finesse.utilities.maps module

Collection of tools for computing different maps.

class finesse.utilities.maps.BinaryReader(fileName)

Bases: object

MetroPro binary data format reader.

read(typeName, size=None)

Read a datatype from the binary file.

Parameters

typenamestr

See BinaryReader.typeNames.

sizeint

Number of bytes to read

seek(offset, refPos=0)

Offset in bytes and refPos gives reference position, where 0 means origin of the file, 1 uses current position and 2 uses the end of the file.

typeNames = {'char': 's', 'double': 'd', 'float': 'f', 'int16': 'h', 'int32': 'i', 'int64': 'q', 'int8': 'b', 'uint16': 'H', 'uint32': 'I', 'uint64': 'Q', 'uint8': 'B'}

exception finesse.utilities.maps.BinaryReaderEOFException

Bases: Exception

finesse.utilities.maps.circular_aperture(x, y, R_ap, x_offset=0, y_offset=0)

Circular aperture map.

Parameters

x, yarray

1D arrays describing uniform 2D grid to compute map over in meters

Rfloat

Radius of aperture in meters

x_offset, y_offsetfloat, optional

Offset of aperture from origin

finesse.utilities.maps.make_coordinates(N, a)

Makes the 1D and square 2D grid of coordinates for map calculations.

Parameters

N_samplesint

Number of samples in each dimension (N x N)

afloat

Dimension of square grid (a x a) to generate

Returns

x,yarray_like[float]

1D arrays for the x and y coordinates

X,Y,Rarray_like[float]

2D Arrays of the X, Y, and radial R coordinates

finesse.utilities.maps.overlap_1D_curvature_coefficients(x, z, weight_spot: float)

Computes the amount of spot size weighted quadratic x**2 term there is present in some 1D data. This gives the same result as overlap_curvature_coefficients() when z does not depend on y.

Parameters

xndarray(dtype=float)

Sample points, ideally should be symmetric about 0.

zndarray(dtype=float)

function at sample points x

weight_spotfloat

Spot size to use as weighting

Returns

quadratic_termdouble

Weighted quadratic term of z

Notes

This function is essentially evaluating a weighted Hermite polynomial overlap integral with z(x) to determine the quadratic term.

\[\int_{\min(x)}^{\max(x)} H_{2}(x) z(x)^2 W(x) dx\]

Where the weighting function is \(W(x) = e^{-x^2}\).

finesse.utilities.maps.overlap_1D_piston_coefficient(x, z, weight_spot: float)

Computes the amount of weighted piston term there is in some 1D data like a surface map. This is computed by evaluating a weighted Hermite polynomial overlap integral in an efficient manner.

Parameters

x, yarray_like

1D Array of x and y describing the 2D plane of z

zarray_like

2D optical path difference [metres]

weight_spotfloat

Beam spot size to weight over

Returns

pistonfloat

amount of piston term

finesse.utilities.maps.overlap_1D_tilt_coefficients(x, z, weight_spot: float)

Computes the amount of spot size weighted linear x term there is present in some 1D data. This gives the same result as overlap_tilt_coefficients() when z does not depend on y.

Parameters

xndarray(dtype=float)

Sample points, ideally should be symmetric about 0.

zndarray(dtype=float)

function at sample points x

weight_spotfloat

Spot size to use as weighting

Returns

linear_termdouble

Weighted linear term of z

Notes

This function is essentially evaluating a weighted Hermite polynomial overlap integral with z(x) to determine the linear term.

\[\int_{\min(x)}^{\max(x)} H_{1}(x) z(x) W(x) dx\]

Where the weighting function is \(W(x) = e^{-x^2}\).

finesse.utilities.maps.overlap_curvature_coefficients(x, y, z, weight_spot: float)

Computes the amount of x and y curvature terms present in a map’s displacement data.

This is computed by evaluating a weighted Hermite polynomial overlap integral in an efficient manner.

Parameters

x, yarray_like

1D Array of x and y describing the 2D plane of z

zarray_like

2D optical path difference [metres]

weight_spotfloat

Beam spot size to weight over

Returns

Bx, Bycomplex

Complex-valued overlap coefficients for the HG20 and HG02 modes

Notes

This function is essentially evaluating a weighted Hermite polynomial overlap integral with z(x).

\[\begin{aligned} B_x &= \left\langle U_{00} | z | U_{20}\right\rangle \\ &= \int z(x,y) U_{00}(x,y) U_{20}^*(x,y) dx dy \\ &= \frac{2}{\pi w^4} \int z(x,y) \left(\frac{8 x^2}{w^2} - 2 \right) \exp\left(-\frac{2(x^2+y^2)}{w^2}\right) dx dy \end{aligned}\]

Where the weighting function is \(W(x) = e^{-x^2}\). Likewise for \(B_y\).

finesse.utilities.maps.overlap_piston_coefficient(x, y, z, weight_spot: float)

Computes the amount of weighted piston term there is in some 2D data like a surface map.

This is computed by evaluating a weighted Hermite polynomial overlap integral in an efficient manner.

Parameters

x, yarray_like

1D Array of x and y describing the 2D plane of z

zarray_like

2D optical path difference [metres]

weight_spotfloat

Beam spot size to weight over

Returns

pistonfloat

amount of piston term

Notes

\[\begin{aligned} \overline{z} &= \left\langle U_{00} | z | U_{00}\right\rangle \\ &= \int z(x,y) U_{00}(x,y) U_{00}^*(x,y) dx dy \\ &= \frac{2}{\pi w^2} \int z(x,y) \exp\left(-\frac{2(x^2+y^2)}{w^2}\right) dx dy \end{aligned}\]

finesse.utilities.maps.overlap_tilt_coefficients(x, y, z, weight_spot: float)

Computes the amount of yaw and pitch terms present in a map’s displacement data.

This is computed by evaluating a weighted Hermite polynomial overlap integral in an efficient manner.

Parameters

x, yarray_like

1D Array of x and y describing the 2D plane of z

zarray_like

2D optical path difference [metres]

weight_spotfloat

Beam spot size to weight over

Returns

alpha_x, alpha_ycomplex

Complex-valued overlap tilt coefficients for the HG10 and HG01 modes

Notes

This function is essentially evaluating a weighted Hermite polynomial overlap integral with z(x).

\[\begin{aligned} \alpha_x &= \left\langle U_{00} | z | U_{10}\right\rangle \\ &= \int z(x,y) U_{00}(x,y) U_{10}^*(x,y) dx dy \\ &= \frac{4}{\pi w^3} \int z(x,y) \frac{2 x}{w} \exp\left(-\frac{2(x^2+y^2)}{w^2}\right) dx dy \end{aligned}\]

Where the weighting function is \(W(x) = e^{-x^2}\). Likewise for \(\alpha_y\).

finesse.utilities.maps.read_metropro_file(filename)

Reading the metroPro binary data files. Translated from Hiro Yamamoto’s ‘LoadMetroProData.m’.

Parameters

filename

Name of metropro data file.

finesse.utilities.maps.read_metropro_header(binary)

Reads header of the metroPro binary format files. Translated from the readerHeader() function within the ‘LoadMetroProData.m’ function written by Hiro Yamamoto.

Parameters

binaryBinaryReader

Name of metropro data file.

finesse.utilities.maps.rms(x, y, z, weight_spot: float, xo: float = 0, yo: float = 0)

Computes the spot weight RMS over some 2D data, such as optical path depth.

\[\sqrt{\overline{z^2} - \overline{z}^2}\]

where

\[\begin{aligned} \overline{z} &= \left\langle U_{00} | z | U_{00}\right\rangle \\ &= \frac{2}{\pi w^2} \int z(x,y) \exp\left(-\frac{2(x^2+y^2)}{w^2}\right) dx dy \end{aligned}\]

and likewise for \(\overline{z^2}\)

Parameters

x, yarray_like

1D Array of x and y describing the 2D plane of z

zarray_like

2D optical path difference [metres]

weight_spotfloat

Beam spot size to weight over

xo, yofloat

Origin of the beam position

Returns

rmsfloat

Root mean squared in units of whatever z is

Notes

Based on Equation 4 in:

A. Brooks, et.al Overview of Advanced LIGO adaptive optics Appl. Opt. 55, 8256-8265 (2016)

finesse.utilities.maps.surface_point_absorber(xs, ys, w, h, power_absorbed, alpha=5.5e-07, kappa=1.38, zero_min=False)

Models the surface deformation from a small point absorber in a coating of a mirror. It calcaultes the thermo-elastic deformation due to excess heat being deposited in the mirror.

Parameters

xs, ysarray

1D array for the x and y axis to calculate the distortion over

wdouble

Area of the absorber size

hdouble

Thickness of mirror

power_absorbeddouble

Amount of power absorbed over the area w

alphadouble, optional

Thermo-elastic coefficient of material, default value for fused silica

kappadouble, optional

Thermal conductivity of the material, default value for fused silica

Returns

Height map in meters

Notes

Equation from:

1. Brooks, et.al “Point absorbers in Advanced LIGO,” Appl. Opt. (2021)