Global Optimization (Particle Swarm)
[1]:
from optiland import optic, optimization
Define a starting lens:
[2]:
lens = optic.Optic()
# add surfaces
lens.surfaces.add(index=0, thickness=50)
lens.surfaces.add(index=1, thickness=5, radius=40, material="N-BK7", is_stop=True)
lens.surfaces.add(index=2, thickness=50, radius=-40)
lens.surfaces.add(index=3)
# set aperture
lens.set_aperture(aperture_type="EPD", value=12)
# add field
lens.fields.set_type(field_type="object_height")
lens.fields.add(y=0)
# add wavelength
lens.wavelengths.add(value=0.55, is_primary=True)
# draw lens
lens.draw(num_rays=5)
[2]:
(<Figure size 1000x400 with 1 Axes>, <Axes: xlabel='Z [mm]', ylabel='Y [mm]'>)
Define optimization problem:
[3]:
problem = optimization.OptimizationProblem()
Add operands (targets for optimization):
[4]:
# RMS spot size target
for field in lens.fields.get_field_coords():
input_data = {
"optic": lens,
"Hx": field[0],
"Hy": field[1],
"surface_number": -1,
"num_rays": 5,
"wavelength": 0.55,
"distribution": "hexapolar",
}
problem.add_operand(
operand_type="rms_spot_size",
target=0,
weight=1,
input_data=input_data,
)
Define variables - we let the radii vary. Note that PSO requires finite bounds for all variables:
[5]:
problem.add_variable(lens, "radius", surface_number=1, min_val=25, max_val=100)
problem.add_variable(lens, "radius", surface_number=2, min_val=-100, max_val=-25)
Check initial merit function value and system properties:
[6]:
problem.info()
╒════╤════════════════════════╤═══════════════════╕
│ │ Merit Function Value │ Improvement (%) │
╞════╪════════════════════════╪═══════════════════╡
│ 0 │ 9.89095 │ 0 │
╘════╧════════════════════════╧═══════════════════╛
╒════╤════════════════╤══════════╤══════════════╤══════════════╤══════════╤═══════════════╤═════════╤═════════╤════════════════╕
│ │ Operand Type │ Target │ Min. Bound │ Max. Bound │ Weight │ Eff. Weight │ Value │ Delta │ Contrib. [%] │
╞════╪════════════════╪══════════╪══════════════╪══════════════╪══════════╪═══════════════╪═════════╪═════════╪════════════════╡
│ 0 │ rms spot size │ 0 │ │ │ 1 │ 1 │ 3.145 │ 3.145 │ 100 │
╘════╧════════════════╧══════════╧══════════════╧══════════════╧══════════╧═══════════════╧═════════╧═════════╧════════════════╛
╒════╤═════════════════╤═══════════╤═════════╤══════════════╤══════════════╕
│ │ Variable Type │ Surface │ Value │ Min. Bound │ Max. Bound │
╞════╪═════════════════╪═══════════╪═════════╪══════════════╪══════════════╡
│ 0 │ radius │ 1 │ 40 │ 25 │ 100 │
│ 1 │ radius │ 2 │ -40 │ -100 │ -25 │
╘════╧═════════════════╧═══════════╧═════════╧══════════════╧══════════════╛
Define optimizer:
[7]:
optimizer = optimization.ParticleSwarm(problem)
Run optimization:
[8]:
optimizer.optimize(maxiter=30, swarm_size=20, seed=42)
PSO start: best merit = 0.495756518209, swarm_size = 20, ndim = 2
Iter 1 | best merit = 0.385379232348 | improvement = 0.110377
Iter 2 | best merit = 0.0342386453248 | improvement = 0.351141
Iter 3 | best merit = 0.025628852796 | improvement = 0.00860979
Iter 4 | best merit = 0.025628852796 | improvement = 0
Iter 5 | best merit = 0.0238220692892 | improvement = 0.00180678
Iter 6 | best merit = 0.0238220692892 | improvement = 0
Iter 7 | best merit = 0.0232647160272 | improvement = 0.000557353
Iter 8 | best merit = 0.0232647160272 | improvement = 0
Iter 9 | best merit = 0.0232647160272 | improvement = 0
Iter 10 | best merit = 0.0232647160272 | improvement = 0
Iter 11 | best merit = 0.0232647160272 | improvement = 0
Iter 12 | best merit = 0.0232647160272 | improvement = 0
Iter 13 | best merit = 0.0232647160272 | improvement = 0
Iter 14 | best merit = 0.0229899364483 | improvement = 0.00027478
Iter 15 | best merit = 0.0229899364483 | improvement = 0
Iter 16 | best merit = 0.0229899364483 | improvement = 0
Iter 17 | best merit = 0.0229512509028 | improvement = 3.86855e-05
Iter 18 | best merit = 0.0229512509028 | improvement = 0
Iter 19 | best merit = 0.0229512509028 | improvement = 0
Iter 20 | best merit = 0.0229512509028 | improvement = 0
Iter 21 | best merit = 0.0229472840767 | improvement = 3.96683e-06
Iter 22 | best merit = 0.0229472840767 | improvement = 0
Iter 23 | best merit = 0.0229472840767 | improvement = 0
Iter 24 | best merit = 0.0229472840767 | improvement = 0
Iter 25 | best merit = 0.0229472840767 | improvement = 0
[8]:
message: Optimization converged: global best stalled within tol=0.001 for 20 iterations.
success: True
fun: 0.02294728407671323
x: [-7.306e-01 -1.275e+00]
nit: 25
nfev: 520
swarm_size: 20
inertia: 0.7
individual: 1.5
social: 1.5
Print merit function value and system properties after optimization:
[9]:
problem.info()
╒════╤════════════════════════╤═══════════════════╕
│ │ Merit Function Value │ Improvement (%) │
╞════╪════════════════════════╪═══════════════════╡
│ 0 │ 0.0229473 │ 99.768 │
╘════╧════════════════════════╧═══════════════════╛
╒════╤════════════════╤══════════╤══════════════╤══════════════╤══════════╤═══════════════╤═════════╤═════════╤════════════════╕
│ │ Operand Type │ Target │ Min. Bound │ Max. Bound │ Weight │ Eff. Weight │ Value │ Delta │ Contrib. [%] │
╞════╪════════════════╪══════════╪══════════════╪══════════════╪══════════╪═══════════════╪═════════╪═════════╪════════════════╡
│ 0 │ rms spot size │ 0 │ │ │ 1 │ 1 │ 0.151 │ 0.151 │ 100 │
╘════╧════════════════╧══════════╧══════════════╧══════════════╧══════════╧═══════════════╧═════════╧═════════╧════════════════╛
╒════╤═════════════════╤═══════════╤══════════╤══════════════╤══════════════╕
│ │ Variable Type │ Surface │ Value │ Min. Bound │ Max. Bound │
╞════╪═════════════════╪═══════════╪══════════╪══════════════╪══════════════╡
│ 0 │ radius │ 1 │ 26.9429 │ 25 │ 100 │
│ 1 │ radius │ 2 │ -27.4896 │ -100 │ -25 │
╘════╧═════════════════╧═══════════╧══════════╧══════════════╧══════════════╛
Draw final lens:
[10]:
lens.draw(num_rays=5)
[10]:
(<Figure size 1000x400 with 1 Axes>, <Axes: xlabel='Z [mm]', ylabel='Y [mm]'>)
