Optical axis shift from tilted plane parallel plate

[lkangas]

Hi,

I'm modeling a system with two lenses, a collimated beam between them, and a 45 degree plane parallel plate in the collimated beam. The plate is 1 mm thick N-BK7.

By introducing a 45 degree 'decenter' to the front surface and a similar 'reverse' to the back surface, my optical axis is now shifted 0.707 mm because it travels normal to the surfaces within the plate, and I now have to introduce an y-shifted decenter to the following elements on the axis. My design expects a 0.335 mm shift of the optical axis, following the amount of shift of an axial ray of the design wavelength.

How should I go about decentering the tilted plate surfaces to prevent needing to manually decenter every consequent element in the train?

[mjhoptics]

Hello @lkangas,
The reverse decenter type also allows the application of an offset after the reverse tilt has been applied. You can apply the necessary shift (.707-.335, if I understand your comment correctly) to the reverse decenter and all of the following elements will be centered on the optical axis ray. You may need an adjustment to the following gap to account for the small z distance taken up by the tilted plate (1-.707).
Hope this helps, feel free to ask further questions.
Regards,
Mike Hayford

[lkangas]

How do I apply the offset after tilting? I managed to calculate the offset value I'd need before tilting, and giving that as the reverse decenter.dec[1], the optical axis after the plate seems to originate from the same point as the axial ray. I think in your description the axis would originate from within the plate, from a point directly above the non-offset point. In my approach the axis starts from the back surface, a bit further right.

However, I still get problems with the following elements not being centered on that axis.

The axial location of the next element can be taken care of by adjusting the gap like you suggested (although I needed some additional trigonometry because of the different starting point). But the element is still not centered on the axis.

I'd like to try the offset after tilting to see whether this problem persists. Let me cook up some code and images too.

[lkangas]

Here's an example highlighting my problem. I used the example doublets and used a thickness of 10 for the plate.

I also illustrated some dots. Dot 1 is the original starting point without offset in the decenter. Dot 3 would be the starting point without any tilt in the plate. Dot 2 is with offset applied after tilting like you suggested (but I don't know how to implement?). The vertical offset is the vertical distance between 1-2 (or 1-4).

Dot 4 is the starting point of the axis with offset applied before tilting (only way I managed to figure out how?). Diagonal distance between 1-4 is the amount of offset I applied. Judging by the plotted rays (deliberately an even number, without the axial ray overlapping) the position is correct.

Point 5 is the horizontal location of the next surface without any adjustment of the gap. In the figure, I did adjust the gap by adding the horizontal distance between 2-4, so the next surface results horizontally at point 6. The axis is also rendered further right from 6 by a distance similar to 5-6, as expected. Distance between 4-6 equals 20 as expected.

Your suggested gap adjustment would be the horizontal distance 1-3 (or rather 2-3) which I don't think is correct.

But remaining problem now is the vertical alignment of the next surface, with the surface vertex being at a distance of about 1.8 above point 6. This is evident also looking at the optical axis following the back surface of the doublet.

import matplotlib.pyplot as plt
import numpy as np
from pathlib import Path

import rayoptics
from rayoptics.environment import OpticalModel, FieldSpec, PupilSpec, WvlSpec
import rayoptics.elem.surface as srf
from opticalglass.schott import SchottGlass

root_pth = Path(rayoptics.__file__).resolve().parent

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']

bk7 = SchottGlass('N-BK7')

osp['fov'] = FieldSpec(osp, key=('object', 'angle'), value=0.0,
                       flds=[1.],
                       is_relative=True)

osp['pupil'] = PupilSpec(osp, key=['object', 'epd'], value=25.)
osp['wvls'] = WvlSpec([(550, 1.0)])

plate_thi = 10
plate_angle = 45
plate_angle_rad = np.deg2rad(plate_angle)

n_plate = bk7.rindex(550)

plate_refr_angle_rad = np.arcsin(np.sin(plate_angle_rad)/n_plate)
axis_shift_along_plate_back_surface = plate_thi*np.tan(plate_refr_angle_rad)
plate_path = plate_thi/np.cos(plate_refr_angle_rad)
plate_path_down = plate_thi * (1 - np.tan(plate_refr_angle_rad)) * np.sin(plate_angle_rad)
plate_path_right = plate_path * np.cos(plate_angle_rad - plate_refr_angle_rad)

# add first lens
sm.gaps[0].thi = 1
opm.add_from_file(root_pth/"codev/tests/CODV_32327.seq", t=20.)
ffl = -ar['parax_data'].fod.ffl
bfl = ar['parax_data'].fod.bfl
sm.gaps[0].thi = ffl

# add tilted plate
sm.add_surface([0, plate_thi, bk7], sd=15)
sm.ifcs[sm.cur_surface].decenter = srf.DecenterData('decenter', alpha=-plate_angle)

sm.add_surface([0, 20, 1], sd=15)
sm.ifcs[sm.cur_surface].decenter = srf.DecenterData('reverse', alpha=-plate_angle)
sm.ifcs[sm.cur_surface].decenter.dec[1] = -axis_shift_along_plate_back_surface

# add second lens
opm.add_from_file(root_pth/"codev/tests/CODV_32327.seq", t=bfl)

# gap adjustment
sm.gaps[5].thi += axis_shift_along_plate_back_surface * np.sin(plate_angle_rad)

opm.update_model()

from rayoptics.environment import InteractiveLayout
layout_plt = plt.figure(FigureClass=InteractiveLayout, opt_model=opm,
                        do_draw_ray_fans=True, num_rays_in_fan=6,
                        do_draw_rays=False, do_paraxial_layout=False).plot()

x = np.sum([x.thi for x in sm.gaps[1:4]]) + plate_path_right + 20
y = -plate_path_down
plt.plot(x, y, '.', ms=20)

x = np.sum([x.thi for x in sm.gaps[1:4]]) + plate_thi
y = 0
plt.plot(x, y, '.', ms=20)

x = np.sum([x.thi for x in sm.gaps[1:4]]) + plate_path_right + 20 - axis_shift_along_plate_back_surface * np.sin(plate_angle_rad)
y = -plate_path_down
plt.plot(x, y, '.', ms=20)

x = np.sum([x.thi for x in sm.gaps[1:4]]) + plate_thi * np.sin(plate_angle_rad)
y = -plate_path_down
plt.plot(x, y, '.', ms=20)

x = np.sum([x.thi for x in sm.gaps[1:4]]) + plate_thi * np.sin(plate_angle_rad) + axis_shift_along_plate_back_surface * np.sin(plate_angle_rad)
y = -plate_path_down
plt.plot(x, y, '.', ms=20)

[mjhoptics]

Hello @lkangas,
I see one crucial misunderstanding. The reverse decenter doesn't just apply the tilts in the reverse order, it applies the decenters after the (reverse) tilt is applied to the coordinates. This makes the calculation of how the offset should be applied very simple.

You did the math above to calculate the refracted path and the results offsets. Here's a way to use ray trace data to accomplish the same outcome. Starting from the point your script ended:

Trace the axial ray to see the current state.

from rayoptics.raytr.trace import trace_ray, list_ray

axial_ray = trace_ray(opm, [0,0], osp['fov'].fields[0], osp['wvls'].central_wvl)
list_ray(axial_ray)

Zero out the decenter to see what the ray offset is coming out of the tilted plate.

sm.ifcs[5].decenter.dec = np.array([0, 0, 0])
opm.update_model()

axial_ray = trace_ray(opm, [0,0], osp['fov'].fields[0], osp['wvls'].central_wvl)
list_ray(axial_ray)

            X            Y            Z           L            M            N               Len
  0:      0.00000      0.00000            0     0.000000     0.000000     1.000000       98.562
  1:      0.00000      0.00000            0     0.000000     0.000000     1.000000            6
  2:      0.00000      0.00000            0     0.000000     0.000000     1.000000          2.5
  3:      0.00000      0.00000            0     0.000000     0.000000     1.000000           20
  4:      0.00000      0.00000            0     0.000000     0.465654     0.884967         11.3
  5:      0.00000      5.26183            0     0.000000     0.707107     0.707107       20.113
  6:      0.00000      3.72068      0.11271     0.000000    -0.020693     0.999786        5.743
  7:      0.00000      3.60184     -0.14555     0.000000    -0.011071     0.999939       2.5966
  8:      0.00000      3.57309    -0.049136     0.000000    -0.037210     0.999307       96.042
  9:      0.00000     -0.00059            0     0.000000    -0.037210     0.999307            0

Use (minus) the y-offset on surface 6 to set the reverse decenter value.

sm.ifcs[5].decenter.dec = np.array([0, -axial_ray.pkg.ray[6].p[1], 0])
opm.update_model()

axial_ray = trace_ray(opm, [0,0], osp['fov'].fields[0], osp['wvls'].central_wvl)
list_ray(axial_ray)

            X            Y            Z           L            M            N               Len
  0:      0.00000      0.00000            0     0.000000     0.000000     1.000000       98.562
  1:      0.00000      0.00000            0     0.000000     0.000000     1.000000            6
  2:      0.00000      0.00000            0     0.000000     0.000000     1.000000          2.5
  3:      0.00000      0.00000            0     0.000000     0.000000     1.000000           20
  4:      0.00000      0.00000            0     0.000000     0.465654     0.884967         11.3
  5:      0.00000      5.26183            0     0.000000     0.707107     0.707107           20
  6:      0.00000      0.00000            0     0.000000    -0.000000     1.000000            6
  7:      0.00000      0.00000  -7.8886e-31     0.000000    -0.000000     1.000000          2.5
  8:      0.00000      0.00000            0     0.000000    -0.000000     1.000000       95.926
  9:      0.00000     -0.00000            0     0.000000    -0.000000     1.000000            0

[lkangas]

Excellent, thank you!

So applying the y offset does indeed work vertically after the back surface in this case, and my offset was off by a factor of sqrt2. The source for my confusion was the expectation that the blue line from the back surface should coincide with the axial ray. After applying an offset of 5.26 it did do that, but then the rest of the coordinates were off and the axial ray wouldn't hit the next vertex.

After using the correct offset, in the image above, the ray trace results are zeroed as you showed and the following elements line up, but the line is now below the new z-axis by about 1.09. I still don't quite get what the line here stands for and what dictates it's vertical position?

[mjhoptics]

The line in question is a graphical representation of an air gap: a single line the length of the gap. There is a rendering bug for the case of a reverse decenter with an offset. That is why the picture is confusing (although it is not much less confusing when the bug is fixed).

Airspaces need a graphical representation so that they can be selected in an interactive environment.
For now, it can safely be ignored.
Mike

[lkangas]

Great, thank you for your generous help and for this awesome library. The gap lines and everything else makes sense now.

Next up will be the generation of additional sequential models to account for internal reflections in the plate. I see I could make my own path iterator for something like a non-sequential tracer, but did not yet think about how to jump between models or maybe modify the model on the fly. I bet I'm going to have more questions soon.