	(REGULAR VERB)

	Syntax:   HOLFITFOC(Nyqrate, Dish_diam, Focal_lngth)

	HOLFITFOC is a verb meant to be used during the processing of
	holographic data and, as such, will have very limited
	applicability to other kinds of data reduction.

	HOLFITFOC fits and removes the affects of pointing or focusing
	errors from the phase or surface-error map produced after the
	inverse Fourier transform of the holographic data.  The
	function fitted to the data is that described in:  "Improved
	Profile Mapping of a Reflector Antenna from Microwave
	Holographic Measurements" by M. P.  Godwin, A. P. Anderson, and
	J. C.  Bennett (1978, Electronic Letters, Vol. 14, No. 5, p
	134).  The fitting algorithm is the iterative, non-linear,
	least-square method known as the Levenberg-Marquardt method and
	is described in P. R.  Bevington "Data Reduction and Error
	Analysis for the Physical Sciences (1969, McGraw-Hill, Chapters
	8, 9, and 11) and in W. H.  Press et al, "Numerical Recipes:
	The Art of Scientific Computing" (1986, Cambridge University,
	Chapter 14).

	HOLFITFOC assumes that Matrix (0) contains the data to be
	fitted in units of surface errors (in cm).  Any undefined
	points in the Matrix are not used in the fit.

	The user must supply three arguments to HOLFITFOC:

		First argument:  The fraction of the inverse of the
			oversampling of the original pre-IFFT data.
			Should be < 1 and usually between 0.75 and
			0.9.

		Second argument:  Dish Diameter in cm.

		Third argument:  Dish Focal Length in cm.

	HOLFITFOC will store into Matrix (0) the original data minus
	the results of the fit (i.e., the residuals of the fit).  In
	Matrix (1), HOLFITFOC will store the model produced by the fit
	(i.e., Matrix (0) plus Matrix (1) after the fit will be the
	same as Matrix (0) before the fit).  One-dimensional Arrays (0)
	and (1) are used for temporary storage by HOLFITFOC.

	The fit provides estimates, and one-sigma standard deviations
	of the estimates, to:

		the lateral-focus offset
		the angle of the lateral offset (relative to the x-axis
			 of the matrix) 
		an overall bias to the data
		the x-axis pointing offset 
		the y-axis pointing offset
		the radial focus offset.

	The units of the estimates for the bias and two focus offsets
	are in cm.  The angle of lateral offset is in radians.  The
	pointing offsets are in units of the angular sampling of the
	pre-IFFT data.

	The fit also provides a listing of the covariance matrix of the
	last iteration of the fit.

        No adverbs are set by HOLFITFOC

	ADVERBS used:

	NITER		Number of iterations performed by the fitting
			algorithm before it will give up.


	EXAMPLE:

	The following steps would take the IFFT of the data in Matrix
	(0) and (1), converts from (real, imaginary) to (amplitude,
	phase), copies the results to Matrices (2) and (3), copies the
	phase data from Matrix (1) to (0); scales the data from phase
	to surface errors; blanks out the data underneath the feed-legs
	and central blockage as well as the area outside the dish; and
	performs the fit.

		MIFFT RIAP
		MCOPY(0,2) MCOPY(1,3)
		MCOPY(1,0)
		MSCALE( lambda / (2*pi) )
		MAKEMASK(4, 56, 4, 15.3, 5)
		HOLFITFOC( 0.86, 4252., 1827.2)

	Note that MSCALE is a procedure found in the mmath.prc file in
	the general procedure library.  RIAP and MAKEMASK are
	procedures found in the holographic procedure library.


         
	    
