Adaptive optics telemetry standard - Design and specification of a novel data exchange format

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Volume 686 (June 2024)

A&A, 686 (2024) A7

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Table C.1

Possible image categories.

Image category	Type	Dimensions (×t)	Unit	Description
Referenceable in multiple tables
`TRANSFORMATION_MATRIX`	flt	3 × 3	n.a.	Matrix that defines 2-dimensional affine transformations using homogeneous coordinates. For more detail see Appendix C.7.
`PUPIL_MASK`	int	w × h	n.a.	Binary image that describes the shape of the pupil. A 1 indicates the presence of the pupil, while a 0 indicates the opposite.
`MODES`	flt	w × h × m	n.a.	Set of m different w × h arrays, each representing the orthonormal basis of the corresponding mode.

AOT_ATMOSPHERIC_PARAMETERS
`LAYERS_WEIGHT`	flt	l	n.a.	Fractional weight of each l turbulence layer (sums to 1).
`LAYERS_HEIGHT`	flt	l	m	Height above observatory at zenith of each l turbulence layer.
`LAYERS_L0`	flt	l	m	Outer scale of turbulence at reference wavelength at zenith of each l turbulence layer.
`LAYERS_WIND_SPEED`	flt	l	ms⁻¹	Wind speed of each l turbulence layer.
`LAYERS_WIND_DIRECTION`	flt	l	deg	Wind direction of each l turbulence layer, with 0° being North, increasing eastward.

AOT_ABERRATIONS
`COEFFICIENTS`	flt	n × m	u.d.	Set of m coefficients (one for each of the orthonormal basis of modes) for each n pupil offset.

AOT_SOURCES_SODIUM_LGS
`PROFILE`	flt	l	n.a.	Normalised LGS profile (each set of l layers Σ = 1) at zenith.

AOT_DETECTORS
`FLAT_FIELD`	flt	w×h	n.a.	Inverse of the detector pixel-to-pixel sensitivity.
`PIXEL_INTENSITIES`	flt	w×h	ADU	Intensity detected in each pixel, for each data frame. This is an image spanning w pixels horizontally and h pixels vertically.
`DARK`	flt	w×h	ADU	Intensity detected in each pixel when there is no light being observed. This is an image spanning w pixels horizontally and h pixels vertically.
`WEIGHT_MAP`	flt	w×h	n.a.	Pixel weight map, where each detector pixel is associated with a number that represents its relative value. Summing up to 1.
`SKY_BACKGROUND`	flt	w×h	ADU	Detector pixel intensities from a source-less direction in the sky.
`BAD_PIXEL_MAP`	int	w×h	n.a.	Binary image which identifies the bad pixels, that is, pixels that should be ignored for the purpose of the analysis. Pixels identified with 1 are considered bad, while 0 is considered normal.

AOT_WAVEFRONT_SENSORS
`MEASUREMENTS`	flt	s_υ × d	u.d.	Wavefront measurements from the wavefront sensor. Each of its s_υ subapertures is able to measure in d dimensions.
`REF_MEASUREMENTS`	flt	s_υ × d	u.d.	Reference measurements.
`SUBAPERTURE_MASK`	int	s × s	n.a.	Representation of the subaperture grid, where the cells corresponding to invalid subapertures are marked as −1 and the cells corresponding to valid subapertures contain their respective index in the sequence of valid subapertures (using zero-based numbering, that is, the initial element is assigned the index 0).
`SUBAPERTURE_INTENSITIES`	flt	s_υ	ADU	Detected average intensity (flux) of each of the s_υ valid subapertures.
`OPTICAL_GAIN`	flt	1

AOT_WAVEFRONT_SENSORS_SHACK_HARTMANN
`CENTROID_GAINS`	flt	s_υ × d	n.a.	Centroid gain factors for each of s_υ subapertures and d dimensions.
`SPOT_FWHM`	flt	s_υ × d	arcsec	Spot full width half maximum for each of s_υ subapertures and d dimensions.

AOT_WAVEFRONT_CORRECTORS_DM
`INFLUENCE_FUNCTION`	flt	w × h × a_υ	m	A set of 2D images, one for each valid actuator, where each image represents the displacement of the surface of the deformable mirror after poking the respective actuator.

AOT_LOOPS
`COMMANDS`	flt	a_υ	m	Commands sent to the associated wavefront corrector. Contains the values sent to each of the a_υ valid actuators of a certain wavefront corrector.
`REF_COMMANDS`	flt	a_υ	m	Reference offset commands for each of a_υ actuators.
`TIME_FILTER_NUM`	flt	i × m	n.a.	One set of time filter numerators per mode being described. If m = 1, it is assumed to be applicable to all modes. The first numerator is the loop gain.
`TIME_FILTER_DEN`	flt	j × m	n.a.	One set of time filter denominators per mode being described. If m = 1, it is assumed to be applicable to all modes. Uses standard transfer function $s y s (z) = {\sum^{}}_{i = 0}^{N - 1} b_{i} z^{i} / {\sum^{}}_{j = 0}^{N} a_{j} z^{j}$ $sys(z) = \mathop {\mathop \sum \nolimits^ }\limits_{N - 1}^{i = 0} {b_i}{z^i}/\mathop {\mathop \sum \nolimits^ }\limits_N^{j = 0} {a_j}{z^j}$ .

AOT_LOOPS_CONTROL
`MODAL_COEFFICIENTS`	flt	m	u.d.	Coefficients respective to each of the m modes being corrected on the wavefront corrector.
`CONTROL_MATRIX`	flt	s_υ × d × a_υ	u.d.	Linear relationship between the wavefront sensor measurements (s_υ × d) and the corrector commands (a_υ).
`MEASUREMENTS_TO_MODES`	flt	s_υ × d × m	u.d.	Linear relationship between the wavefront sensor measurements (s_υ × d) and the modes to be corrected (m).
`MODES_TO_COMMANDS`	flt	m × a_υ	u.d.	Linear relationship between the modes (m) to be corrected and the corrector commands (a_υ).
`INTERACTION_MATRIX`	flt	a_υ × d × s_υ	u.d.	Represents the measurements of the wavefront sensor (d × s_υ) in response to each actuator of the wavefront corrector (a_υ).
`COMMANDS_TO_MODES`	flt	a_υ × m	u.d.	Represents the modal response (m) to each actuator of the wavefront corrector (a_υ).
`MODES_TO_MEASUREMENTS`	flt	m × d × s_υ	u.d.	Linear relationship between the modal response (m) and the wavefront sensor measurements (d × s_υ).
`RESIDUAL_COMMANDS`	flt	a_υ	u.d.	Reconstructed corrector commands before time filtering.

AOT_LOOPS_OFFLOAD
`OFFLOAD_MATRIX`	flt	a1_υ × a2_υ	u.d.	Linear relationship between the commands from one actuator (a1) and the corresponding commands that get offloaded to another actuator (a2).

Notes. The unit “n.a.” stands for “not applicable”, meaning that the data is a dimensionless quantity, such as countable quantities, ratios and proportions. The unit “u.d.” stands for “user defined” meaning that the user is free to pick a unit as long as it is consistent with the rest of the data. All images in this table may vary over time. In such cases, the images must have an extra t dimension, which must defined after all the other specified dimensions. It is recommended that images with a t contain a TIME_UID keyword in their header, whose value is a AOT_TIME row-reference with time data of t length. The t dimension may be omitted if it is of size 1.

w and h are (respectively) the width and height of the image in pixels, s_υ is the number of valid subapertures (ordered as defined via SUBAPERTURE_MASK), d is the number of dimensions being measured by the wavefront sensor, a_υ is the number of valid actuators, m is the number of modes being controlled.

If an image of data type flt can be accurately described with a int type, users may opt to do so. However, this does not apply to the inverse.

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