Basic Optical Concepts Oliver Dross, LPI Europe 1 Refraction- Snell's Law Snell’s Law: n φ φ n i i Sin ( i ) = f φ Media Boundary Sin ( f ) ni n f φ f 90 Refractive Medium 80 internal 70 external 60 50 40 30 angle of exitance 20 10 0 0 10 20 30 40 50 60 70 80 90 angle of incidence 2 Refraction and TIR Exit light ray n f φ φ f f = 90° Light ray refracted along boundary φ φ n c i i φ Totally Internally Reflected ray i Incident light rays Critical angle for total internal reflection (TIR): φ 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” 3 Fresnel and Reflection Losses Reflection: -TIR is the most efficient reflection: n An optically smooth interface has 100% reflectivity 1 Fresnel Reflection -Metallization: Al (typical): 85%, Ag (typical): 90% n2 Refraction: -There are light losses at every optical interface -For perpendicular incidence: 1 Internal 0.9 2 Reflection − 0.8 External n1 n2 R = 0.7 Reflection + 0.6 n1 n2 0.5 0.4 Reflectivity -For n 1 =1 (air) and n 2=1.5 (glass): R=(0.5/2.5)^2=4% 0.3 -Transmission: T=1-R. 0.2 0.1 -For multiple interfaces: T tot =T 1 *T 2*T 3… -For a flat window: T=0.96^2=0.92 0 -For higher angles the reflection losses are higher 0 10 20 30 40 50 60 70 80 90 Incidence Angle [deg] 4 Black body radiation & Visible Range 3 Visible Range 6000 K 2.5 2 5500 K 1.5 5000 K 1 4500 K Radiance per wavelength [a.u.] [a.u.] wavelength wavelength per per Radiance Radiance 0.5 4000 K 3500 K 0 2800 K 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 Wavelength [nm] • 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 5 CIE 1931 Color Palette CIE 1931 Color Diagram: Typical High Flux -Colors are represented by (x,y) coordinates LED Colors (Chip material) -Different source spectra can have the same (x,y) point, same color appearance GREEN (InGaN) -Two light sources represented as two points in diagram can mix (by varying their intensities) to any color on a straight line between them -Pure Colors (spectrum has only on wavelength) are on “rim” of the color chart RED ORANGE (AlInGaP) -LEDs are almost pure, filtered incandescent is (usually) not -Unfiltered incandescent light is represented by RED( AlInGaP) the black body curve. BLUE GREEN (InGaN) -Typical tungsten bulbs have a color WHITE( InGaN temperature of 2800 K, their light is yellowish (Blue) + Phosphor) (point A) -A black body at 6500 K emits almost pure white light (point C) BLUE (InGaN) 6 Color Mixing The intensity/flux of two light beams is specified in terms of quantities Y 1 and Y 2 and the color is specified by chromaticity coordinates x 1, y 1, x 2, y 2. The sum of the light beams is given by: y ⋅m + y ⋅m x ⋅m + x ⋅m y = 1 1 2 2 , and x = 1 1 2 2 sum + sum + m1 m2 m1 m2 Y X Z Y Y Note that m = i = i = i = X +Y + Z , = 1 = 2 i y x z i i i with m1 , and m2 . i i i y1 y2 (see definition of x, y and z) Example: 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). 7 Colorimetric quantities X = 683 ⋅ ∫ P(λ) ⋅ x(λ) dλ Y = 683 ⋅ ∫ P(λ) ⋅ y(λ) dλ (⇒ intensity [cd]) Z = 683 ⋅ ∫ P(λ) ⋅ z(λ) dλ P( λ) is the radiated spectrum of the light source X x = (i.e. the spectral intensity of the source) X + Y + Z Y x( λ), y( λ) and z( λ) are the CIE color matching functions y = X + Y + Z (sometimes also called x-bar, y-bar and z-bar) Z z = X + Y + Z X, Y and Z are the colorimetric quantities (Y is equal to the photometric intensity) + + = x y z 1 x, y and z are the color coordinates (x and y are the coordinates in the CIE-Diagram) 8 Color Purity • Color Purity defines “how far away” a color is from it’s corresponding pure color • Reference is Illuminant E(0.333,0.333) • Color Purity= a/b 9 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 sources close to the black body curve (white light) 10 Typical LED Spectra 1 AlInGaP Amber 0.9 AlInGaP Red 0.8 InGaN Blue InGaN Green 0.7 InGaN White 0.6 0.5 0.4 RelRel IntensityIntensity [a.u.] [a.u.] 0.3 0.2 0.1 0 400 450 500 550 600 650 700 750 800 Wavelength [nm] 11 InGaN white LED Structure Converted rays Phosphor Blue InGaN Chip naked chip Spectrum: with phosphor 400 500 600 700 λ/nm 12 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 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). 13 Eye Response Near Darkness Daylight Condition <3.2 mlx >100lx (Scotopic) (Photopic) In most night vision cases (night traffic, etc), the eye is in an intermediate state between scotopic and photopic called “mesopic” vision 14 Intensity I and Solid Angle Ω Definitions: d dΦ I = dΩ << A for d :r π 2 r Ω = A = d r 2 4r 2 Radiometric Intensity: Iv [W/sr] Photometric Intensity: I [lm/sr] or [cd], Candela Solid Angle Units: Ω [sr], Steradian 15 Conversion from Intensity to flux Flux in the far field of a source emitted into a solid angle element : dΦ = I(θ,ϕ)dΩ Rewrite in integral Form : Φ = ∫∫ I(θ,ϕ)sin( θ )dθdϕ Total Flux for rotational Symmetry : π Φ = 2π ∫ I(θ )sin( θ )dθ 0 16 Lambertian Emitter 2 θ Typical radiation pattern of a flat surface : (i.e. LED chip top surface) θ = θ I( ) I0 cos( ) Total flux in a cone with an opening Intensity angle 2 θ: Total Included Flux 1 0.9 θ 0.8 0.7 Φ = 2π I(θ )' sin( θ )' dθ ' 0.6 ∫ 0.5 0 0.4 0.3 θ 0.2 = π θ θ θ IntensityIntensity [cd],[cd], FluxFlux [lm/pi] [lm/pi] 0.1 2 ∫ I0 cos( )' sin( )' d ' 0 0 10 20 30 40 50 60 70 80 90 0 Off Axis Angle = π 2 θ sin ( )I0 The total flux of a Lambertian source of 1 cd on axis is π lm! To collect for example 90% of the Flux of a Lambertian source, the optics must ± capture a cone 72 deg off axis angle 17 Uniform Emitter θ 2 Typical radiation pattern of a spherical surface (i.e. the sun), or of, as a rough approximation, an incandescent filament. θ = = I( ) I0 const Intensity Total flux in a cone with an opening Total Included Flux 1 angle 2 θ: 0.9 θ 0.8 0.7 Φ = π θ θ θ 0.6 2 ∫ (I( )' sin( )' d ' 0.5 0 0.4 0.3 θ 0.2 = π ⋅ θ θ IntensityIntensity [cd],[cd], FluxFlux [lm/[lm/ 4 4 pi] pi] 0.1 2 I0 ∫sin( )' d ' 0 0 20 40 60 80 100 120 140 160 180 0 Off Axis Angle = π ⋅ − θ 2 I0 1( cos( )) π The total flux of a uniform source (integral from 0 to 2 pi) of I0 =1 cd is 4 lm! 18 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 Conventional lens fresnel lens 19 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 Conventional lens TIR lens 20 Nonimaging Optics (NIO) optimum transfer of NIO luminous power A B A B Source Source IMAGING NONIMAGING OPTICAL SYSTEM OPTICAL SYSTEM Receiver Receiver A’ B’ Source image No Source image 21 NIO Design Rules A B Source Basic conservation and design rules: •Flux conservation NONIMAGING •Etendue conservation OPTICAL SYSTEM •Luminance conservation •Edge ray principle Receiver 22 Flux Conservation and Efficiency Flux conservation: A passive optical system always decreases the source flux due to absorption and reflection losses within the optical system: Source Lost Φ ≤ Φ out in flux Φ Φ in source Collection Efficiency: OPTICAL The collection efficiency is the fraction of the source flux SYSTEM captured by the optical system η = Φ Φ coll in / source Lost flux Φ target Optical Efficiency: Target 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 Φ interval).