solid_waffle.ftsolve

Fourier-domain flat correlation prediction code for solid-waffle.

Attributes

N

Functions

`center`(arr)	Transforms kernel so that it looks as expected to the eye.
`decenter`(arr)	Transforms kernel from human-readable to numpy-readable.
`flip`(arr)	Transforms decentered a_i,j -> decentered a_-i,-j.
`pad_to_N`(arr, N)	Zero-pads array out to size NxN (if arr is smaller than this).
`p2kernel`(cov, np2[, N_integ])	Constructs a pairwise correlation kernel from a 2x2 covariance matrix.
`op2_to_pars`(op2[, cmin])	Fits a quantum yield model to a Phi-kernel.
`p2kernel_test`()	Test function for p2kernel.
`solve_corr`(bfek, N, I_, g, betas, sigma_a, tslices, avals)	Predicts the unequal-time correlation function C_{abcd}(Delta i, Delta j).
`eval_cnl`(betas, I_, t)	Evaluates the derivative of a non-linearity polynomial.
`solve_corr_many`(bfek, N, I_, g, betas, sigma_a, ...[, ...])	Predicts a sequence of similar unequal-time correlation functions.
`solve_corr_vis`(bfek, N, I_, g, betas, sigma_a, ...[, ...])	Predicts the unequal-time correlation function C_{abcd}(Delta i, Delta j) for visible light.
`solve_corr_vis_many`(bfek, N, I_, g, betas, sigma_a, ...)	Predicts a sequence of similar unequal-time correlation functions, for visible light.

Module Contents

center(arr)[source]

Transforms kernel so that it looks as expected to the eye.

Parameters:: arr (np.array) – 2D array kernel, square with odd side length.
Returns:: Returns version of kernel with (0,0) in center, y=-1 down, x=-1 left, etc. Centered arrays should NOT be used for calculations! For display only.
Return type:: np.array

See also

decenter: Inverse function.

decenter(arr)[source]

Transforms kernel from human-readable to numpy-readable.

Only decentered arrays should be used for calculations.

Parameters:: arr (np.array) – 2D array kernel, square with odd side length, human-readable.
Returns:: Decentered array.
Return type:: np.array

See also

center: Inverse function.

flip(arr)[source]

Transforms decentered a_i,j -> decentered a_-i,-j.

The function is its own inverse.

Parameters:: arr (np.array) – 2D array kernel, square with odd side length, human-readable.
Returns:: Flipped array.
Return type:: np.array

pad_to_N(arr, N)[source]

Zero-pads array out to size NxN (if arr is smaller than this).

Parameters:

arr (np.array) – 2D input array, odd size, square, assumed to be centered.
N (int) – Size to pad arr to. Must be odd. Does nothing if arr is already this big.

Returns:

The padded array.

Return type:

np.array

p2kernel(cov, np2, N_integ=256)[source]

Constructs a pairwise correlation kernel from a 2x2 covariance matrix.

Parameters:

cov (list or np.array of float) – Length 3; [Cxx, Cxy, Cyy].
np2 (int) – Kernel radius to generate.
N_integ (int, optional) – Number of integration steps.

Returns:

p2_output – The p2 kernel, of shape (2*`np2`+1, 2*`np2`+1) so that p2_output[np2+j, np2+i] is the probability that if one charge generated in a flat field lands in (0,0), the other lands in (i,j).

Return type:

np.array of float

op2_to_pars(op2, cmin=0.01)[source]

Fits a quantum yield model to a Phi-kernel.

Parameters:

op2 (np.array) – The Phi-kernel, omega/(1+omega)*p2 (where omega is the 2-charge probability and p2 is the pairwise charge diffusion probability kernel). This is the combination that can be extracted from a correlation function.
cmin (float, optional) – Minimum semi-minor axis of the covariance. (Prevents regularity problems.)

Returns:

Entries are [omega, cxx, cxy, cyy, change in last step, number of iterations].

Return type:

list

p2kernel_test()[source]: Test function for p2kernel.

solve_corr(bfek, N, I_, g, betas, sigma_a, tslices, avals, avals_nl=[0, 0, 0], outsize=2)[source]

Predicts the unequal-time correlation function C_{abcd}(Delta i, Delta j).

Parameters:

bfek (np.array) – Compound kernel [K^2 a+KK*] (assumed to be centered).
N (int) – Size to use for boudary conditions (must be odd, larger is more accurate).
I (float) – Current (elementary charges per pixel per frame).
g (float) – Gain in e/DN.
betas (np.array of float) – Array of classical non-linearity coefficients [beta_2…beta_n].
sigma_a (float) – Sum of the BFE kernel, in e^-1.
tslices (list of int) – List of time slices [ta, tb, tc, td].
avals (list or tuple of float) – The alpha values for the linear IPC kernel [aV, aH, aD]. Dimensionless.
avals_nl (list or tuple of float, optional) – The alpha values for NL-IPC kernel [aV_nl, aH_nl, aD_nl]. Units 1/e..
outsize (int, optional) – The “radius” of output (so the BFE kernel has size (2*outsize+1, 2*outsize+1).

Returns:

An array of size (N, N) describing C_{abcd}(Delta i, Delta j) in “decentered” mode.

Return type:

np.array

eval_cnl(betas, I_, t)[source]

Evaluates the derivative of a non-linearity polynomial.

Parameters:

betas (np.array) – The coefficients, in order starting from 2nd order (beta_2), then 3rd order (beta_3), etc.
I (float) – The current in electrons per pixel per frame.
t (float) – The time in frames since reset.

Returns:

The derivative g*dS/dQ (where g is the gain in e/DN; S is the signal in DN; and Q is the charge in e).

Return type:

float

solve_corr_many(bfek, N, I_, g, betas, sigma_a, tslices, avals, avals_nl=[0, 0, 0], outsize=2)[source]

Predicts a sequence of similar unequal-time correlation functions.

Parameters:

bfek (np.array) – Compound kernel [K^2 a+KK*] (assumed to be centered).
N (int) – Size to use for boudary conditions (must be odd, larger is more accurate).
I (float) – Current (elementary charges per pixel per frame).
g (float) – Gain in e/DN.
betas (np.array of float) – Array of classical non-linearity coefficients [beta_2…beta_n].
sigma_a (float) – Sum of the BFE kernel, in e^-1.
tslices (list of int) – List of time slices [ta, tb, tc, td, tn]. Should have tn>=1.
avals (list or tuple of float) – The alpha values for the linear IPC kernel [aV, aH, aD]. Dimensionless.
avals_nl (list or tuple of float, optional) – The alpha values for NL-IPC kernel [aV_nl, aH_nl, aD_nl]. Units 1/e..
outsize (int, optional) – The “radius” of output (so the BFE kernel has size (2*outsize+1, 2*outsize+1).

Returns:

The mean correlation function, sum_{k=0}^{tn-1} C_{ta+k,tb+k,tc+k,td+k} / tn, as a shape (N, N) array, decentered.

Return type:

np.array

See also

solve_corr: equivalent version with tn=1.

solve_corr_vis(bfek, N, I_, g, betas, sigma_a, tslices, avals, avals_nl=[0, 0, 0], outsize=2, omega=0, p2=0)[source]

Predicts the unequal-time correlation function C_{abcd}(Delta i, Delta j) for visible light.

Parameters:

bfek (np.array) – Compound kernel [K^2 a+KK*] (assumed to be centered).
N (int) – Size to use for boudary conditions (must be odd, larger is more accurate).
I (float) – Current (elementary charges per pixel per frame).
g (float) – Gain in e/DN.
betas (np.array of float) – Array of classical non-linearity coefficients [beta_2…beta_n].
sigma_a (float) – Sum of the BFE kernel, in e^-1.
tslices (list of int) – List of time slices [ta, tb, tc, td].
avals (list or tuple of float) – The alpha values for the linear IPC kernel [aV, aH, aD]. Dimensionless.
avals_nl (list or tuple of float, optional) – The alpha values for NL-IPC kernel [aV_nl, aH_nl, aD_nl]. Units 1/e..
outsize (int, optional) – The “radius” of output (so the BFE kernel has size (2*outsize+1, 2*outsize+1).
omega (float, optional) – The probability of getting 2 charges.
p2 (np.array, optional) – The pairwise separation probability for 2 charges generated at the same point in a flat field.

Returns:

An array of size (N, N) describing C_{abcd}(Delta i, Delta j) in “decentered” mode.

Return type:

np.array

See also

solve_corr: Similar but for IR flats.

solve_corr_vis_many(bfek, N, I_, g, betas, sigma_a, tslices, avals, avals_nl=[0, 0, 0], outsize=2, omega=0, p2=0)[source]

Predicts a sequence of similar unequal-time correlation functions, for visible light.

Parameters:

bfek (np.array) – Compound kernel [K^2 a+KK*] (assumed to be centered).
N (int) – Size to use for boudary conditions (must be odd, larger is more accurate).
I (float) – Current (elementary charges per pixel per frame).
g (float) – Gain in e/DN.
betas (np.array of float) – Array of classical non-linearity coefficients [beta_2…beta_n].
sigma_a (float) – Sum of the BFE kernel, in e^-1.
tslices (list of int) – List of time slices [ta, tb, tc, td, tn]. Should have tn>=1.
avals (list or tuple of float) – The alpha values for the linear IPC kernel [aV, aH, aD]. Dimensionless.
avals_nl (list or tuple of float, optional) – The alpha values for NL-IPC kernel [aV_nl, aH_nl, aD_nl]. Units 1/e..
outsize (int, optional) – The “radius” of output (so the BFE kernel has size (2*outsize+1, 2*outsize+1).
omega (float, optional) – The probability of getting 2 charges.
p2 (np.array, optional) – The pairwise separation probability for 2 charges generated at the same point in a flat field.

Returns:

The mean correlation function, sum_{k=0}^{tn-1} C_{ta+k,tb+k,tc+k,td+k} / tn, as a shape (N, N) array, decentered.

Return type:

np.array

See also

solve_corr_vis: equivalent version with tn=1.

N = 21[source]