OF = 1.5

-2,-1,0,1,2 waves of

• Z4
• Z5
• Z6

• Even
• Fibonacci
• Hexapolar

Need a way of doing the conversion to Zernike Coefficients in POPPY, report below

OF = 1

The real ray tracing has been trouble to implement because of the conversion of what a "real ray" is to the paraxial convention with ABCD matrices. Since the beamlet code runs on ABCD matrices we can compute the matrix to determine the beamlet propagation.

A real ray is specified by 6 dimensions: Their positions in three orthogonal directions and the associated direction cosines. However, ray transfer matrices don't operate on the z-axis, so we need to convert the direction cosines into slopes in the xz and yz plane.

The method I had derived for this conversion is shown below

Figure comparing observatory point-spread functions produced by equivalent Fresnel and GBD models

OF = 1

Parabolic Phase

In the event that the paraxial assumption is wrong we need to use 4 rays to constrain all degrees of freedom in the nonorthogonal ABCD matrix. The neat thing is that this is 4 systems of 4 separate equations, so it's easier to make a symbolic math tool solve it.

the rays may not be well matched to the ABCD matrix - must check that they map to the same points. Here shows that the MATLAB default ordering is not the same as the numpy.ravel ordering

Through focus comparison

System Specifications:

• EFL = 50e-4m
• EPD = 5e-4m
• Numbeamlets = 3500
• Beam Waist = 5wl (11um)

At the aperture

10% of focus

20% of focus

30% of focus

40% of focus

50% of focus

60% of focus

70% of focus

80% of focus

90% of focus

100% of focus

110% of focus

120% of focus

130% of focus

140% of focus

150% of focus

160% of focus

170% of focus

180% of focus

190% of focus

200% of focus

All coronagraph designs are some approach to the problem of "maximize planet light, minimize starlight" but not all algorithms are created equal. This is where I will be collecting information about the different approaches.

• Introduction
  • Astrophysical Motivation
  • Survey of the state of the art of High-contrast imaging design
    • Ray Tracers: What they are used for and how they work
    • Propagators: What they are used for and how they work
    • Discrepancy in Diffraction Calculations (OpticStudio FFT / Huygens & POPPY)
  • The Need for better modeling in High-contrast imaging instrument design
    • Unifying ray model and diffraction model
    • Design & Tolerancing w/ Physical Optics
    • Simplify the design process
  • Hybrid Propagation Physics Implementation Review
    • Gaussian Beamlet Decomposition
    • Fresnel Diffraction (POPPY)
  • Previous Work (Ashcraft and Douglas 2020)
• Methods
  • Gaussian Beam Parameters
  • Spatial Decomposition of Entrance Pupil (Even - maybe comment on other sampling schemes)
  • The Fiducial Observatory & Coronagraph
  • Paraxial Model w/ WFE
    • Ray Transfer Matrix for Arbitrary WFE
    • Tests for Optical Surface Errors (?)
  • DESCOPE: Real Model w/ WFE
  • Accelerated Computing
    • FIG: Compare multi-threading options on CPUs v.s. numcores for numpy FFT and GBD
    • FIG: DESCOPE - GPUs?
• Results
  • Paraxial Model
    • FIG: Observatory PSF w/o WFE v.s. Fresnel PSF
    • FIG: Observatory PSF w/ WFE v.s. Fresnel PSF
    • FIG: Lyot Coronagraph PSF w/o WFE v.s. Fresnel PSF
    • FIG: Lyot Coronagraph PSF w/ WFE v.s. Fresnel PSF
  • DESCOPE: Real Model
    • FIG: Observatory PSF w/o WFE v.s. Fresnel PSF
    • FIG: Observatory PSF w/ WFE v.s. Fresnel PSF
    • FIG: Lyot Coronagraph PSF w/o WFE v.s. Fresnel PSF
    • FIG: Lyot Coronagraph PSF w/ WFE v.s. Fresnel PSF
• Conclusion

Observatory - Hubble Space Telescope

Based on Hubble Aberration Statistics: https://www.spiedigitallibrary.org/proceedings/Download?urlId=10.1117%2F12.672040

Coronagraph - NICMOS

NICMOS paper: http://nicmosis.as.arizona.edu:8000/PUBLICATIONS/CALWS_2002.pdf

The real ray tracing has been trouble to implement because of the conversion of what a "real ray" is to the paraxial convention with ABCD matrices. Since the beamlet code runs on ABCD matrices we can compute the matrix to determine the beamlet propagation.

A real ray is specified by 6 dimensions: Their positions in three orthogonal directions and the associated direction cosines. However, ray transfer matrices don't operate on the z-axis, so we need to convert the direction cosines into slopes in the xz and yz plane.

The method I had derived for this conversion is shown below

So far I've been filtering out the rays outside the pupil radius in order to create a circular aperture - but Ewan pointed out this might produce a slightly oversized pupil since the 1/e radius exists outside of the pupil. This would result in a tighter PSF, which we were observing here

Test variable overlap factors to see if there is one that is better at recovering high spatial frequencies. We use this phase screen.

Running 512 x 512 beamlets on a 256x256 array of Kolmogorov Phase Error and propagating to focus, then Fresnel Propagating through a coronagraph.

I think we can do OPDs by adjusting optical element power in the C matrix via a gradient of the surface OPD

of = 1.7

The Fourier and Zak transform matrices for 1D signals

Despite using the exact same ray-tracing script I'm getting this error, why?

I think it worked for the Collins Integral

So I'm trying to figure out how to recreate a thin lens at focus, the best possible comparison for a reflector is a Parabolic Mirror. So I created an optical system with the following specifications

• EPD = 2400mm
• Wavelength = 1 um
• FOV = 0 deg
• RoC = -11040 mm
• EFL = 5520 mm
• F/# = 2.3
• Conic = -1

I'm using the ZOS-API to trace rays from a collimated entrance pupil to focus. I need to trace two resets with some differential value applied to the angle and translation in order to parse the ABCD information from the ray data. Unfortunately the plots aren't looking like what I expect. A ray transfer matrix for a lens followed by free space is

So we should expect a zero for all of the A elements, a distance for the on-diagonal B elements and zero for the off-diagonal B elements, the negative inverse of the B distance for the on-diagonal C elements and zero for the off-diagonal C elements, and an Identity matrix for the D elements.

Unfortunately that is not currently the case

I can say that the A & D elements look approximately like they should (the diagonal on the A's is questionable), but the B and C elements don't look like what is expected. To understand what might be going on I plotted the raw ray data.

A couple notes

1. The giant jump in the x dimension is SUPER concerning, what is causing this?
2. The collection of rays going to zero in Y and B are also concerning, what is causing this?
3. Why do we have angle in a and b? I suspect that these rays are after the primary mirror.

Z4

+1/2

+1

+3/2

Z5

+1/2

+1

+3/2

I think I flipped the coordinate system sending the ray transfer matrix over to Python, test this matrix with GBD and see the results. Need to intelligently filter NaN values.

OF = 1

Compare with Fresnel PSF, use this format

Determine the gaussian amplitude by a fourier transform of the input Efield

From the Zemax docs

The only disadvantage of the Huygens PSF is speed. Direct integration is slow when compared to the FFT method (see the previous section for details). The computation time depends upon the pupil grid size squared times the image grid size squared, times the number of wavelengths. OpticStudio accounts for any symmetry the system has. The Huygens PSF automatically uses all available processors for maximum speed on multiple CPU computers.

I think I finally understand Worku's amplitude decomposition.

For a given field to be decomposed - if you already have determined the positions and sizes of the gaussian beamlets, you can solve this matrix equation with the moore-penrose pseudo-inverse. Maybe doing a test implementation for the 1D case would be useful.

Let's start with a Hubble-based design w/ an unobscured aperture and an annular field stop - we can switch to a band limited occulter if necessary but the Lyot is the simplest solution. A $lambda; / D is 0.18048"

I wonder if Eps Eri would be a decent case motivating some FoV calculations. It apparently has two debris disks at 3 AU and 20 AU, and it's about 3.2 parsecs from the Sun.

Apparently 1 AU is 206265 parsecs, how neat

3/(3.2206265) * 206265= 0.93 arcsec or ~ 5λ/D
20/(3.2206265) * 206265 = 6.25 arcsec or ~ 34λ/D

Compare w/ Fraunhofer PSF, use this format

Here's the Zemax FFT PSF

Here are the first 11 Noll Zernikes, note that the decomposition claims there are coefficients of higher order!

Z 1 -0.01843507 : 1
Z 2 0.00000000 : 4^(1/2) (p) * COS (A)
Z 3 -0.42899450 : 4^(1/2) (p) * SIN (A)
Z 4 -0.01063694 : 3^(1/2) (2p^2 - 1)
Z 5 0.00000000 : 6^(1/2) (p^2) * SIN (2A)
Z 6 0.00389342 : 6^(1/2) (p^2) * COS (2A)
Z 7 -0.15086501 : 8^(1/2) (3p^3 - 2p) * SIN (A)
Z 8 0.00000000 : 8^(1/2) (3p^3 - 2p) * COS (A)
Z 9 0.00000038 : 8^(1/2) (p^3) * SIN (3A)
Z 10 0.00000000 : 8^(1/2) (p^3) * COS (3A)
Z 11 0.00000480 : 5^(1/2) (6p^4 - 6p^2 + 1)

using the ray projection method

Just feeding it the direction cosines directly

Looks like the biggest differences are in the C submatrix, which is interesting. The patterns are more elliptical than directly astigmatic, which is less intuitive to me. Might be worth trying the aberrated case for a comparison.