shesha.util.influ_util Namespace Reference

Computation of the influence functions used by the DM. More...

Functions
def	besel_orth (m, n, phi, r)
	TODO docstring. More...
def	bessel_influence (xx, yy, type_i=PatternType.SQUARE)
	TODO docstring. More...
def	makeRigaut (float pitch, float coupling, x=None, y=None)
	Compute 'Rigaut-like' influence function. More...
def	makeRadialSchwartz (float pitch, float coupling, x=None, y=None)
	Compute radial Schwartz influence function. More...
def	makeSquareSchwartz (float pitch, float coupling, x=None, y=None)
	Compute Square Schwartz influence function. More...
def	makeBlacknutt (float pitch, float coupling, x=None, y=None)
	Compute Blacknutt influence function Attention, ici on ne peut pas choisir la valeur de coupling. More...
def	makeGaussian (float pitch, float coupling, x=None, y=None)
	Compute Gaussian influence function. More...
def	makeBessel (float pitch, float coupling, np.ndarray x=None, np.ndarray y=None, bytes patternType=PatternType.SQUARE)
	Compute Bessel influence function. More...

Detailed Description

Computation of the influence functions used by the DM.

Author

COMPASS Team https://github.com/ANR-COMPASS

Version

5.0.0

Date

2020/05/18

Copyright

GNU Lesser General Public License

This file is part of COMPASS https://anr-compass.github.io/compass/

Copyright (C) 2011-2019 COMPASS Team https://github.com/ANR-COMPASS All rights reserved. Distributed under GNU - LGPL

COMPASS is free software: you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation, either version 3 of the License, or any later version.

COMPASS: End-to-end AO simulation tool using GPU acceleration The COMPASS platform was designed to meet the need of high-performance for the simulation of AO systems.

The final product includes a software package for simulating all the critical subcomponents of AO, particularly in the context of the ELT and a real-time core based on several control approaches, with performances consistent with its integration into an instrument. Taking advantage of the specific hardware architecture of the GPU, the COMPASS tool allows to achieve adequate execution speeds to conduct large simulation campaigns called to the ELT.

The COMPASS platform can be used to carry a wide variety of simulations to both testspecific components of AO of the E-ELT (such as wavefront analysis device with a pyramid or elongated Laser star), and various systems configurations such as multi-conjugate AO.

COMPASS is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details.

You should have received a copy of the GNU Lesser General Public License along with COMPASS. If not, see https://www.gnu.org/licenses/lgpl-3.0.txt.

Function Documentation

besel_orth()

def shesha.util.influ_util.besel_orth	(		m,
			n,
			phi,
			r
	)

TODO docstring.

   :parameters:

       m:

       n:

       phi:

       r:

   :return:

B

Definition at line 60 of file influ_util.py.

    """
    # fonction de bessel fourier orthogonale (BFOFS)
    if (m == 0):
        B = sp.jn(0, sp.jn_zeros(0, n)[n - 1] * r)
    elif (m > 0):
        B = sp.jn(m, sp.jn_zeros(m, n)[n - 1] * r) * np.sin(m * phi)
    else:
        B = sp.jn(np.abs(m),
                  sp.jn_zeros(np.abs(m), n)[n - 1] * r) * np.cos(np.abs(m) * phi)
    return B
 
 

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bessel_influence()

def shesha.util.influ_util.bessel_influence	(		xx,
			yy,
			type_i = PatternType.SQUARE
	)

TODO docstring.

   :parameters:

       xx:

       yy:

type_i (optional)

:return:

    influ

Definition at line 86 of file influ_util.py.

    """
 
    # base sur l article numerical model of the influence function of deformable mirrors based on bessel Fourier orthogonal functions
    # corespond a 3.2pitch
 
    influ = np.zeros(xx.shape, dtype=np.float32)
 
    # construction des tableaux :
 
    # construction des coordonnée cartesienne
    # x = np.arange(size)-middle # -->
    # y = (np.arange(size)-middle)*-1 # -->
    #xx,yy = np.meshgrid(x,y)
    # passage en coordonnée polaire
    r = np.sqrt(xx**2 + yy**2)
    phi = np.arctan2(yy, xx)  # +(np.pi/8.) #petite correction de rotation
 
    # coef for square IF
    a0 = [
            0.3826, 0.5207, 0.2841, -0.0146, -0.1103, -0.0818, -0.0141, 0.0123, 0.0196,
            0.0037
    ]
    am = [-0.0454, -0.1114, -0.1125, -0.0397, 0.0146, 0.0217, 0.0085, -0.0012, -0.0040]
    a = [-0.0002, -0.0004, -0.0001, 0.0004, 0.0005, 0.0003, 0.0001, 0, 0]
 
    # search coef for hexagonal IF (m =0, 6, -6 --> 28 term)
    # a0 ->10
    # a6 ->9
    # am6 ->9
 
    if type_i == PatternType.HEXA or type_i == PatternType.HEXAM4:
        sym = 6
 
    else:
        sym = 4
 
    # calcul pour m = 0
    for i in range(len(a0)):
        btemp = (a0[i] * besel_orth(0, i + 1, phi, r))
 
        influ = influ + btemp
    #print("fin cas m=",0)
 
    # calcul pour m=6
    for i in range(len(a)):
        influ = influ + (a[i] * besel_orth(sym, i + 1, phi, r))
    #print("fin cas m=",sym)
 
    # calcul pour m=-6
    for i in range(len(am)):
        influ = influ + (am[i] * besel_orth(-sym, i + 1, phi, r))
    #print("fin cas m=",-sym)
 
    return influ
 
 

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makeBessel()

def shesha.util.influ_util.makeBessel	(	float	pitch,
		float	coupling,
		np.ndarray	x = None,
		np.ndarray	y = None,
		bytes	patternType = PatternType.SQUARE
	)

Compute Bessel influence function.

:parameters:

pitch (float) : pitch of the DM expressed in pixels

coupling (float) : coupling of the actuators

x indices of influence function in relative position x local coordinates (float). 0 = top of the influence function

y indices of influence function in relative position y local coordinates (float). 0 = top of the influence function

:return:

influ (np.ndarray(dims=3,dtype=np.float64)) : cube of the IF for each actuator

Definition at line 352 of file influ_util.py.

        influ: (np.ndarray(dims=3,dtype=np.float64)) : cube of the IF for each actuator
    """
    smallsize = int(np.ceil(pitch * 3.2))
 
    if (x is None or y is None):
        return smallsize
    else:
        # size_pitch = smallsize/np.float32(p_dm._pitch) # size of influence fonction in pitch
        # xdg= np.linspace(-1*(size_pitch/3.2),size_pitch/3.2, smallsize,dtype=np.float32)
        # x = np.tile(xdg, (smallsize,1))
        # y = x.T
        influ_u = bessel_influence(x / (1.6 * pitch), y / (1.6 * pitch), patternType)
        influ_u = influ_u * (influ_u >= 0)
        return influ_u

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makeBlacknutt()

def shesha.util.influ_util.makeBlacknutt	(	float	pitch,
		float	coupling,
			x = None,
			y = None
	)

Compute Blacknutt influence function Attention, ici on ne peut pas choisir la valeur de coupling.

La variable a ete laissee dans le code juste pour compatibilité avec les autres fonctions, mais elle n'est pas utilisee.

:parameters:

pitch (float): pitch of the DM expressed in pixels

coupling (float) : coupling of the actuators

x indices of influence function in relative position x local coordinates (float). 0 = top of the influence function

y indices of influence function in relative position y local coordinates (float). 0 = top of the influence function

:return:

influ (np.ndarray(dims=3,dtype=np.float64)) : cube of the IF for each actuator

Definition at line 274 of file influ_util.py.

    """
    smallsize = int(np.ceil(4 * pitch + 1))
    if (x is None or y is None):
        return smallsize
    else:
        cg = smallsize // 2
        xx = x / float(cg)
        yy = y / float(cg)
        a = np.array([0.355768, 0.487396, 0.144232, 0.012604], dtype=np.float32)
        ok = np.where((np.abs(xx) < 1) * (np.abs(yy) < 1))
        sc = np.zeros(xx.shape)
        sc[ok] = (a[0] + a[1] * np.cos(np.pi * xx[ok]) +
                  a[2] * np.cos(2 * np.pi * xx[ok]) + a[3] * np.cos(3 * np.pi * xx[ok])) *\
            (a[0] + a[1] * np.cos(np.pi * yy[ok]) +
             a[2] * np.cos(2 * np.pi * yy[ok]) + a[3] * np.cos(3 * np.pi * yy[ok]))
 
        return sc
 
 

makeGaussian()

def shesha.util.influ_util.makeGaussian	(	float	pitch,
		float	coupling,
			x = None,
			y = None
	)

Compute Gaussian influence function.

Coupling parameter is not taken into account

:parameters:

pitch (float) : pitch of the DM expressed in pixels

coupling (float) : coupling of the actuators

x indices of influence function in relative position x local coordinates (float). 0 = top of the influence function

y indices of influence function in relative position y local coordinates (float). 0 = top of the influence function

:return:

influ (np.ndarray(dims=3,dtype=np.float64)) : cube of the IF for each actuator

Definition at line 309 of file influ_util.py.

    """
    irc = 1.16136 + 2.97422 * coupling + \
        (-13.2381) * coupling**2 + 20.4395 * coupling**3
    tmp_c = 1.0 / np.abs(irc)
 
    smallsize = int(np.ceil(2 * irc * pitch + 10))
    if (smallsize % 2 != 0):
        smallsize += 1
 
    if (x is None or y is None):
        return smallsize
    else:
        sig = pitch / np.sqrt(-2 * np.log(coupling))
        gauss = np.exp(-0.5 * ((x / sig)**2 + (y / sig)**2))
        # gauss /= gauss.max()
        # xdg = np.linspace(-1, 1, smallsize, dtype=np.float32)
        # x = np.tile(xdg, (smallsize, 1))
        # y = x.T
        # sig = 0.8
        # gauss = 1 / np.cos(np.exp(-(x**2 / sig + y**2 / sig))**2)
        # # Force value at zero on array limits
        # gauss -= gauss[gauss.shape[0] // 2].min()
        # gauss[gauss < 0.] = 0
        # gauss /= gauss.max()  # Normalize
        return gauss
 
 

makeRadialSchwartz()

def shesha.util.influ_util.makeRadialSchwartz	(	float	pitch,
		float	coupling,
			x = None,
			y = None
	)

Compute radial Schwartz influence function.

:parameters:

pitch (float) : pitch of the DM expressed in pixels

coupling (float) : coupling of the actuators

x indices of influence function in relative position x local coordinates (float). 0 = top of the influence function

y indices of influence function in relative position y local coordinates (float). 0 = top of the influence function

:return:

influ (np.ndarray(dims=3,dtype=np.float64)) : cube of the IF for each actuator

Definition at line 205 of file influ_util.py.

    """
    k = 6  # order of the Schwartz function
    #
    a = pitch / np.sqrt(k / (np.log(coupling) - k) + 1.)
    smallsize = int(2 * np.ceil(a) + 2)
    if (x is None or y is None):
        return smallsize
    else:
        r = (x * x + y * y) / (a * a)
        ok = np.where(r < 1)
        sc = np.zeros(r.shape)
        sc[ok] = np.exp((k / (r[ok] - 1.0)) + k)
        #influ[:,:,:] = sc[:,:,None] * np.ones(ntotact)[None,None,:]
        return sc
 
 

makeRigaut()

def shesha.util.influ_util.makeRigaut	(	float	pitch,
		float	coupling,
			x = None,
			y = None
	)

Compute 'Rigaut-like' influence function.

:parameters:

pitch (float) : pitch of the DM expressed in pixels

coupling (float) : coupling of the actuators

x indices of influence function in relative position x local coordinates (float). 0 = top of the influence function

y indices of influence function in relative position y local coordinates (float). 0 = top of the influence function

:return:

influ (np.ndarray(dims=3,dtype=np.float64)) : cube of the IF for each actuator

Definition at line 158 of file influ_util.py.

    """
    irc = 1.16136 + 2.97422 * coupling + \
        (-13.2381) * coupling**2 + 20.4395 * coupling**3
 
    p1 = 4.49469 + (7.25509 + (-32.1948 + 17.9493 * coupling) * coupling) * coupling
    p2 = 2.49456 + (-0.65952 + (8.78886 - 6.23701 * coupling) * coupling) * coupling
 
    tmp_c = 1.0 / np.abs(irc)
    ccc = (coupling - 1. + tmp_c**p1) / (np.log(tmp_c) * tmp_c**p2)
 
    smallsize = int(np.ceil(2 * irc * pitch + 10))
    if (smallsize % 2 != 0):
        smallsize += 1
    # clip
    if (x is None or y is None):
        return smallsize
    else:
        # normalized coordiantes in local ref frame
        x = np.abs(x) / (irc * pitch)
        y = np.abs(y) / (irc * pitch)
 
        x[x < 1e-8] = 1e-8
        x[x > 2] = 2.
        y[y < 1e-8] = 1e-8
        y[y > 2] = 2.
        tmp = (1. - x**p1 + ccc * np.log(x) * x**p2) * \
            (1. - y**p1 + ccc * np.log(y) * y**p2)
        tmp = tmp * (x <= 1.0) * (y <= 1.0)
        return tmp
 
 

makeSquareSchwartz()

def shesha.util.influ_util.makeSquareSchwartz	(	float	pitch,
		float	coupling,
			x = None,
			y = None
	)

Compute Square Schwartz influence function.

:parameters:

pitch (float) : pitch of the DM expressed in pixels

coupling (float) : coupling of the actuators

x indices of influence function in relative position x local coordinates (float). 0 = top of the influence function

y indices of influence function in relative position y local coordinates (float). 0 = top of the influence function

:return:

influ (np.ndarray(dims=3,dtype=np.float64)) : cube of the IF for each actuator

Definition at line 237 of file influ_util.py.

    """
    k = 6  # order of the Schwartz function
    #
    a = pitch / np.sqrt(k / (np.log(coupling) - k) + 1.)
 
    if (x is None or y is None):
        smallsize = int(2 * np.ceil(a) + 2)
        return smallsize
    else:
        xx = (x / a)**2
        yy = (y / a)**2
        ok = np.where((xx < 1) * (yy < 1))
        sc = np.zeros(xx.shape)
        sc[ok] = np.exp((k / (xx[ok] - 1)) + k) * \
            np.exp((k / (yy[ok] - 1)) + k)
        return sc