Source code is in file PIAACMCsimul.c

PIAACMC_designcodes

The main function in the source code is PIAACMCsimul_exec(), which takes two arguments: the configuration index (usually a 3 digit integer) and the mode (integer) which describes the operation to be performed to the PIAACMC design.

Mode	Description
0	Compute on-axis propagation for specified configuration. If configuration does not exist, create idealized monochromatic PIAACMC (intended to create a new index) and compute on-axis propagation
1	Optimize Lyot stop(s) locations (scan)
2	Optimize focal plane mask transmission for idealized monochromatic PIAACMC (scan)
3	Run without focal plane mask (for testing and calibration)
4	Linear optimization around current design, free parameters = PIAA optics cosines shapes (track progress by looking at val.opt file)
5	Optimize Lyot stops shapes and positions
10	Setup polychromatic optimization
11	Compute polychromatic response to zones, store result in FPMresp
12	Search for best mask solution using FPMresp, random search
13	Optimize PIAA optics shapes and focal plane mask transmission (idealized PIAACMC)
40	Optimize PIAA optics shapes and focal plane mask transmission (idealized PIAACMC)
41	Optimize PIAA optics shapes and focal plane mask zones (polychromatic)
100	Evaluate current design: polychromatic contrast, pointing sensitivity
101	Transmission as a function of angular separation
200	Make focal plane mask OPD map

The following variables can be set :

Variable	Description
PIAACMC_size	Array size (1024, 2048, etc...)
PIAACMC_pixscale	Pixel scale [m]
PIAACMC_dftgrid	Sampling interval in DFTs
PIAACMC_centobs0	Input central obstruction
PIAACMC_centobs1	Output central obstruction
PIAACMC_nblambda	Number of wavelength points
PIAACMC_resolved	1 if resolved source (3 points at r = 0.01 l/D, 120 deg apart)
PIAACMC_fpmtype	1 if physical mask, 0 if idealized mask
PIAACMC_FPMsectors	Number of sectors in focal plane mask
PIAACMC_NBrings	Number of rings in focal plane mask
PIAACMC_fpmradld	Focal plane mask outer radius

Initialization rules (function PIAAsimul_initpiaacmc() )

if configuration directory exists, use it and load configuration file ( function PIAAsimul_loadpiaacmcconf ), otherwise, create it
load/create Cmodes
load/create Fmodes
load mode coefficients for piaa shapes if they exist. If not:
- create radial apodization for centrally obscured idealized monochromatic PIAACMC
- fit / extrapolate radial apodization profile with cosines
- using above fit, create 2D radial sag for both PIAA optics ( -> PIAA_Mshapes.txt)
- make 2D sag maps for both optics ( -> piaa0z.fits, piaa1z.fits)
- fit 2D sag maps with Cmodes and Fmodes coefficients ( -> piaa0Cmodes, piaa0Fmodes, piaa1Cmodes, piaa1Fmodes )
load/create focal plane mask zone map. This is the map that defines the geometry (which ring is where)
load/create focal plane mask thickness array
load/create focal plane mask transmission array
load/create Lyot stops

Code breakdown

PIAACMCsimul_exec() :
- PIAAsimul_initpiaacmcconf(): Load/Creates/initializes piaacmcconf structure and directory
  - perform default initialization
  - PIAAsimul_loadpiaacmcconf(): Loading PIAACMC configuration from "piaacmcconfxxx/piaacmcparams.conf" if it exists
  - Creating/loading Cmodes and Fmodes
  - IMPORT / CREATE PIAA SHAPES
    - create 2D prolate iteratively
    - PIAACMCsimul_load2DRadialApodization():fit PIAA shapes with Cosine modes
    - PIAACMCsimul_init_geomPIAA_rad(): compute radial PIAA sag from cosine apodization fit
    - PIAACMCsimul_mkPIAAMshapes_from_RadSag(): Make 2D sag shapes from radial PIAA sag
  - MAKE FOCAL PLANE MASK
  - MAKE LYOT STOPS
  - PIAAsimul_savepiaacmcconf(): save configuration
- PIAACMCsimul_makePIAAshapes(): construct PIAA shapes from fitting coefficients
  - construct 2D PIAA mirror shapes from piaa0Cmodescoeff, piaa0Fmodescoeff, piaa1Cmodescoeff, piaa1Fmodescoeff
- PIAACMCsimul_computePSF(): Compute PSF

Output Files

APLCmaskCtransm.txt ?? fpm_ampl.fits fpm_pha.fits FPmask.tmp.fits

Configuration :

Output file	Notes
./piaaconfxxx/piaacmcparams.conf	Configuration parameters
./piaaconfxxx/conjugations.txt	Conjugations
./piaaconfxxx/lambdalist.txt	list of wavelength values
./piaaconfxxx/pupa0_[size].fits	input pupil (created by default if does not exist)

Wavefront Modes :

Output file	Notes
Cmodes.fits	circular radial cosine modes (40 modes, hard coded)
Fmodes.fits	Fourier modes (625 modes = 10 CPA, hard coded)
./piaaconfxxx/ModesExpr_CPA.txt	modes definition
./piaaconfxxx/APOmodesCos.fits	Cosine modes for fitting 2D apodization profile

PIAA mirrors, apodization, fits:

Output file	Notes
./piaaconfxxx/APLCapo.1.400.0.300.info	file written by prolate generation function coronagraph_make_2Dprolate in coronagraphs.c
./piaaconfxxx/apo2Drad.fits	idealized PIAACMC 2D apodization
./piaaconfxxx/piaam0z.fits	PIAA M0 shape (2D sag)
./piaaconfxxx/piaam1z.fits	PIAA M1 shape (2D sag)
./piaaconfxxx/PIAA_Mshapes.txt	PIAA shapes (radial txt file, cols: r0, z0, r1, z1)
./piaaconfxxx/piaa0Fz.fits	PIAA M0 shape, Fourier components (2D file)
./piaaconfxxx/piaa1Fz.fits	PIAA M1 shape, Fourier components (2D file)
./piaaconfxxx/piaa0Cmodes.fits	idealized PIAACMC mirror 0 cosine modes (copied from ./piaaref/)
./piaaconfxxx/piaa0Fmodes.fits	idealized PIAACMC mirror 0 Fourier modes (copied from ./piaaref/)
./piaaconfxxx/piaa1Cmodes.fits	idealized PIAACMC mirror 1 cosine modes (copied from ./piaaref/)
./piaaconfxxx/piaa1Fmodes.fits	idealized PIAACMC mirror 1 Fourier modes (copied from ./piaaref/)
./piaaconfxxx/piaa0Cres.fits	idealized PIAA M0 cosine fit residual
./piaaconfxxx/piaa1Cres.fits	idealized PIAA M1 cosine fit residual
./piaaconfxxx/piaa0Cz.fits	idealized PIAA M0 cosine fit sag
./piaaconfxxx/piaa1Cz.fits	idealized PIAA M1 cosine fit sag
./piaaconfxxx/piaa0Fz.fits	idealized PIAA M0 Fourier fit sag
./piaaconfxxx/piaa1Fz.fits	idealized PIAA M1 Fourier fit sag

Idealized PIAACMC reference point:

Output file	Notes
./piaaconfxxx/piaaref/APLCmaskCtransm.txt	idealized PIAACMC focal plane mask transmission
./piaaconfxxx/piaaref/apo2Drad.fits	idealized PIAACMC output apodization
./piaaconfxxx/piaaref/piaa0Cmodes.fits	idealized PIAACMC mirror 0 cosine modes
./piaaconfxxx/piaaref/piaa0Fmodes.fits	idealized PIAACMC mirror 0 Fourier modes
./piaaconfxxx/piaaref/piaa1Cmodes.fits	idealized PIAACMC mirror 1 cosine modes
./piaaconfxxx/piaaref/piaa1Fmodes.fits	idealized PIAACMC mirror 1 Fourier modes

Focal plane mask:

Focal plane mask design defined by :

[s] Sectors flag (0: no sectors, 1: sectors), variable PIAACMC_FPMsectors
[r] Resolved target flag (0: point source, 1: resolved source)
[mr] Mask radius in units of 0.1 l/D
[rrr] number of rings, variable piaacmc[0].NBrings
[zzz] number of zones

Output file	Notes
fpmzmap[s]_[rrr]_[zzz].fits	Zones map
fpm_zonea[r][s]_[mr]_[rrr]_[zzz].fits	amplitude for each zone
fpm_zonea[r][s]_[mr]_[rrr]_[zzz].fits	thickness for each zone

IDEALIZED OR PHYSICAL MASK
Idealized mask is a single zone mask with thickness adjusted for lambda/2 phase shift and a (non-physical) partial transmission. Physical mask consist of 1 or more zones with full transmission. Each zone can have a different thickness.

By default, a non-physical mask is first created with transmission piaacmc[0].fpmaskamptransm read from piaacmcparams.conf. Computations indices using a physical mask:

set transmission to 1.0: piaacmc[0].fpmaskamptransm = 1.0.
set focal plane mask radius to larger value: piaacmc[0].fpmRad = 0.5*(LAMBDASTART+LAMBDAEND)*piaacmc[0].Fratio * PIAACMC_MASKRADLD

Lyot stops:

Output file	Notes
./piaaconfxxx/LyotStop0.fits	Lyot Stop 0
./piaaconfxxx/LyotStop1.fits	Lyot Stop 1

Amplitude & Phase at planes:

Files are /piaaconfxxx/WFamp_nnn.fits and WFpha_nnn.fits, where nnn is the plane index.
Complex amplitude is shown AFTER the element has been applied, in the plane of the element.

Plane index	description
000	Input pupil
001	Fold mirror used to induce pointing offsets
002	PIAA M0
003	PIAA M1
004	PIAAM1 edge opaque mask
005	post-focal plane mask pupil
006	Lyot Stop 0
007	Lyot Stop 1
008	invPIAA1
009	invPIAA0
010	back end mask

Performance Evaluation:

Plane index	description
./piaaconfxxx/scoringmask0.fits	Evaluation points in focal plane, hardcoded in PIAACMCsimul_computePSF()
./piaaconfxxx/CnormFactor.txt	PSF normalization factor used to compute contrast
./piaaconfxxx/flux.txt	total intensity at each plane

Low-level C code

Key functions

Every time a PSF is computed, the following 3 functions are created in that order:

PIAAsimul_initpiaacmcconf
- initialize piaacmc
- create modes for aspheric optical surfaces description
- CREATE DMs (Cmodes and Fmodes)
- IMPORT / CREATE PIAA SHAPES
- if does not exist: Creating 2D apodization for idealized circular monochromatic PIAACMC
- compute radial PIAA sag, make 2D sag maps
- MAKE FOCAL PLANE MASK
- MAKE LYOT STOPS (LOADING/CREATING LYOT MASK)
PIAACMCsimul_init(piaacmc, 0, xld, yld) : initializes optical system to piaacmc design
PIAACMCsimul_makePIAAshapes(piaacmc, 0) : create 2D PIAA shapes (piaam0z and piaam1z) from coefficient values and modes
OptSystProp_run(optsyst, 0, startelem, optsyst[0].NBelem, piaacmcconfdir, 0) : perform optical propagation

Note that the last 3 functions are wrapped togeter in the computePSF function, which allows multi-point (extended sources) :

PIAACMCsimul_computePSF(float xld, float yld, long startelem, long endelem, int savepsf, int sourcesize, int extmode, int outsave) : compute PSF
- PIAACMCsimul_init(piaacmc, 0, xld+rad1, yld)
- PIAACMCsimul_makePIAAshapes(piaacmc, 0)
- OptSystProp_run(optsyst, 0, startelem, optsyst[0].NBelem, piaacmcconfdir, 0)

Full PIAACMC design in monochromatic light

The first step of the optimization process is to compute the PIAACMC optics and focal plane mask in the idealized case: monochromatic light, point source, and ideal focal plane mask (circular, phase-shifting and partially transmissive). Steps are shown in the figure below and correspond to steps in the runPIAACMC state machine.

APLC design

The scripts produce an APLC design by setting PIAAmode = 0. In that case, only step000 in the figure above is executed.

Focal plane mask optimization

Overall flow

FPM optimization is done as mode = 13 in the main routine. It is called from the runPIAACMC script. The PIAACMCsimul_run(char *confindex, long mode) function loop-calls the PIAACMCsimul_exec(char *confindex, long mode) function with mode 13 until search time is reached.

Each search proceeds as follows :

a starting point is picked. A random integer zeroST encodes the starting poing:
- 0:
- 1: start at zero
- 2: start at best solution
run PIAACMCsimul_exec in mode 13
- randomly move next to starting point
- compute value and store it to valref variable
- enter gradient search loop
  - compute local derivatives
  - compute SVD of Jacobian matrix to identify vectors of steepest descent
  - for each alphareg = 0, 0.25, 0.5, 0.75, 1.0:
    - do a linescan descent along the vector identified by SVD, with the alphareg regularization coefficient
    - the best value is stored as bestval and the corresponding parameters into data.image[IDoptvec].array.F[i]
    - store best values in PIAACMCSIMUL_VAL, and reference value in PIAACMCSIMUL_VALREF
computePSF_FAST_FPMresp = 1 : uses pre-computed complex amplitude zones response to evaluate FPM solutions
PIAACMC_FPM_FASTDERIVATIVES = 1

To stop the optimization and have the current best solution adopted, enter a small value in the searchtime.txt file, so that the optimization process completes.

Regularization

There are two regularization:

Focal plane mask zone sags can be included in the linear optimization as extra components to the optimization vector
PIAA shapes coefficients are simply added to the evaluation metric

Key files

fpm_zonez_.....best.fits is the optimal solution
mode13_....bestval.txt is the corresponding value

To restart the optimization from scratch, remove these two files.

Average contrast = 5.964e-05 0.001 -> Average contrast = 8.57575e-07, 1.9e-7 0.01 -> Average contrast = 7.99085e-07, 2.0e-7 7.8294e-07