File:Shack-Hartmann.gif
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Summary
| Description |
English: A Shack-Hartmann sensor is made my an array of small lenses and a camera. If the light hitting the lenses is collimated, we will get a number of equispaced foci on the camera. But if the light is not collimated, the position of the foci will change in a predictable way, so we can reconstruct where the ray were coming from. |
| Date | |
| Source | https://mathstodon.xyz/@j_bertolotti/114557956224616668 |
| Author | Clodovendro |
| Permission (Reusing this file) |
https://mathstodon.xyz/@j_bertolotti/114533575175127912 |
Mathematica 14.0 code
rlens = 1; nlens = 10; f = 2;
lensy = Table[y, {y, -(nlens - 1)/2, (nlens - 1)/2, 2*rlens}];
rspacing = 0.2; (*tentative value*)
radii = Table[r, {r, -rlens + rspacing/2, rlens, rspacing}];
nrays = Dimensions[radii][[1]]*Dimensions[lensy][[1]];
frames1 = Table[
\[Theta]in =
Table[\[Pi]/50*Sin[\[Pi]/2 t]^2, {r, radii}, {y, lensy}];
Graphics[{
Thick, Yellow,
Table[Line[{10 {-Cos[\[Theta]in[[r, y]]],
Sin[\[Theta]in[[r, y]]]} + {0,
radii[[r]] + lensy[[y]]}, {0,
radii[[r]] + lensy[[y]]}}], {r, 1,
Dimensions[radii][[1]]}, {y, 1, Dimensions[lensy][[1]]}],
Table[
Line[{{0, radii[[r]] + lensy[[y]]},
10 {Cos[\[Theta]in[[r, y]] + radii[[r]]/
f], -Sin[\[Theta]in[[r, y]] + radii[[r]]/f]} + {0,
radii[[r]] + lensy[[y]]}}], {r, 1,
Dimensions[radii][[1]]}, {y, 1, Dimensions[lensy][[1]]}]
,
Gray, Table[Ellipsoid[{0, y}, {0.2, rlens}], {y, lensy}]
}, PlotRange -> {{-10, 1.5 f}, {-(nlens/2)*rlens - 1,
nlens/2*rlens}}, Background -> Black]
, {t, 0, 1, 0.1}];
frames2 = Table[
\[Theta]in =
Table[-(\[Pi]/50)*Sin[\[Pi]/2 t]^2, {r, radii}, {y, lensy}];
Graphics[{
Thick, Yellow,
Table[Line[{10 {-Cos[\[Theta]in[[r, y]]],
Sin[\[Theta]in[[r, y]]]} + {0,
radii[[r]] + lensy[[y]]}, {0,
radii[[r]] + lensy[[y]]}}], {r, 1,
Dimensions[radii][[1]]}, {y, 1, Dimensions[lensy][[1]]}],
Table[
Line[{{0, radii[[r]] + lensy[[y]]},
10 {Cos[\[Theta]in[[r, y]] + radii[[r]]/
f], -Sin[\[Theta]in[[r, y]] + radii[[r]]/f]} + {0,
radii[[r]] + lensy[[y]]}}], {r, 1,
Dimensions[radii][[1]]}, {y, 1, Dimensions[lensy][[1]]}]
,
Gray, Table[Ellipsoid[{0, y}, {0.2, rlens}], {y, lensy}]
}, PlotRange -> {{-10, 1.5 f}, {-(nlens/2)*rlens - 1,
nlens/2*rlens}}, Background -> Black]
, {t, 0, 1, 0.1}];
frames3 = Table[
\[Theta]in =
Table[(r + y)/50*Sin[\[Pi]/2 t]^2, {r, radii}, {y, lensy}];
Graphics[{
Thick, Yellow,
Table[Line[{10 {-Cos[\[Theta]in[[r, y]]],
Sin[\[Theta]in[[r, y]]]} + {0,
radii[[r]] + lensy[[y]]}, {0,
radii[[r]] + lensy[[y]]}}], {r, 1,
Dimensions[radii][[1]]}, {y, 1, Dimensions[lensy][[1]]}],
Table[
Line[{{0, radii[[r]] + lensy[[y]]},
10 {Cos[\[Theta]in[[r, y]] + radii[[r]]/
f], -Sin[\[Theta]in[[r, y]] + radii[[r]]/f]} + {0,
radii[[r]] + lensy[[y]]}}], {r, 1,
Dimensions[radii][[1]]}, {y, 1, Dimensions[lensy][[1]]}]
,
Gray, Table[Ellipsoid[{0, y}, {0.2, rlens}], {y, lensy}]
}, PlotRange -> {{-10, 1.5 f}, {-(nlens/2)*rlens - 1,
nlens/2*rlens}}, Background -> Black]
, {t, 0, 1, 0.1}];
frames4 = Table[
\[Theta]in =
Table[-((r + y)/50)*Sin[\[Pi]/2 t]^2, {r, radii}, {y, lensy}];
Graphics[{
Thick, Yellow,
Table[Line[{10 {-Cos[\[Theta]in[[r, y]]],
Sin[\[Theta]in[[r, y]]]} + {0,
radii[[r]] + lensy[[y]]}, {0,
radii[[r]] + lensy[[y]]}}], {r, 1,
Dimensions[radii][[1]]}, {y, 1, Dimensions[lensy][[1]]}],
Table[
Line[{{0, radii[[r]] + lensy[[y]]},
10 {Cos[\[Theta]in[[r, y]] + radii[[r]]/
f], -Sin[\[Theta]in[[r, y]] + radii[[r]]/f]} + {0,
radii[[r]] + lensy[[y]]}}], {r, 1,
Dimensions[radii][[1]]}, {y, 1, Dimensions[lensy][[1]]}]
,
Gray, Table[Ellipsoid[{0, y}, {0.2, rlens}], {y, lensy}]
}, PlotRange -> {{-10, 1.5 f}, {-(nlens/2)*rlens - 1,
nlens/2*rlens}}, Background -> Black]
, {t, 0, 1, 0.1}];
frames5 = Table[
\[Theta]in =
Table[Sin[2 (r + y)]/25*Sin[\[Pi]/2 t]^2, {r, radii}, {y,
lensy}];
Graphics[{
Thick, Yellow,
Table[Line[{10 {-Cos[\[Theta]in[[r, y]]],
Sin[\[Theta]in[[r, y]]]} + {0,
radii[[r]] + lensy[[y]]}, {0,
radii[[r]] + lensy[[y]]}}], {r, 1,
Dimensions[radii][[1]]}, {y, 1, Dimensions[lensy][[1]]}],
Table[
Line[{{0, radii[[r]] + lensy[[y]]},
10 {Cos[\[Theta]in[[r, y]] + radii[[r]]/
f], -Sin[\[Theta]in[[r, y]] + radii[[r]]/f]} + {0,
radii[[r]] + lensy[[y]]}}], {r, 1,
Dimensions[radii][[1]]}, {y, 1, Dimensions[lensy][[1]]}]
,
Gray, Table[Ellipsoid[{0, y}, {0.2, rlens}], {y, lensy}]
}, PlotRange -> {{-10, 1.5 f}, {-(nlens/2)*rlens - 1,
nlens/2*rlens}}, Background -> Black]
, {t, 0, 1, 0.1}];
ListAnimate[
Join[frames1, Reverse@frames1, frames2, Reverse@frames2, frames3, Reverse@frames3, frames4, Reverse@frames4, frames5,
Reverse@frames5] ]
Licensing
I, the copyright holder of this work, hereby publish it under the following license:
 
|
This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. |
| The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
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File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 14:23, 27 May 2025 | | 480 × 407 (3.19 MB) | Clodovendro | Uploaded own work with UploadWizard |
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