2. Camera, Optics

2.2. Camera,Camera, OpticsOptics

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung 2.1.2.1. CameraCamera

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung Virtual image, perspective projection [1]

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung How large a pinhole? [1]

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung Shrinking the aperture [2]

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung Same function with large pinhole: Lens [1]

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung 광전효과광전효과(Photoelectric(Photoelectric Effect)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 radiation of very short wavelength, such as visible or ultraviolet light. Electrons emitted in this manner may be referred to as "photoelectrons".

Symbol for photodiode.

Light-matter interaction

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

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

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

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

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 tubes but 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

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung ImageImage Sensor:Sensor: CCDCCD

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.

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

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung ImageImage Sensor:Sensor: CCDCCD

Vertical smear.

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

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung ImageImage Sensor:Sensor: CMOS,CMOS, APSAPS (Active(Active PixelPixel Senor)Senor)

An active-pixel sensor (APS), also commonly written active pixel sensor, is an image sensor consisting 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.

A three-transistor active pixel sensor. http://en.wikipedia.org/wiki/Active_pixel_sensor

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung ImageImage Sensor:Sensor: CMOS,CMOS, APSAPS (Active(Active PixelPixel Senor)Senor)

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

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung InterlacedInterlaced .vs..vs. ProgressiveProgressive ScanScan

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

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

- Image sensor의 sensitivity좋아야  Shuttering speed 높일수있고 motion blur 줄일 수있음. - Rolling shutter .vs. global shuttering  노출의 동기화  global shuttering 선호

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

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

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.

짧은 shuttering 선호

Shutter speed can have a dramatic impact on A pinwheel photographed at three different the appearance of moving objects. Changes in shutter speeds background blurring are apparent from the need to adjust the aperture size to achieve proper exposure. 화면이 어두워질 수 있음  Sensitivity 좋은 소자 필요

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

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

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) Shutter http://www.ptgrey.com/support/kb/index.asp?a=4&q=115

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

고속으로 움직이면서 촬영하는 자동차응용의 경우, global shuttering 필요

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

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung Shuttering:Shuttering: stoboscopicstoboscopic effecteffect

Extraordinary stroboscopic effect Stroboscope: Grinder

http://youtu.be/rVSh-au_9aM http://youtu.be/8mQaXaRVUoM

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung HDRC(HighHDRC(High DynamicDynamic RangeRange CMOS)CMOS) 카메라카메라

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

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung 원적외선원적외선(FIR:(FIR: FarFar InfraRedInfraRed)) 카메라카메라

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

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung 원적외선원적외선(FIR:(FIR: FarFar InfraRedInfraRed)) 카메라카메라

Flir Systems - "Path Finder" Automotive Infrared Camera

http://youtu.be/PM9OcBpZaPo

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung 근적외선근적외선(NIR:(NIR: NearNear InfraRedInfraRed)) 카메라카메라

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.

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

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung 근적외선근적외선(NIR:(NIR: NearNear InfraRedInfraRed)) 카메라카메라

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung Color:Color: BayerBayer FilterFilter

어떻게 color 영상을 획득하나?

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

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung Color:Color: BayerBayer FilterFilter

Bayer Demosaicing

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

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung Color:Color: BayerBayer FilterFilter

Bayer Demosaicing

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

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung Color:Color: ThreeThree--CCDCCD CameraCamera

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

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung 원적외선원적외선(FIR:(FIR: FarFar InfraRedInfraRed)) 카메라카메라

열화상은 어떻게 온도를 측정하는가?

http://globale- http://logicalmystery.blogspot.kr/2012/09/therm solutions.blogspot.kr/2012/11/thermographic- al-camerasreally-why-updated.html camera-thermal-imaging.html

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung 원적외선원적외선(FIR:(FIR: FarFar InfraRedInfraRed)) 카메라카메라

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

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung Modeling Projection [2]

y y d z -d z

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung Homogeneous Coordinates [2]

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung Homogeneous Coordinates: Geometric intuition [2]

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung Lines in 2D Homogeneous Coordinates [3]

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung Lines and Points in 2D Homogeneous Coordinates [3]

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung Pinhole Camera Model in Homogeneous Coordinates [3]

숨겨진 가정은?  focal length f에 초점이 맞는 영상이 생긴다.  물체까지의 거리가 초점거리 f에 비하여 월등히 크다.

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung Principal Point [3]

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung Considering Imaging Element [3]

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung Effects of Perspective Transformation [2]

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

(a) Keeping the camera (b) Tilting the camera (c) Shifting the lens level, with an ordinary upwards results in upwards results in a lens, captures only the vertical perspective. picture of the entire bottom portion of the subject. building.

Perspective transform의 Z는 image plane으로부터의 수직거리이다!!! (Optical center로부터의 거리가 아니다.) http://en.wikipedia.org/wiki/Perspective_control_lens

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

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

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

Picture taken with a 50mm lens Same picture taken with a 50mm lens on a normal 35mm Camera with Perspective Control

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

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

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

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung Vanishing Points [2]

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung More than One Vanishing Point [2]

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

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung Weak Perspective [4] (x, y, z)  s(x, y) • s is constant for all points. • Parallel lines no longer converge, they remain parallel.

O -x

f Z x  X Z f Z  const  X  Z

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung Weak Perspective [4] Weak perspective Perspective

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung Orthographical Projection [4]

 X  x When the camera is at a  (roughly constant) distance Y  y  from the scene, take m=1.

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung Affine Camera [4]

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung Constant object size [5]

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung Dolly zoom [6]

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

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung Depth of field [2]

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

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

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

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

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.

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

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

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

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

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

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.

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung 2.2.2.2. OpticsOptics

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

1. Basics of optics 2. Ideal lens 3. Spherical lens  thin lens formula

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung Wavefronts and Rays [1]

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung Diffraction (회절) [1]

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung Refraction, Refractive Index

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung Refraction, Snell’s Law [1]

travel time t is common

t = d1/v1 = d2/v2

light speed c is constant

cd1/v1 = cd2/v2 d1 c/v1= d2 c/v2

Using the refractive index’s definition

d1 n1 = d2 n2

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung Reflection [1]

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung Surface Shape of Ideal Lens [2]

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

nSAnADCit  (5.1) n SAt AD C (5.2) ni

eccentricity A D

ni=1 nt

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

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung [참고] 비구면 렌즈의 곡면 방정식 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.

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung [참고] 비구면 렌즈의 곡면 방정식 http://cafe.naver.com/prepare2win.cafe?iframe_url=/ArticleRead.nhn%3Farticleid=395

1. 빛 경로 추적

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung [참고] 비구면 렌즈의 곡면 방정식 http://cafe.naver.com/prepare2win.cafe?iframe_url=/ArticleRead.nhn%3Farticleid=395

2. 최단경로에 의한 동일 시간 가정

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung [참고] 비구면 렌즈의 곡면 방정식 http://cafe.naver.com/prepare2win.cafe?iframe_url=/ArticleRead.nhn%3Farticleid=395

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung Surface Shape of Practical Lens [2]

• Spherical lens is more easy to manufacture.

Aspherical lens Spherical lens

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung Equation of Spherical Surface with Radius R [2]

OPL n12 loi n l

By applying cosine rule to triangle SAC and ACP (Notice that cos   cos  180  ) 

2 2 lo R soo R2cos R s  R 

2 2 li R sii R2cos R s   R 

2222 OPL n12 R soo R2cos R s R  n R s ii R 2cos R s  R 

dOPL  Based on Fermat s principle  0 ’ d  nR s Rsin nR s R sin nn121 ns21io ns 12oi0   llRloi i l o 22lloi 

Assuming  is sufficiently small, that is, A approaches V, (first-order optics, paraxial-ray optics, or Gaussian optics) nn nn cos  1, lslsooii , 12 21 soisR

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung Lens Maker’s Equation [2]

nnnn nnnn 1221 1221 ssoi11 R 1 ssoi11 R 1 nnnn nnnn 2112 2112 ssssdiioi1121 , + ssoi22 R 2 ds ii12 s R 2

nn1111 nd 2 nn21   ssoi12 RR 12 sds i 1 i 1

R R 1 2 Assuming d0, n1~1 so1=so, si2=si

11 1 1 n 1  s d  o1 ssoi  RR12 si1

so2 si2 E-mail: [email protected] http://web.yonsei.ac.kr/hgjung Thin Lens Equation [3]

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

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung Thin Lens Equation [2] As f =f 11 1 i o lim sfii   so   sf 111 ii  11 1 lim sfoo  ssoi f si  sfoo

11 1 1 n 1   ssoi  RR12

111 n 1   f RR12

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung Thin Lens Equation [2]

11 1 lim sii f   111 so   s f   ii ss f 11 1 oi lim soo f  si  sfoo

So Si

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung Thin Lens Equation [2]

물체가 초점거리 안쪽에 존재하면, 허상: So가 f보다 작으면, Si는음수 111   ssoi f

So Si

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung Thin Lens Equation [2]

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 f

So Si

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung Thin Lens Equation [2]

f f

So Si

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung The Seidel Aberrations

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung Graphical Description of Ray Aberration Curves

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung Spherical aberration [1]

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

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung Spherical Aberration and Aspherics

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung Correcting Spherical Aberration

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

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung Correcting Chromatic Aberration: Achromatic doublet

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

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

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

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung Curvature of Field

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung Flattening the Field

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung Focal vs. Afocal Systems

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung Real vs. Virtual Images

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung Determining Focal Length

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung Combinations of Lenses

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

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung Reverse Telephoto Lens

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

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung Afocal Systems with Focal Systems

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung The f/number

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung Depth of Focus

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung Aperture stop, Vignetting

Effect: Darkens pixels near the image boundary

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung The Relation between Irradiance and Radiance

Irradiance on a plane

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung The Relation between Irradiance and Radiance

/cosθ /cosθ θx x x k L  x 2 kk LL'coscos  x 2 xxcos S/cosθ

θ S k L  S 2 kk LL'coscos22   S 2 S 2 cos2 

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung The Relation between Irradiance and Radiance

2  d 4 EL cos  4 f

E-mail: [email protected] http://web.yonsei.ac.kr/hgjung The Relation between Irradiance and Radiance

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

LkD 2 LkDD' cos  kD2 cos  L cos

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

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

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