Basics of opical imaging (NON IMAGING OPTICS)

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Basics of opical imaging (NON IMAGING OPTICS)

Transcript of Basics of opical imaging (NON IMAGING OPTICS)

  • 1. Basic Optical Concepts 1 Graduate School of Tsinghua University A basic Introduction to OPTICAL IMAGING TAYYAB FAROOQ Graduate School of TsingHua University Shenzhen, P.R CHINA

2. n i n f i Media Boundary Refraction- Snell's Law i f f i n n Sin Sin = )( )( Snells Law: 2 f Refractive Medium 0 10 20 30 40 50 60 70 80 90 0 10 20 30 40 50 60 70 80 90 angle of incidence angleofexitance internal external Graduate School of Tsinghua University 3. Refraction and TIR Light ray refracted along boundary f c = 90 f i n i n f Exit light ray 3 Totally Internally Reflected ray Incident light rays i c i n i Critical angle for total internal reflection (TIR): c= Arcsin(1/n) = 42 (For index of refraction ni =1.5,n= 1 (Air)) Total internal reflection is the only 100% efficient reflection in nature Graduate School of Tsinghua University 4. Fresnel and Reflection Losses Reflection: -TIR is the most efficient reflection: An optically smooth interface has 100% reflectivity -Metallization: Al (typical): 85%, Ag (typical): 90% Refraction: -There are light losses at every optical interface n1 n2 Fresnel Reflection 4 -There are light losses at every optical interface -For perpendicular incidence: -For n1 =1 (air) and n2=1.5 (glass): R=(0.5/2.5)^2=4% -Transmission: T=1-R. -For multiple interfaces: T tot =T1 *T2*T3 -For a flat window: T=0.96^2=0.92 -For higher angles the reflection losses are higher 2 21 21 + = nn nn R 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 10 20 30 40 50 60 70 80 90 Incidence Angle [deg] Reflectivity Internal Reflection External Reflection Graduate School of Tsinghua University 5. Black body radiation & Visible Range 1 1.5 2 2.5 3 Radianceperwavelength[a.u.] 6000 K 5500 K 5000 K Visible Range 5 Every hot surface emits radiation An ideal hot surface behaves like a black body Filaments (incandescent) behave like this. The sun behaves like a black body 0 0.5 1 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 Wavelength [nm] Radianceperwavelength[a.u.] 5000 K 4500 K 4000 K 3500 K 2800 K Graduate School of Tsinghua University 6. Color Mixing The intensity/flux of two light beams is specified in terms of quantities Y1 and Y2 and the color is specified by chromaticity coordinates x1, y1, x2, y2. The sum of the light beams is given by: ,thatNote iii iii i ZYX ZXY m ++==== .and,with and, 21 21 2211 21 2211 Y m Y m mm mxmx x mm mymy y sumsum == + + = + + = 7 Light Source 1: Y1 = 10lm; x1 = 0.1; y1 = 0.2 (yellow) Light Source 2: Y2 = 20lm; x2 = 0.4; y2 = 0.5 (blue) Light Source Sum: Y = 30lm; x = 0.23; y = 0.33 (bluish white) REMARK: Twice as much yellow flux than blue flux but it still appears bluish, because the blue is "stronger" than yellow (m1 > m2, in this particular case). Example: z)andyx,ofdefinition(see ,thatNote iii iii i ZYX zxy m ++==== .and,with 2 2 2 1 1 1 y Y m y Y m == Graduate School of Tsinghua University 7. Colorimetric quantities )()(683 [cd])intensity()()(683 )()(683 = = = = X x dzPZ dyPY dxPX P() is the radiated spectrum of the light source (i.e. the spectral intensity of the source) 8 1=++ ++ = ++ = ++ = zyx ZYX Z z ZYX Y y ZYX X x (i.e. the spectral intensity of the source) x(), y() and z() are the CIE color matching functions (sometimes also called x-bar, y-bar and z-bar) X, Y and Z are the colorimetric quantities (Y is equal to the photometric intensity) x, y and z are the color coordinates (x and y are the coordinates in the CIE-Diagram) Graduate School of Tsinghua University 8. Correlated Color Temperature Correlated Color Temperature (CCT) is the temperature of a black body source most similar in color to a source in question Only applicable for 10 Only applicable for sources close to the black body curve (white light) Graduate School of Tsinghua University 9. Typical LED Spectra 0.5 0.6 0.7 0.8 0.9 1 RelIntensity[a.u.] AlInGaP Amber AlInGaP Red InGaN Blue InGaN Green InGaN White 11 0 0.1 0.2 0.3 0.4 0.5 400 450 500 550 600 650 700 750 800 Wavelength [nm] RelIntensity[a.u.] Graduate School of Tsinghua University 10. Converted rays Phosphor Blue InGaN Chip Spectrum:naked chip InGaN white LED Structure 12 Spectrum: 400 500 600 naked chip with phosphor 700 /nm Graduate School of Tsinghua University 11. The Human Eye Response All radiation which can be see with the eye is considered light (approx. 400nm to 750nm) Radiation is measured in radiometric units, and Light is measured in photometric units. The sensitivity of the eye is dependant on the wavelength of the light (e.g. the eye is 10,000 times more sensitive to 555nm-Green 13 light (e.g. the eye is 10,000 times more sensitive to 555nm-Green than to 750nm-Red). The response of the eye is logarithmic (high dynamic range). The average human eye can only see the difference of a factor of two to one in intensity (the eye is a bad detector). Graduate School of Tsinghua University 12. Lambertian Emitter Typical radiation pattern of a flat surface : (i.e. LED chip top surface) )cos()( 0 II = Total flux in a cone with an opening angle 2 : 0.8 0.9 1 Intensity[cd],Flux[lm/pi] Intensity Total Included Flux 2 17 The total flux of a Lambertian source of 1 cd on axis is lm! To collect for example 90% of the Flux of a Lambertian source, the optics must capture a cone 72 deg off axis angle 0 2 0 0 0 )(sin ')'sin()'cos(2 ')'sin()'(2 I dI dI = = = 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 10 20 30 40 50 60 70 80 90 Off Axis Angle Intensity[cd],Flux[lm/pi] Graduate School of Tsinghua University 13. Uniform Emitter Typical radiation pattern of a spherical surface (i.e. the sun), or of, as a rough approximation, an incandescent filament. 0.8 0.9 1 Intensity[cd],Flux[lm/4pi] Intensity Total Included Flux constII == 0)( Total flux in a cone with an opening angle 2 : 2 18 ))cos(1(2 ')'sin(2 ')'sin()'((2 0 0 0 0 = = = I dI dI The total flux of a uniform source (integral from 0 to 2 pi) of I0 =1 cd is 4 lm! 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 20 40 60 80 100 120 140 160 180 Off Axis Angle Intensity[cd],Flux[lm/4pi] Graduate School of Tsinghua University 14. Fresnel Lenses -For collimating light -To make a conventional lens thinner -Works only by refraction -Fresnel teeth can be on the in- and outside of lens -Not very efficient for large off-axis angles 19 Conventional lens fresnel lens Graduate School of Tsinghua University 15. TIR Lenses -For collimating light -To make a conventional lens thinner -Works by refraction AND total internal reflection -Teeth are on the inside of lens -Very efficient for large off-axis angles, no so efficient for small angles -TIR Reflection has NO losses if the surface of the facet it perfect! TIR 20 TIR lensConventional lens Graduate School of Tsinghua University 16. optimum transfer of luminous powerNIO Source A B Source A B Nonimaging Optics (NIO) 21 IMAGING OPTICAL SYSTEM Receiver A B NONIMAGING OPTICAL SYSTEM Receiver Source image No Source image Graduate School of Tsinghua University 17. NIO Design Rules Source A B Basic conservation and design rules: Flux conservation Etendue conservation 22 NONIMAGING OPTICAL SYSTEM Receiver Etendue conservation Luminance conservation Edge ray principle Graduate School of Tsinghua University 18. in A passive optical system always decreases the source flux due to absorption and reflection losses within the optical system: Flux conservation: Flux Conservation and Efficiency inout OPTICAL Source Lost flux Collection Efficiency: source 23 OPTICAL SYSTEM Target out Optical Efficiency: sourcetargetopt = / The optical efficiency of a system depends on the definition of the useful flux that falls onto the desired target (either a surface or far field angle interval). target sourceincoll = / The collection efficiency is the fraction of the source flux captured by the optical system Lost flux Graduate School of Tsinghua University 19. source Illuminance dA d E = Flux emitted by a surface element Illuminance [Lux]: Source Source A E = Average Source Illuminance: 24 Target target TargetA SourceA SourceA Example: A 100 lm 1x1 mm2 LED chip has a total emitting surface of typically 2 mm2 (including its 4 lateral surfaces!) => E=50 lm/mm2 Typical values for a filament: 50 lm/ mm2 Flux received or emitted by a surface element Sun: 10-100000 lx Received by surface: Desktop illumination: 500 lx ECE LB: 6 lx, HB: 32 lx @ 25 m Graduate School of Tsinghua University 20. Luminance [cd/m2]: Perceived brightness of a source Luminance Source SourceA dA dI L = Intensity emitted or received by a surface element Or flux per surface and solid angle Average Source Luminance for Lambertian sources: L n 25 If the source emits into a full hemisphere, the second half of the equation holds. L in general is a function of angle. L is constant for lambertian sources With the index of refraction (n) of medium surrounding the source Typical values for a filament bulb (n=1): 5-20 cd/ mm2 Good bulb (automotive halogen): approx. 25 cd/ mm2 White LEDs: up to: 100 cd/ mm, constantly improving Sun: 1500 cd/ mm2 = = 22 nAn E L Source SourceSource Source SourceL Graduate School of Tsinghua University 21. n No optical system can increase the brightness of a source*. Transmittance t takes into account all reflective and absorptive losses of central rays contributing to the hot spot. Luminance Conservation Sourceout LtL = Source SourceA SourceL Luminance Conservation: Conservation of brightness 26 spot. OPTICAL SYSTEM Aperture ApA Source max Ap Lt I A OutL Minimum Optics Aperture Size for Hotspot: A real aperture, that is not totally flashed as seen from the hotspot will have to be larger! Example: Desired Intensity: 1000 cd, source luminance: 2.1 cd / mm2, t=0.7: Aap>680 mm2 *A system that adds up different colors into the same light path (by dichroic mirrors) and light recycling systems (like BEF films) are the only exceptions Graduate School of Tsinghua University