipedia.org/wiki/Scheimpflug_principle



The 24 mm PC-E lens shown in its tilt mode

Pentax-mount Arax 35 mm f/2.8 TS at max tilt and no shift.



http://1.bp.blogspot.com/-wqgFh-V5yrU/TYp4iH9seOI/AAAAAAAAAdY/BDMeT1R2N6U/s1600/Scheimpflug_diptych.jpg



http://www.treklens.com/gallery/North_America/Canada/photo512860.htm


ReferencesReferences

1. Trevor Darrell, “Cameras and Lenses,” MIT lecture material of computer vision and applications (6.891), 2004.

2. Rajesh Rao, “Cameras and image formation,” Washington Univ. lecture material of computer vision (CSE 455), 2009.

3. Dan Huttenlocher, “Camera geometry,” Cornell Univ. lecture material of computer vision (CS 664), 2008.

4. Chandra Kambhamettu, “Camera graphics,” Delaware Univ. lecture material of computer vision (CISC 4/689), 2007.

5. “Telephoto lens,” Wikipedia, accessed on 4 Sep. 2009.6. “Dolly zoom,” Wikipedia, accessed on 4 Sep. 2009.


2.2. Optics2.2. Optics


ObjectivesObjectives

1. Basics of optics2. Ideal lens3. Spherical lens thin lens formula


Wavefronts and Rays [1]Wavefronts and Rays [1]


Diffraction (Diffraction (회절회절) [1]) [1]


Refraction, Refractive IndexRefraction, Refractive Index


Refraction, SnellRefraction, Snell’’s Law [1]s Law [1]

travel time t is commont = d1/v1 = d2/v2

light speed c is constantc d1/v1 = c d2/v2d1 c/v1= d2 c/v2

Using the refractive index’s definitiond1 n1 = d2 n2


Reflection [1]Reflection [1]


Surface Shape of Ideal Lens [2]Surface Shape of Ideal Lens [2]

S

AD

nt

ni=1

• Penetrating wavefront should be a plane.• Irrespective of position A, optical path length should be the same.

(5.1)

(5.2)

i t

t

i

n SA n AD C

nSA AD Cn

eccentricity

• When the eccentricity is larger than 1, the surface shape is a hyperbola.


[[참고참고] ] 비구면비구면 렌즈의렌즈의 곡면곡면 방정식방정식

http://cafe.naver.com/prepare2win.cafe?iframe_url=/ArticleRead.nhn%3Farticleid=395

구면수차가 없는 렌즈의 곡면방정식을 구하기 위해 다음과 같은 상황을 가정해보자. 렌즈의 중심축상 한 지점에서 출발한 빛살들이 렌즈 내부에서 전부 평행광선을 이룬다.이때 렌즈를 좌우 대칭으로 정하면 평행광선을 이룬 빛살들은 렌즈를 빠져나온 후 정확히 한점으로 모일 것이다. 즉 이것은 이 렌즈의 구면수차가 없음을 의미한다.이 글의 목표는 이 조건을 만족하는 곡면의 방정식을 구하는 것이다.

여기서는 두 가지 방법-굴절각을 이용한 방법과 최단경로 원칙을 이용한 방법으로 렌즈곡면 방정식을 구해보자.




1. 빛 경로 추적







2. 최단경로에 의한 동일 시간 가정








Surface Shape of Practical Lens [2]Surface Shape of Practical Lens [2]

• Spherical lens is more easy to manufacture.

Aspherical lens Spherical lens


Equation of Spherical Surface with Radius R [2]Equation of Spherical Surface with Radius R [2]

1 2o iOPL n l n l

By applying cosine rule to triangle SAC and ACP(Notice that ) cos cos 180

22

22

2 cos

2 cos

o o

i i

lo R s R R s R

li R s R R s R

2 22 21 22 cos 2 coso o i iOPL n R s R R s R n R s R R s R

Based on Fermat’s principle 0

d OPLd

1 2sin sin0

2 2o i

o i

n R s R n R s Rl l

2 11 2 1 i o

o i i o

n s n sn nl l R l l

Assuming is sufficiently small, that is, Assuming is sufficiently small, that is, AA approaches approaches VV,,(first(first--order optics, paraxialorder optics, paraxial--ray optics, or Gaussian optics)ray optics, or Gaussian optics)

cos 1, , o o i il s l s

1 2 2 1

o i

n n n ns s R


Lens MakerLens Maker’’s Equation [2]s Equation [2]

R1

so1si1

so2si2

R2

d

1 2 2 1

1 1 1o i

n n n ns s R

2 1 1 2

2 2 2o i

n n n ns s R

2 1 1 2

1 2 2i i

n n n nd s s R

1 1 2

2 11 2 1 2 1 1

1 1

o i i i

n n n dn ns s R R s d s

1 1 2 1 , i i o is s s s d

1 2 2 1

1 1 1o i

n n n ns s R

+

Assuming d0, n1~1so1=so, si2=si

1 2

1 1 1 11o i

ns s R R


Thin Lens Equation [3]Thin Lens Equation [3]

http://www.hirophysics.com/Anime/thinlenseq.html



As fi=folimo

i iss f

limi

o oss f

1 1 1

i is f

1 1 1

o os f

1 1 1

o is s f

1 2

1 1 1 11o i

ns s R R

1 2

1 1 11nf R R



limo

i iss f

limi

o oss f

1 1 1

i is f

1 1 1

o os f

1 1 1

o is s f

f

So Si



f

SoSi

물체가 초점거리 안쪽에 존재하면, 허상: So가 f보다 작으면, Si는 음수

1 1 1

o is s f



실상과 허상에서의 렌즈의 초점거리와 배율과의 관계는?

실상: 초점거리가 커질수록, 배율 증가 렌즈가 얇을수록, 배율 증가

허상: 초점거리가 커질수록, 배율 감소 렌즈가 두꺼울수록, 배율 증가

f

So Si

f



f

SoSi

실상과 허상에서의 렌즈의 초점거리와 배율과의 관계는?

실상: 초점거리가 커질수록, 배율 증가 렌즈가 얇을수록, 배율 증가

허상: 초점거리가 커질수록, 배율 감소 렌즈가 두꺼울수록, 배율 증가

f


The Seidel AberrationsThe Seidel Aberrations


Graphical Description of Ray Aberration CurvesGraphical Description of Ray Aberration Curves


Spherical aberration [1]Spherical aberration [1]


Spherical aberrationSpherical aberration


Spherical Aberration and Spherical Aberration and AsphericsAspherics


Correcting Spherical AberrationCorrecting Spherical Aberration


Chromatic AberrationChromatic Aberration


Correcting Chromatic Aberration: Achromatic doubletCorrecting Chromatic Aberration: Achromatic doublet


ComaComa


AstigmatismAstigmatism


DistortionDistortion


Curvature of FieldCurvature of Field


Flattening the FieldFlattening the Field


Focal vs. Focal vs. AfocalAfocal SystemsSystems


Real vs. Virtual ImagesReal vs. Virtual Images


Determining Focal LengthDetermining Focal Length


Combinations of LensesCombinations of Lenses


Telephoto LensTelephoto Lens


Reverse Telephoto LensReverse Telephoto Lens


AfocalAfocal SystemsSystems


AfocalAfocal Systems with Focal SystemsSystems with Focal Systems


The f/numberThe f/number


The f/numberThe f/number


Depth of FocusDepth of Focus


Aperture stop, Aperture stop, VignettingVignetting

Effect: Darkens pixels near the image boundary


The Relation between Irradiance and RadianceThe Relation between Irradiance and Radiance

Irradiance on a plane



2

2

2

2 22

cos

' cos cosS

kLS

k kL LS

S

x

x/cosθ

θ

S/cosθ

θ

2

2cos

' cos cosx

kLx

k kL Lx x

x

x/cosθ



24cos

4dE Lf


Irradiance is proportional to the area into which orthogonal light ray is impinged.


D cosθ

D

θ

D

D cosθ

2

2' cos cos cosL kDL kD D kD L


ReferencesReferences

1. Richard C. Juergens, “Fundamentals of Optical Engineering,” Raytheon Missile Systems, RLI TED0045, 2005.

2. Eugene Hecht, “Optics, 4th edition,” Addison Wesley Longman, Inc., 2002.3. http://www.hirophysics.com/Anime/thinlenseq.html

Documents

2. Camera, Optics - Yonsei Universityweb.yonsei.ac.kr/hgjung/Lectures/AUE859/2. Camera, Optics... · 2014-12-29 · E-mail: [email protected] Virtual image, perspective projection