<p> hatch, scale </p>

9f0a2fc3-2a8f-4276-b8ba-909f27e53c68 67 3 5 decimal

&[DATE] &[TIME] - &[FILENAME]

You need that one for scaling grayscale image M lo hi Scale hi lo - (M M Min - M Max M Min - 106 -^+ / (* lo + :

Erzeugt eine Matrix für die Darstellung vertikaler Linien zwischen den Funktionen f(x) und 
g(x) im Bereich von x1 bis x2 mit 2*n Linien. Generates a matrix for 2*N vertical lines (hatching) 
between functions f(x) and g(x) in x-range from x1 to x2 f g x.1 x.2 N hatch dx x.2 x.1 - N / (: h x.1 x.1 f x.1 x.1 g 22 mat : x x.1 x.2 dx - x.1 dx + range h h x dx 2 / + x dx 2 / + g x dx 2 / + x dx 2 / + f x dx + x dx + f x dx + x dx + g 42 mat stack : for h 41 line :

x r Ψ 12 r * sqrt / x r - ≥ (x r ≤ (* 0 cases :

x f x 2 Ψ abs (2^:

Fourier Quantum: pin hole diffraction

x g 0 :

coordinate-space prob. density

f g 2 - 2 20 hatch 2 1 sys

W 0.5 : M 0.0375 : xo 0 : 13 mat U 10000 : α 4 : 12 mat 21 line

x q 0.1 12 x xo - (* U * W / (α^+ (M^/ :

asymmetric mapping x f 11 x 0.175^+ / :

The mapping function

x q x f

r 0.5 : (pin hole radius ≡ Δ 31 : (size momentum ≡ N 31 : (canvas size ≡ N Δ ≥ (Δ>N not diffraction ≡ px py 12 mat position momentum ≡ N odd to escape divide zero j 0 N range : px Δ - 2 Δ * j * N / + : py Δ - 2 Δ * j * N / + : 12 mat 81 line

Fourier transform of position wave function into 
momentum representation to get diffraction pattern 
@ the detection screen ... recast Φ(px,py2single. px py Φ i px x * y py * + (* - exp y r 2^x 2^- sqrt - r 2^x 2^- sqrt int x r - r int ≡

Δ N 12 mat 21 ≡ (4 min * ≡ Δ N 12 mat 31 ≡ (9 min * ≡ 21 mat

Convert/recast the double integral into single scalar integral [acc 50] px py Φ i py / i r 2^x 2^- sqrt py * x px * + (* - exp * i py / i r 2^x 2^- sqrt - (py * x px * + (* - exp * - x r - r int :

t0 1 time :

P m 1 N range n 1 N range Fo m 1 - n 1 - el px m el py n el Φ abs (2^: for for Fo 21 line :

P P : x f x f : fmap P f vectorize : CoC fmap - 0255 Scale : 41 line

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<= CoC 31/31

1 time t0 - min 9

Airy CoC [Circle of Confusion] xx r Ψ 12 r * sqrt / xx r - ≥ (xx r ≤ (* 0 cases : r 2 : v r Φ 12 π * sqrt / (i v * xx * - exp xx r Ψ * xx r - r int * : 31 line

X1 1.57 0.25 1.57 0.25 - 22 mat :

X2 π 0.25 π 0.25 - 22 mat :

Airy x 5 - 5 4.95 - range : j 1 x rows range Airy j el x j el r Φ abs (2^eval : for x Airy augment 31 line :

x r Φ abs 2 ^ X1 X2 3 1 sys Airy

π 2 / r Φ abs (2^π r Φ abs (2^21 mat 31031 -^* 31031 -^* 21 mat

r 0.25 : (pin hole radius ≡ N 20 : (canvas size ≡ 21 line

position wave fnct
@ hole screen j 0 N range : x 1 - 2 j * N / + vectorize : y 1 - 2 j * N / + vectorize : 31 line

You need that one for scaling grayscale image M lo hi Scale hi lo - (M M Min - M Max M Min - 106 -^+ / (* lo + :

position wave function @ hole screen x y Ψ 1 x r - ≥ (x r ≤ (* y r 2^x 2^- sqrt Re - ≥ (* y r 2^x 2^- sqrt Re ≤ (* 0 cases :

coordinate-space wave function pin i 1 N range j 1 N range hole i 1 - j 1 - el x i el y j el Ψ (2^eval : for for hole 21 line :

pin pin 0255 Scale :

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Etoile C:\SmathFile\EtoileScintillante.png READBMP :

x f 11 x 0.25^+ / :

fmap Etoile f vectorize :

Δ N >

Maroc fmap 0255 Scale :

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Etoile 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Maroc