; Fast way of making a modulation pattern

function modpat1d,NX,F1D,theta,aspp,xoffset,yoffset,dx,dy,xpixel,ypixel
;+
;  FUNCTION MODPAT1D.PRO
;  
;  PURPOSE:
;          Projects a 1-dimensional modulation pattern onto a 2-dimensional
;            array.  The vector F1d must have 1-arcsec pixels.
;          The pattern pixel locations given by the vectors xpixel and ypixel
;          used to project F1d, are optional; they will be created by the 
;          program if they do not exist, and then used in subsequent calls.
;          The array F1D must be at least 2048 pixels (arcsec) long.


;  INPUTS:
;          NX = size of 2-D modulation pattern to be produced
;          F1D = 1-D array of values to be projected.  Must be larger
;                than 2047 pixels in size.  1 pixel = 1 arc sec
;          theta = angle (radians) of F1D vector, CW from the x axis
;          aspp = arc sec per pixel in modulation pattern map
;          xoffset = x position of map center (in arc sec)
;          yoffset = y position of map center (in arc sec)
;          xpixel = vector of pixel indices of the x coordinate
;          ypixel = vector of pixel indices of the y coordinate
;          dx,dy = aspect position of telescope axis from sun center (arc sec)
;
;  CALLING SEQUENCE:
;
;          RESULT=modpat1d(NX,F1D,theta,aspp [,xpixel,ypixel])
;              Result is a reformed, 1-D version of the modulation pattern.
;              Use reform(result,nx,nx) to make it 2-dimensional if required.
;
;  METHOD:
;          Each pixel of the modulation is read from the F1d "lookup table".
;          The appropriate index in F1d is found by projecting a perpendicular
;          from (xpixel,ypixel) in the modulation pattern onto the line
;          passing through (dx,dx) with an orientation theta measured CCW
;          from the x axis.  For the finest HESSI collimator, pitch=4.3,
;          so there are over 4 points per cycle for all collimators.
;          There is no interpolation, since that would slow the program, but
;          if better sampling is required, the lookup table F1d can be
;          increased in size without appreciable decrease in speed.
;
;  SPEED:
;          Each call to function modpat1d takes about 3.8 ms on a Sun Ultra-1,
;          or about 1.4 ms on a Sun Ultra-10, or a 333-MHz Pentium II.
;          This suggests that one single-collimator back-projection map would 
;          take about 4 s (for an Ultra-1, or proportionately less for the 
;          faster machines), assuming 1000 photons or 1000 time bins.
;
;  VERSION: 1.0 EJS 22 June 1998
;-