Symbols

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Discussion of HESSI Symbols Greek Symbols under Xwindows

There are a great number of algebraic quantities involved in imaging spectroscopy with the HESSI instrument, so it is worthwhile adopting some conventions on what symbols we will use. This is a first stab at choosing a set of unique symbols for HESSI imaging. Later we should add more symbols relevant to spectroscopy.

Symbol	Meaning	IDL var
t _i	Time at the center of the i’th time bin (usually in units of 64 binary m s)	time
N_i	Number of counts in i’th time bin	counts
x_i^A,y_i^A	Yaw, pitch offset of sun-center from imager axis in spacecraft coordinates for the i’th time bin ( m radians (from aspect solution)	x_asp,y_asp
X_m,Y_m	Pixel m offset from map center in inertial coordinates (X_m=X_c+m₁ dx, Y_m=Y_c+m₂ dy)	X_pixoff,Y_pixoff
a _i	Roll angle ( m µ radians), of spacecraft X-axis relative to celestial north and measured CCW (from aspect solution)	roll_angle
b	Grid slit orientation in spacecraft coordinates ( m radians) (from parameter file)	grid_angle
X^M,Y^M	Map center offset from Sun center in inertial coordinates (user input)	X_map, Y_map
x^M,y^M	Map center offset from imager axis in spacecraft coordinates	x_map_sc,y_map_sc
	x^M = x^A + X^M cos a + Y^M sin a
	y^M = y^A + Y^M cos a - X^M sin a
t _i	Live time (binary fraction)	livetime
T (x^M,y^M)	Grid-response-matrix transmission (from hsi_grm -- Step 5)	gridtran
A_h (x^M,y^M)	Grid-response-matrix amplitude (from hsi_grm -- Step 5)	modamp
Q_h (x^M,y^M)	Peak grid-response-matrix offset (from hsi_grm -- Step 5)	peak_resp_offset
p	Subcollimator pitch (FltPt m radians)	ang_pitch
Q _i	Phase of map center relative to line of maximum response (Step 6)	phase_map_ctr
	Q = 2 p h (x ^M cos b + y ^M sin b ± Q)/p (incorporates aspect, grids, map-center)
L _mi	Phase of pixel m relative to phase of map center	phase_pixel
	L _mi = 2 p h (X_mcos( a _i +b ) + Y_msin ( a _i +b ) ) / p
E_mi	Expected counts in time bin i from pixel m:
	E_mi = F_mi t _iT_i( 1 +A _ih cos[ Q _{i +} L _{mi ] )}	counts_exp
F	Postulated flux	flux
h	Harmonic(1,2,3,...)	h
u,v	Coordinates in Fourier plane (visibility coverage)	u,v
i	Time bin index	i
m	Map pixel index	m

Guidelines: 1. Use Greek for angles and phases, with upper case reserved for large (i.e. >1^° ) angles.
2. Capital X,Y for inertial coordinates, l.c. x,y for spacecraft coordinates.
3. Superscripts for labels, subscripts for vector or matrix indices.
4. Phase is reserved for arguments of periodic functions, and to which arbitrary multiples of 2 p can be added.

Responsible NASA Official: Gordon D. Holman

Web Design: Merrick Berg, Brian Dennis, Gordon Holman, & Gilbert Prevost

Heliophysics Science Division
NASA/Goddard Space Flight Center
Laboratory for Solar Physics/ Code 671
Greenbelt, MD, 20771, USA
Gordon.D.Holman@nasa.gov

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This site last updated November 10, 2008.