spect_gen v3.3
07-OCT-94 MJF
22-JAN-96 MJF
22-MAR-99 MJF
29-JAN-15 MjF

	 Semi-empirical spectral generation.

Example:

	spect_gen << EOF
	Z  angle  waveform  kVp dkeV
	EOF

directories/links:
        _database : path to database directory

arguments:

	Z : atomic number of target.
		NOTE: 74 (tungsten), 45 (rhodium) and 42 (molybdenum) are the only permitted values.
	angle: x-ray emission angle from target in degrees
	waveform: 1 for constant potential, 2 for single phase, full wave rect.
	          3 for mono-energetic
	kVp:  peak electron acceleration voltage.
	dkeV: increment for spectral table.

associated files:

	read: none

	write:  spectra.tmp (see spectra.tmp.doc)

Method: 

	The basic semi-empirical model is that of Storm which
	has been implemented in a fashion similar to Sulc and Judy.
	The continuum is estimated from an empirical formula that
	Storm fit to integral solutions based on bremmstrahlung cross
	sections. The characteristic radiation peaks are predicted by
	an equation of Webster as subsequently reported by Storm.
	It is of the form a(kVp - Ek)**b where b is of the order 1.6.
	Tungsten constants were published by Storm.
	The self-absorption term is computed using the method originally
	suggested by Storm. The self-absorption term requires electron
	range information which is computed from Tabata's equation.
	The accuracy of the model has been checked against published
	tables of Fewell. The characteristic coefficients for Molybdenum
	were estimated by comparison to Fewell. A numeric method for
	determining spectra from single phase generators is used which
	integrates over a sine wave kVp profile.

Comments:

	Note that the spect.tmp file format allows considerable
	flexibility in the units of the spectra (i.e. ergs versus photons
	or /sr versus /cm^2). However the units are always expressed in
	/keV.  That is if the energy increment, dkeV, is changed the
	values for the continuum portion of the spectra do not change. 
	Integrations must explicitly multiply each value by dkeV to get
	the correct numeric sum.  However, for the characteristic peaks,
	their value will change as dkeV since they represent emission at
	a unique energy.

	As currently implemented, the energy interval labeled 'x' keV
	covers the 1 keV interval from 'x' to 'x+1' keV.

	The total number of spectral data points is currently limited
	to 300.

Note:	With xspect3.3, a second utility is available for computing
	x-ray spectra with is called spect_gen2. 
	This is an advanced routine which can be used for targets
	of arbitrary Z and includes compensation for target roughness.
	For compatibility with older scripts, both spectral generation
	codes are being maintained. See spect_gen2.doc for details.

References:

	Storm E, Calculated Bremsstrahlung Spectra from Thick Tungsten
	Targets, Phys. Rev. A, V5, No 6, pgs 2328-2338, 1978.

	Storm E, Emission of Characteristic L and K Radiation from Thick
	Tungsten Targets, J. of Applied Physics, V43, No 6, pgs 2790-2796,1972.

	Szulc M and Judy PF, Effect of X-ray source Filtration on dose and
	Image Performance on CT Scanners, Medical Physics, 6:479, 1979.

	Tabata T, Ito R, and Okabe S, Generalized Semiempirical Equations
	for the Extrapolated Range of Electrons, Nucl. Inst. and Methods,
	V103, pg 8591, 1972.

	Fewell T, Shuping R, and Hawkins K, Handbook of Computed Tomography
	X-ray Spectra, FDA 81-8162, 1981.

	Fewell T, Shuping R, Handbook of Mammographic X-ray Spectra, 
	FDA 17-8071m 1978.