Ray tracing - ESRF

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$A method for detailed simulations of neutron diffraction from ... - ESRF$

Focus is not perfect because of : ❑ aberrations ❑ source dimensions and depth [emittances] ❑ waviness and roughness errors of mirrors All these effects can be studied by ray-<strong>tracing</strong>. Example: circular source (diameter: 10 μm) divergences: 100 μrad p=30m θ=89.8 deg q=10m Toroidal Mirror Ellipsoidal Mirror Manuel Sánchez del Río -13- Experiments Division Programming Group Ferrara, March 11 1994 EUROPEAN SYNCHROTRON RADIATION FACILITY
The model is not sufficient: The ray may not exist after the mirror [it is absorbed] We must extend the model E s out = E s in * R s E p out = E p in * R p θ inc=89.9deg Reflectivity ~ probability of observation or intensity after reflection. We must include a new variable in the ray: I I out = I in R(E,θ,...) In fact, R is polarization-dependent, so it is better to store the Electric field: I = | E s exp(iφ s ) + E p exp(iφ p ) | 2 ray i = ( x, v, i, flag, E s , E p , φ s , φ p , φ g , 2π/λ) This permits also to work with polarized light, analyze the polarization degree and polarization properties through the beamline. |Es|=|Ep| φp = φs + π/2 circular pol. light Rs, Rp and phase change are given by a physical model of reflectivity. For mirrors the Fresnel equations are coded in the program. Manuel Sánchez del Río -14- Experiments Division Programming Group Ferrara, March 11 1994 EUROPEAN SYNCHROTRON RADIATION FACILITY
Page 1 and 2: Ray tracing ❑ A powerful tool whi
Page 3 and 4: What CAN be calculated with SHADOW?
Page 5 and 6: 1- Simplest case: The spherical sou
Page 7 and 8: The inversion method f(φ) cdf(φ)
Page 9: Tracing an Optical Element (i.e. MI
Page 13 and 14: Other O.E.s can be easily modeled:
Page 15 and 16: Gratings: Monochromators ❑ They c
Page 17 and 18: Mirror optics: Thermal Analysis (fi
Page 19 and 20: Mirror optics: Slope/Figure errors
Page 21 and 22: Slope/Figure errors with real profi
Page 23 and 24: Imaging properties of spherically b
Page 25 and 26: Collimation of X-rays (from plasmas
Page 27 and 28: Theory I Geometrical model S 1 k' 1
Page 29 and 30: Perfect crystals IV Tracing a polyc
Page 31 and 32: Benchmarks II Du Mond diagrams (J.W
Page 33 and 34: High resolution I Collimating pre-m
Page 35 and 36: High resolution III Normal incidenc
Page 37 and 38: Focusing optics I Polychromatic foc
Page 39 and 40: Focusing optics I Polychromatic foc
Page 41 and 42: Diffraction & Coherence I Fraunhofe
Page 43 and 44: Introduction They are formed by a l
Page 45 and 46: Mosaic Crystals: are formed by a la
Page 47 and 48: Ray tracing modeling with SHADOW k
Page 49 and 50: Beam evolution in the ⊥ plane usi
Page 51 and 52: Topographic studies on Highly Orien
Page 53: Theoretically calculated mirror pro

Ray tracing - ESRF

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