d5e6da5a-1513-48e0-a2a9-4edf6ef8ea0a 20 2 5 decimal

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

A 10 : (matrix mask ≡ R 1 : (radius center ≡ d 4 : (slit width ≡ α 16 : (≡ size 50 : (canvas size ≡ 51 line

You need that one for scaling grayscale image M lo hi Scale hi lo - (M M Min - M Max M Min - 1012 -^+ / (* lo + :

outer holes position i 0 A range : x i 0 * 1 + : y i 0 * : 31 line

Coordinates 
space wave function k 0 size range : xx A R * - 2 A * k * size / + vectorize : yy A R * - 2 A * k * size / + vectorize : 31 line

Position wave
function Δ A : N 50 : i 0 N range : px Δ - 2 Δ * i * N / + : py Δ - 2 Δ * i * N / + : 51 line

The 'mask pattern of the space wave function xx yy Ψ 1 A sqrt / 1 d sqrt / xx x m 1 + el d α / - (≥ (xx x m 1 + el d α / + ≤ (* yy y m 1 + el d 2 / - (≥ (* yy y m 1 + el d 2 / + ≤ (* 0 cases m 1 A sum 11 line * :

Display mask m 1 size range n 1 size range M m n el xx m el yy n el Ψ abs (2^eval : for for

M M 0255 Scale :

iVBORw0KGgoAAAANSUhEUgAAADIAAAAyCAIAAACRXR/mAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAAuSURBVFhH7c0hDgAgEAPB/v/RBNPgCO4wM3qTDQAAAMCxXtoN6/yuHQAAwEfJBrAbQX2OHO1UAAAAAElFTkSuQmCC

Mask pattern

a x m el d α / - (≡ b x m el d α / + (≡ c y m el d 2 / - (≡ d y m el d 2 / + (≡ 14 mat

i Clear 1

Optimiz => SYMBOLIC ... a bit faster px py Ψ 12 π * d * A sqrt * / i x m el d α / + (* px * - exp i x m el d α / - (* px * - exp - (i y m el d 2 / + (* py * - exp - i y m el d 2 / - (* py * - exp + (* px py * 1012 -^+ / m 1 A sum 11 line * :

px py * 1768

Sanity check 5050 Ψ abs 2^55 Ψ abs (2^11 Ψ abs 2^31 mat 4.571 1011 -^* 0 0.013 31 mat

Memo Vector Algebra:

The dot product of two vectors is the vector sum of their product.

Each NUM component is a vector, their dot product is a number

... as well as DENOM [QED].

]]>

Optimiz => Numeric P m 1 N range n 1 N range Fo m n el px m el py n el Ψ abs (2^eval : for for Fo 21 line :

The Fourier diffraction integral leaves some undesirable cross hair to be removed.

t0 1 time :

M c DelColRow N 0 : ct 1 : n 1 M cols range n c ≠ N 1 ct el M n col : ct ct 1 + : 21 line if for Unest v N 1 el : j 2 N cols range v v N j el augment : for v 71 line :

P P : P P N 2 / 1 + DelColRow : P P transpose N 2 / 1 + DelColRow transpose : slit P 0255 Scale : 41 line

Mask

M 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

Diff'n

slit

1 time t0 - min 2.5

Fourier Quantum

Adapted from Mathcad 11, mathengjmg [web site].

Written permission from Frank Rioux.

http://www.users.csbsju.edu/~frioux/workinprogress.html

M is the mask pattern in preparation for diffraction.

]]>