Derivation of Mueller matrix from Zemax Tetsu Anan

Transcription

1 Derivation of Mueller matrix from Zemax Tetsu Anan

2 Definition of Stokes Q, U, & V Ichimoto et al Stenflo 1994 View towards the sun, that is, from the direction of the observer Signs of Stokes U & V change, when light is reflected Coordinates in Zemax doesn t change, when light is reflected => We should change the sign of U & V in Zemax manually

3 Jones vector Polarization Ray Trace procedure in Zemax can calculate polarization state of light passing (X, Y) field & pupil coordinates, in Jones description, at each surface Jones vector J! = # $% &'( ) # * % &'( +, where the electric field vector of light E Jones vector cannot describe depolarization, = Re # $% &' /01( ) # * % &' /01( + Interaction with a medium! 2 = 3! ω: 2 2 complex matrix

4 Mueller matrix Mueller matrix M derived from ω! = # $ $ # '(, where is tensor product, is complex conjugation, T = i i 0, and T 1 = 1 2 However, the definition of V in the output is opposite to our definition. Then! = )# $ $ # '( ), where * = i i Stenflo 1994 Solar Magnetic Fields chap

5 Method

6 Step 1 1. Edit Lens Data 2. Open the Polarization Ray Trace

7 Step 2 Edit Settings in Polarization Ray Trace Generate a polarized light source (JX, JY, X, Y-Phase) Specify the ray path (HX, HY, PX, PY) and wavelength No check

8 Step 3 Read E field before (after) coating of S & P pol. at the interestring surface from output of the Polarization Ray Trace An example of the output regarding with a surface (surface 3, silver coated mirror) Tracing ray to surface 3: Path length through air (tau): E+00 Internal absorption per mm (alpha): E+00 Internal Transmittance of ray (IT): Propagation Phase Factors (pc,ps): Coordinates on surface (x,y,z): E E E+00 Direction cosines of incident ray (l1,m1,n1): Cosine of angle of incident ray : ( deg) Cosine of angle of exit ray : ( deg) Direction cosines of exit ray (l2,m2,n2): Direction cosines of normal (ln,mn,nn): Direction cosines of S vector (sx,sy,sz): Direction cosines of P vector (px,py,pz): E field before coating (xyz) (Exr,Eyr,Ezr): (Exi,Eyi,Ezi): E field before coating (s&p) (Esr,Epr): (Esi,Epi): Ray intensity before coating (I1): Coating : SILVER Intensity Reflection coefficients (Rs,Rp): Intensity Transmission coefficients (Ts,Tp): Intensity Absorption coefficients (As,Ap): Diattenuation (D): Field Amplitude Reflection S pol (rsr,rsi): Field Amplitude Reflection P pol (rpr,rpi): Field Amplitude Transmission S pol (tsr,tsi): Field Amplitude Transmission P pol (tpr,tpi): Field Reflection Phase (Prs,Prp): Field Reflection Retardance (P-S) (Sr): ( deg) Field Reflection Retardance (P-S+pi) (Sr): ( deg) Field Transmission Phase (Pts,Ptp): Field Transmission Retardance (P-S) (St): ( deg) Field Transmission Retardance (P-S+pi) (St): ( deg) Ray Amplitude Reflection S pol (rsr,rsi): Ray Amplitude Reflection P pol (rpr,rpi): Ray Amplitude Transmission S pol (tsr,tsi): Ray Amplitude Transmission P pol (tpr,tpi): Ray Reflection Phase (Prs,Prp): Ray Reflection Retardance (P-S) (Sr): ( deg) Ray Reflection Retardance (P-S+pi) (Sr): ( deg) Ray Transmission Phase (Pts,Ptp): Ray Transmission Retardance (P-S) (St): ( deg) Ray Transmission Retardance (P-S+pi) (St): ( deg) Electric field after coating (Esr,Epr): (Esi,Epi): Ray intensity after coating (I2): Direction cosines of new S vector (sx,sy,sz): Direction cosines of new P vector (px,py,pz): E field after (Exr,Eyr,Ezr): (Exi,Eyi,Ezi): X, Y, and Z direction Amplitude (Ax, Ay, Az): X, Y, and Z direction Phase (Px, Py, Pz): Phase difference between X and Y (Pxy): ( deg) Major, Minor semi axis XY ellipse (EM, Em): Angle of XY polarization ellipse (Ap): ( deg) Ray intensity out (I2):

9 Polarization property of the surface in Jones description 2 sets of E field before/after coating with different polarized light source! ",$ = ' (( ' ()! ",*! %,$ ' )( ' ))! %,*! ",$ = ' (( ' ()! ",*! %,$ ' )( ' ))! %,* where E (S,P),(a,b) is E field (after, before) in (S, P) pol. If you consider rays pass some points on a pupil, you need to derive average ω matrix after calculation of the ω for each ray Sampling points on a pupil should be in symmetry around the optical axis Þ ω00, ω01, ω10, ω11 Þ Mueller matrix positive Q-direction is S-direction no depolarization zemax2mm.pro

10 Example

11 Exercise 1 Folding mirror Silver coating

12 Exercise 1 Zemax λ: nm Silver coating n= i A ray pass center on pupil Normalized by (0,0) Stenflo n= i Incidence angle 45 Normalized by (0,0)

13 Summary I present a principle, a method, and an example of derivation of the Mueller matrix from Zemax We should manually change the sign of U & V in case of reflector Definition of V in Mueller matrix derived with a method described in Stenflo 1993 is opposite to our definition It does not have depolarization effect I developed a IDL function named zemax2mm.pro It is succeed in derivation of Mueller matrix of silver coated folding mirror It does not have depolarization effect

14 Coating COATING.DAT Coating Materials: e.g. AIR, AG Wavelength, Index (n), Extinction (k) Coating Definitions: Coating name: e.g. HEAR1, 3 layer(s) Material, Thickness, Absolute, Loop, Taper e.g. MGF2, 0.25, 0, 0 ZRO2, 0,50, 0, 0 CEF3, 0.25, 0, 0 or S or P Polarization: T, tr, ti. R, rr, ri, A, TIR or Wavelength, Rs, Rp, Ts, Tp, Ars, Arp η=n+ik Absolute: μm Loop: Taper: