MV-4920 Physical Modeling Remote Sensing Basics Mapping VR/Simulation Scientific Visualization/GIS Smart Weapons Physical Nomenclature Atmospherics Illumination Surface physics EO/IR

Computer Graphics Remote Sensing THESE FOUR COMMUNITIES DIFFER *NOMENCLATURE *EQUATIONS *APPROACH Radiometrics Photometrics Why NOMENCLATURE?

Surface Rendering Model Atmospheric Propagation Model Illumination Model Sensor Model Thermal Load Model Components of the Radiometric Sensing Problem.

Radiometric Nomenclature Radiance L=  {L (x,y, , , ) } d [watts/cm 2 sr] Irradiance E =    {L (x,y, , , ) } d sin(  ) d  d  or Emittance when radiation is from a surface [watts/cm 2 ] Spectral radiance = L (x,y, , , ) [watts/cm 2 sr ] Flux (power)  =      {L (x,y, , , ) } sin(  ) d d  d  dx dy [watts] Also used alternative definition Radiance N=  {N (x,y, , , ) } d [watts/cos(  )cm 2 sr] Collimated incident flux J =    {N (x,y, , , ) } d sin(  ) d  d  [watts /cm p 2 ] “ance” ending implies radiation measurement quantities Radiant Intensity I =    {L (x,y, , , ) } d dxdy [watts/ sr]

Radiance -L- radiance means watts flowing into a unit area ( A s ) from a solid angle  i [watts/ cm s 2 sr i ] Radiometric Nomenclature  e = A e /R 2 Incident spectral radiance L i (x,y,  i,  i, ) Emitted spectral radiance L e (x,y,  e,  e, ) 1cm  i = A i /R 2 R AsAs Alternative definition(causes lots of confusion) Radiance- N - radiance means watts flowing into a unit area ( A p ) perpendicular to the ray from a solid angle  i [watts/ cm p 2 sr i ] cm p 2 = cos (  ) cm s 2 and N cos (  ) = L 

H = irradiance = the watts flowing into a unit surface from all angles [watts/ cm s 2 sr i ] 1cm LiLi AsAs irradiance =  {radiance}d  Radiometric Nomenclature irradiance =  {L i (x,y,  i,  i, ) } sin(  i ) d  i d  i ii  i emittance = the watts flowing out of a unit surface from all angles

I = radiant intensity = the watts flowing into a unit solid angle from a point source [watts/ sr i ] 1m radiant intensity =  {radiance}dxdy Radiometric Nomenclature Point source radiance L i (x,y, , , ) = {P in watts/4  sr }  (x-x i )  (y-y i ) radiant intensity =  {P in watts/4  sr }  (x-x i )  (y-y i ) dxdy= P in w/4  sr example: Radiant intensity from a 100 watt bulb on a 1cm radius surface at 1 meter is (100/ 4  ) .01 2 =.0025w Power in (P in )  = A /R 2 1cm

Radiometric Nomenclature “ivity” ending implies intrinsic surface measurement quantities absorbtivity  = power absorbed / power incident =  abs /  in reflectivity  = power reflected/power incident =  ref /  in transmissivity  = power transmitted/power incident =  trans /  in emissivity  = power emitted/power emitted from a blackbody =  abs /  in Add “spectral” to indicate wavelength dependence. Spectral reflectivity =  ( ) power reflected/power incident at wavelength No standard but general indicators add “bidirectional” And “function” to indicate directional dependence.

SBDRF - Spectral Bidirectional Reflectance Distribution Function  (  i,  i  r,  r, ) [ sr -1 ] ratio of the spectral reflected radiance to the incident flux per unit area Radiometric Nomenclature AlAl AiAi AsAs J in watts/cm p When wavelength independent it is called BDRF - Bidirectional Reflectance Distribution Function -  (  i,  i  r,  r )  (  i,  i  r,  r, ) = N (x r,y r,  r,  r, )/E(x s,y s  i,  i ) E(x s,y s  i,  i ) Simplistic Interpretation: BDRF relates the power in at one angle to power out at another J out watts/cm p

But that is too simple Radiometric Nomenclature A l area of lens AsAs Power out (P out ) Power out is collected from a detector area A d projected through a lens of area A l onto a surface area A s. The power leaving the surface at angles to hit the detector is L (x,y,  r,  r,)  l A s = L (x,y,  r,  r,) A d A l /(f 2 cos(  r )) = N (x p,y p,  r,  r,) A d A l / f 2  l A s = A d A l /(f 2 cos(  r )) A d area of detector f focal length  l Solid angle of lens at surface

Look how BDRF is measured. Radiometric Nomenclature ArAr AiAi AsAs J in = P in  in Incident power E(x,y,  i,  i ) A s = J in cos(  i ) A i Power in (P in ) Power out (P out )  in Power leaving the surface in the direction of the lens L (x,y,  r,  r,)  l A s P in  in cos(  i )  (  i,  i  r,  r ) A d A l / f 2 = P out N (x p,y p,  r,  r,)  l A r Illumination Surface Sensor

The BDRF for a Lambertian surface as  (  i,  i  r,  r ) =  / .  = E in /E out the reflectivity Lambertian Surface AdAd AsAs J in I Most natural surfaces are Lambertian to first order. How bright a Lambertian surface looks Depends upon the illumination power J in and angles  i,  i Does not depend upon the view angles  r,  r Power leaving the surface L (x,y,  r,  r,) cos(  r ) must decrease as the cos(  r ) since A s increases as 1/ cos(  r ) ii rr

Solar radiance at the top of the atmosphere is L i (x,y, , , ) = {J in watts/cm p 2 }cos(  )  (  -  i )  (  -  i ) Solar irradiance on a surface x,y is E in =   {L (x,y, ,  ) } sin(  ) d  d  = J in cos(  i )=.14 cos(  i ) Reflected radiance from the surface is L (x s,y s,  r,  r,) = (  /  ).14 cos(  i ) cos(  r ) The Emittance from the surface into the upper hemisphere is E out =   L (x s,y s,  r,  r,) sin(  ) d  d  = .14 cos(  i ) The power hitting a detector size A d through lens A l focal length f assuming the surface covers the field of view is P out = (  /  ) (A d A l /(f 2 cos(  r ))).14 cos(  i ) cos(  r ) Solar Radiation Example:

ArAr AiAi AsAs J in =.14 watts/cm p Irradiance =.07 Power out (P out ) Lambertian surface with reflectivity of.7 Reflected radiance L at  r = 60deg.0078watts/cm s 2 sr Emittance =.049w/ cm s 2  i = 60deg  r = 60deg Lens radius 10cm focal length 20 cm detector 1 sq mm 1 km from surface (.0078)(10 -2 )(3.14)(10 2 ) / (.5x 20 2 ) =.12mw Ground area in m = (10 5 /20) 2 (10 -2 )/ (.5)= 50 m 2

J I ie g Surface Normal AsAs  i,  i = incidence angle e,  r = emission angle ,  i -  r = azimuthal angle between the planes of incidence and emission g = phase angle (angle between incidence and emission angles) 0,  i = incident azimuth angle, set to zero in Hapke nomenclature  = single scattering albedo, J in,J = irradiance* at the upper surface of the medium; source is highly collimated radiation; infinite distance from medium N,I = radiance at the detector = I(i,e,g)  (  i,  i  r,  r )cos(  i ), r(i,e,  ) reflectance function Radiometric Nomenclature vs. Hapke Nomenclature

K( ) - At a frequency of 540x10 12 Hertz is defined as 1 lm/683watts of radiant power Photometric Units Photometric units are similar to radiometric units; however the radiation is weighted to match the human eye using a photometric curve(luminous efficacy) K( ). Flux [watts]  * K( ) =  Luminous flux [Lumens] Irradiance [watts/cm 2 ] E * K( ) *10 -4 = E Illuminance [Lux = Lumens/m 2 ] Radiometric Photometric Ref: // Radiance [watts/sr-cm 2 ] L * K( ) *10 -4 = L Luminance [Lux /sr]

[1]Handbook of Military Infrared Technology, W.L Wolfe,1965 ONR Dep of Navy Washington p4 [2] Ref: A Survey of BRDF Representation for Computer Graphics, Szymon Rusinkiewicz [3] Hapke, B., (1993). Theory of Reflectance and Emittance Spectroscopy. Cambridge University Press, [4] Shepard, M.K., R.E. Arvidson, and E.A.Guinness; (1993) Specular Scattering on a Terrestrial Playa and Implications for Planetary Surface Studies. JGR, vol. 98, no. E10, pgs. 18, ,718. [5]Toward A Standard Rendering Equation For Intrinsic Earth Surface Classification 00S-SIW-070.doc [6] Toward Standards for Interoperability and Reuse in IR Simulation [7]R. Driggers, P Cox, T. Edwards,Introduction to Infrared And Electro-Optical Systems, Artech House, Inc., 1999 ISBN