Even Asphere Sag Depth

[jakecarr3]

I've been working with a few aspheric surfaces and noticed the aspheric profile didn't look right in the pictures. So I checked the sag depth and it doesn't match.

I used the sag depth calculator here to verify.

I've been entering the coefficients like an even asphere A2, A4, A6, A8, etc. I tried adding extra 0s in the coefficients like if it took even and odd terms with A1, A2, A3, A4 etc. terms, but the sag depth is unchanged. If I zero out all the coefficients and just leave the cc, the sag value reported stays the same too. Only if I change the cc, the sag depth updates so I think it's somehow not getting the asphere terms.

opm.radius_mode = True
sm.do_apertures = False

sm.add_surface([95.867658, 5.08, 2.6563, 45.72])
sm.ifcs[sm.cur_surface].profile = RadialPolynomial(r=95.867658, cc=0, coefs=[0., 8.180497E-7, -7.007436E-12,  -5.576895E-15, 4.688910E-18])
print(sm.ifcs[sm.cur_surface].profile.sag(45.72, 0.))

Output
11.604442713583566

Should be 15.19550

Another Example

sm.add_surface([48.358836, -5.08, 'refl', 36.575])
sm.ifcs[sm.cur_surface].profile = RadialPolynomial(r=48.358836, cc=-2.474466, coefs=[0., 3.460039E-6, 1.053395E-10, 2.273815E-13, 1.045178E-16])
print(sm.ifcs[sm.cur_surface].profile.sag(36.575, 0.))

Output
11.73271321584345

Should be 19.35262

[mjhoptics]

Hello @jakecarr3,
Thank you for your question. The profile class that you want to use is the EvenPolynomial, rather than the RadialPolynomial. The RadialPolynomial profile includes odd terms as well as even (e.g. A1, A3, A5, etc.). I think the doc could be clearer on this; I'll resolve the issue when I've done that.
Thanks for the clear report.
Mike Hayford

from rayoptics.environment import *

opm = OpticalModel()
sm  = opm['seq_model']
osp = opm['optical_spec']
pm = opm['parax_model']
em = opm['ele_model']
pt = opm['part_tree']
ar = opm['analysis_results']

opm.radius_mode = True
sm.do_apertures = False
sm.gaps[0].thi = 1e11

Radial vs Even Polynomials

RadialPolynomial profile

The RadialPolynomial profile includes both even and odd terms in r. The entries for rad_poly correspond to the 2nd, 3rd, 4th, and 5th powers of r.

Note that creating standalone profile instances requires you to explicitly call the update() method on the profile instance.

rad_poly = RadialPolynomial(r=95.867658, cc=0, coefs=[0., 8.180497E-7, -7.007436E-12,  -5.576895E-15, 4.688910E-18])
rad_poly.update()
print(f"radial poly sag = {rad_poly.sag(45.72, 0.):12.5f}")

radial poly sag =     11.60615

EvenPolynomial profile

The EvenPolynomial profile include only even powers of r. The entries for even_poly correspond to the 4th, 6th, 8th, and 10th powers of r.

The update() method for the profile must be called for the sag() evaluation to be correct.

even_poly = EvenPolynomial(r=95.867658, cc=0, coefs=[0., 8.180497E-7, -7.007436E-12,  -5.576895E-15, 4.688910E-18])
even_poly.update()
print(f"even poly sag = {even_poly.sag(45.72, 0.):12.5f}")

even poly sag =     15.19550

The RadialPolynomial may be used as long as the odd polynomial terms are explicitly entered as zero.

rad_poly1 =  RadialPolynomial(r=95.867658, cc=0, coefs=[0., 0., 0., 8.180497E-7, 0., -7.007436E-12,  0., -5.576895E-15, 0., 4.688910E-18])
rad_poly1.update()
print(f"radial poly 1 sag = {rad_poly1.sag(45.72, 0.):12.5f}")

radial poly 1 sag =     15.19550

Use of update_model()

Normally, when entering profiles as part of the model definition, the call to update_model() on the optical model will update all of the profiles in the model, as seen below.

sm.add_surface([95.867658, 5.08, 2.6563], sd=45.72)
rad_poly2 =  RadialPolynomial(r=95.867658, cc=0, coefs=[0., 0., 0., 8.180497E-7, 0., -7.007436E-12,  0., -5.576895E-15, 0., 4.688910E-18])
sm.ifcs[sm.cur_surface].profile = rad_poly2

sm.add_surface([95.867658, 5.08, 2.6563], sd=45.72)
even_poly1 = EvenPolynomial(r=95.867658, cc=0, coefs=[0., 8.180497E-7, -7.007436E-12,  -5.576895E-15, 4.688910E-18])
sm.ifcs[sm.cur_surface].profile = even_poly1

opm.update_model()

listobj(even_poly1)
print(f"even poly 1 sag = {even_poly1.sag(45.72, 0.):12.5f}")

profile: EvenPolynomial
c=0.010431046516229696,   r=95.867658   conic cnst=0
coefficients: [0.0, 8.180497e-07, -7.007436e-12, -5.576895e-15, 4.68891e-18]

even poly 1 sag =     15.19550

listobj(rad_poly2)
print(f"radial poly 2 sag = {rad_poly2.sag(45.72, 0.):12.5f}")

profile: RadialPolynomial
c=0.010431046516229696,   r=95.867658   conic cnst=0.0
coefficients: [0.0, 0.0, 0.0, 8.180497e-07, 0.0, -7.007436e-12, 0.0, -5.576895e-15, 0.0, 4.68891e-18]

radial poly 2 sag =     15.19550

Example 2, using the EvenPolynomial

example2 = EvenPolynomial(r=48.358836, cc=-2.474466, coefs=[0., 3.460039E-6, 1.053395E-10, 2.273815E-13, 1.045178E-16])
example2.update()

print(f"example2 sag = {example2.sag(36.575, 0.):12.5f}")

example2 sag =     19.35262

[jakecarr3]

Even Polynominal and update for the win! That worked perfectly. Thanks for your help and all the work you've done putting this together.