Welcome to AOTools’s documentation!¶
Contents:
Phase Screen Creation¶
Submodules¶
Phase Screen Creation¶
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aotools.turbulence.phasescreen.ft_phase_screen(r0, N, delta, L0, l0, FFT=None)[source]¶ Creates a random phase screen with Von Karmen statistics. (Schmidt 2010)
Parameters: Returns: numpy array representing phase screen
Return type: ndarray
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aotools.turbulence.phasescreen.ft_sh_phase_screen(r0, N, delta, L0, l0, FFT=None)[source]¶ Creates a random phase screen with Von Karmen statistics with added sub-harmonics to augment tip-tilt modes. (Schmidt 2010)
Parameters: Returns: numpy array representing phase screen
Return type: ndarray
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aotools.turbulence.phasescreen.ift2(G, delta_f, FFT=None)[source]¶ Wrapper for inverse fourier transform
Parameters: - G – data to transform
- delta_f – pixel seperation
- FFT (FFT object, optional) – An accelerated FFT object
An implementation of the “infinite phase screen”, as deduced by Francois Assemat and Richard W. Wilson, 2006.
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class
aotools.turbulence.infinitephasescreen.PhaseScreen(nSize, pxlScale, r0, L0, nCol=2, random_seed=None)[source]¶ Bases:
objectA “Phase Screen” for use in AO simulation.
This represents the phase addition light experiences when passing through atmospheric turbulence. Unlike other phase screen generation techniques that translate a large static screen, this method keeps a small section of phase, and extends it as neccessary for as many steps as required. This can significantly reduce memory consuption at the expense of more processing power required.
The technique is described in a paper by Assemat and Wilson, 2006. It essentially assumes that there are two matrices, “A” and “B”, that can be used to extend an existing phase screen. A single row or column of new phase can be represented by
X = A.Z + B.bwhere X is the new phase vector, Z is some number of columns of the existing screen, and b is a random vector with gaussian statistics.
This object calculates the A and B matrices using an expression of the phase covariance when it is initialised. Calculating A is straightforward through the relationship:
A = Cov_xz . (Cov_zz)^(-1).B is less trivial.
BB^t = Cov_xx - A.Cov_zx(where B^t is the transpose of B) is a symmetric matrix, hence B can be expressed as
B = UL,where U and L are obtained from the svd for BB^t
U, w, U^t = svd(BB^t)L is a diagonal matrix where the diagonal elements are w^(1/2).
On initialisation an initial phase screen is calculated using an FFT based method. When ‘addRows’ is called, a new vector of phase is added to the phase screen using nCols columns of previous phase. Assemat & Wilson claim that two columns are adequate for good atmospheric statistics. The phase in the screen data is always accessed as <phasescreen>.scrn.
Parameters: -
addRow(nRows=1, axis=0)[source]¶ Adds new rows to the phase screen and removes old ones.
Parameters:
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makeAMatrix()[source]¶ Calculates the “A” matrix, that uses the existing data to find a new component of the new phase vector. This is for propagating in axis 0.
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makeBMatrix()[source]¶ Calculates the “B” matrix, that turns a random vector into a component of the new phase.
Finds a B matrix for the case of generating new data on each side of the phase screen.
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makeSingleBMatrix(cov_xx, cov_zx, A_mat)[source]¶ Makes the B matrix for a single direction
Parameters: - cov_xx – Matrix of XX covariance
- cov_zx – Matrix of ZX covariance
- A_mat – Corresponding A matrix
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makeXXCovMatrix()[source]¶ Uses the seperation between the new phase points to calculate the theoretical covariance between them
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makeXXSeperation()[source]¶ Calculates a matrix where each element is the seperation in metres between points in the new phase data points.
Returns: Array of seperations Return type: ndarray
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makeXZCovMat()[source]¶ Uses the seperation between new and existing phase points to calculate the theoretical covariance between them
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makeXZSeperation()[source]¶ Calculates a matrix where each element is the seperation in metres between points in the new phase data and the existing data.
Returns: Array of seperations Return type: ndarray
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makeZXCovMatrix()[source]¶ Uses the seperation between the existing and new phase points to calculate the theoretical covariance between them
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makeZXSeperation()[source]¶ Calculates a matrix where each element is the seperation in metres between points in the existing phase data and the new data.
Returns: Array of seperations Return type: ndarray
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makeZZCovMat()[source]¶ Uses the seperation between the existing phase points to calculate the theoretical covariance between them
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Centroiders¶
Centroider module¶
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aotools.image_processing.centroiders.brightestPxl(img, threshold, **kwargs)[source]¶ Centroids using brightest Pixel Algorithm (A. G. Basden et al, MNRAS, 2011)
Finds the nPxlsth brightest pixel, subtracts that value from frame, sets anything below 0 to 0, and finally takes centroid.
Parameters: - img (ndarray) – 2d or greater rank array of imgs to centroid
- threshold (float) – Percentage of pixels to use for centroid
Returns: Array of centroid values
Return type: ndarray
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aotools.image_processing.centroiders.centreOfGravity(img, threshold=0, **kwargs)[source]¶ Centroids an image, or an array of images. Centroids over the last 2 dimensions. Sets all values under “threshold*max_value” to zero before centroiding
Parameters: - img (ndarray) – 2d or greater rank array of imgs to centroid
- threshold (float) – Percentage of max value under which pixels set to 0
Returns: Array of centroid values
Return type: ndarray
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aotools.image_processing.centroiders.corrConvolve(x, y)[source]¶ 2D convolution using FFT, use to generate cross-correlations.
Parameters: Returns: cross-correlation of x and y
Return type: ndarray
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aotools.image_processing.centroiders.correlation(im, threshold, ref)[source]¶ Correlation Centroider, currently only works for 3d im shape. Performs a simple thresholded COM on the correlation.
Parameters: - im – subap images (t, y, x)
- threshold_fac – threshold for COM (0=all pixels, 1=brightest pixel)
- ref – reference image (t, y, x)
Returns: centroids of im, given as x, y
Return type: ndarray
Normalised Fourier Transforms¶
aotools.fouriertransform module¶
Module containing useful FFT based function and classes
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aotools.fouriertransform.ft(data, delta)[source]¶ A properly scaled 1-D FFT
Parameters: - data (ndarray) – An array on which to perform the FFT
- delta (float) – Spacing between elements
Returns: scaled FFT
Return type: ndarray
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aotools.fouriertransform.ft2(data, delta)[source]¶ A properly scaled 2-D FFT
Parameters: - data (ndarray) – An array on which to perform the FFT
- delta (float) – Spacing between elements
Returns: scaled FFT
Return type: ndarray
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aotools.fouriertransform.ift(DATA, delta_f)[source]¶ Scaled inverse 1-D FFT
Parameters: - DATA (ndarray) – Data in Fourier Space to transform
- delta_f (ndarray) – Frequency spacing of grid
Returns: Scaled data in real space
Return type: ndarray
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aotools.fouriertransform.ift2(DATA, delta_f)[source]¶ Scaled inverse 2-D FFT
Parameters: - DATA (ndarray) – Data in Fourier Space to transform
- delta_f (ndarray) – Frequency spacing of grid
Returns: Scaled data in real space
Return type: ndarray
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aotools.fouriertransform.irft(DATA, delta_f)[source]¶ Scaled real inverse 1-D FFT
Parameters: - DATA (ndarray) – Data in Fourier Space to transform
- delta_f (ndarray) – Frequency spacing of grid
Returns: Scaled data in real space
Return type: ndarray
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aotools.fouriertransform.irft2(DATA, delta_f)[source]¶ Scaled inverse real 2-D FFT
Parameters: - DATA (ndarray) – Data in Fourier Space to transform
- delta_f (ndarray) – Frequency spacing of grid
Returns: Scaled data in real space
Return type: ndarray