User's Guide to Sigma0 1.0

Table of Contents

Introduction
What to Read
Sigma0 Functionality
Supported Data Types
Statistics and Computations
Mouse Tracking
Annotation Options
Output Options
Requirements
Supported image sizes
Input Data File Formats
Compressed Stokes Matrix Format
Byte Image Format
Printers
Differences Between MacSigma0 and Sigma0
Known Bugs
References

JPL AIRSAR (A. Freeman)

Copying the application
Starting the application
Tutorial
Displaying an image
Exploring the data
Manipulating what you see
Saving what we see
Analyzing the data
Getting the most out of Sigma0
Low memory conditions

About the File Menu
Open compressed Stokes
Open byte image
Open Mac PICT
Open Win BMP
After the image is opened
About this data
Close
Save as Byte, BMP, TIFF
Quit

Copy

Coordinates
Draw Selected On All

Display sigma_0
Add Captions
Normal size
Zoom in
Zoom out

Select rectangles
Select lines
Select polygons
Mean and std dev
Analyze Reflector
Line options

Introduction
Compressed Stokes Matrix Data
Image Geometry
The Stokes matrix
Basic calculations
Image generation (TP, HH, HV, VV, RL, RR)
Image generation (HHVV*, HHHV*, HVVV*)
Image generation (HHVV* phase)
Image generation (correlation coefficients)
Calculation of Incidence Angle
Calculation of statistics
TP, HH, HV, VV, RL, RR, |HHVV*|, |HHHV*|, |HVVV*|
HHVV* phase, HHHV* phase, HVVV* phase
Correlation coefficient
Incidence Angle
Histogram Generation
Mouse Tracking
Overlaid Values
Byte Images
Calculation of statistics
Histogram Generation
Mouse Tracking
Overlaid Values

Data Transfer
Data Reduction
"Reduce.for" Program Listing

1. Overview

   
   
   
   

Introduction

• JPL AIRSAR
  A multi-polarimetric airborne synthetic aperture radar developed and
  operated by the Jet Propulsion Laboratory. This includes the single-
  frequency L-band sensor mounted on the NASA CV990 aircraft and its
  replacement, the multi-frequency P-, L-, and C-band sensors mounted
  on the NASA DC-8. If you have access to the World Wide Web, sample AIRSAR
  data can be obtained from http://southport.jpl.nasa.gov.
  
  
• JPL SIR-C
  A multi-polarimetric spaceborne synthetic aperture radar developed and
  operated by the Jet Propulsion Laboratory and Alenia Spazio (Italy). SIR-C data
  sets (in AIRSAR format) can be found on the NASA/JPL SIR-C Educational cd-
  roms (SIR-CED01 and SIR-CED02) which can be obtained for free from the
  EROS Data Center, Sioux Falls, South Dakota 57198.
  
  

What to Read

Sigma0 Functionality

• JPL AIRSAR
  The radar data can be used to synthesize a variety of images. For instance, the
  total power image displays the sum of the polarized and unpolarized compo-
  nents of the backscatter for each pixel. Other images which can be synthe-
  sized are HH, HV, VV, RL, RR, HHVV*, HHHV*, HVVV*, HHVV* phase, and three
  

• BYTE IMAGES
  Byte images are displayed as is. The user must enter the image dimensions.
  
  
• PICT IMAGES
  PICT images are displayed as is. Reading in of PICT images is currently only
  supported on the Macintosh version of Sigma0.
  
  
• BMP IMAGES
  BMP images are displayed as is.
  
  
  

• JPL AIRSAR
  If the synthesized image is a total power image, then the mean total power and
  mean relative standard deviation are calculated for the selected area. Means
  and relative standard deviations are always calculated for HH, HV, VV, HHVV*
  phase and the HH-VV correlation coefficient. In addition, an appropriate
  incidence angle is calculated (either the center incidence angle or the mean
  incidence angle, depending on the shape of the selected area), the number of
  selected pixels are displayed, and a normalized histogram of the selected area is
  displayed.
  
  
• BYTE IMAGE
  The mean and relative standard deviations of the selected area are displayed.
  A normalized histogram of the selected area is shown.
  
  

• JPL AIRSAR
  The mouse's location is given in (sample, line). The (0,0) origin is in the
  upper left-hand corner. Samples increase to the right and lines increase to
  the bottom. The dn (ie. byte pixel value) of the pixel is in the third column. In
  the fourth column, the value shown depends on the image type:
  
  

• BYTE IMAGE
  The mouse's location is shown as (sample, line) with the (0,0) origin being
  in the upper left-hand corner. The third value shown is the display number or
  byte pixel value.
  

• JPL AIRSAR
  The superimposed value depends on the type of image synthesized:
  
  

• BYTE IMAGE
  pixel value
  
  

Requirements

Supported image sizes

Input Data File Formats

• compressed Stokes matrix data format
  
• byte image format
  
• PICT image format (Macintosh version only)
  
• BMP image format
  
  

             Column numbers:
      Field  12345678901234567890123456789012345678901234567890

        1    RECORD LENGTH IN BYTES =                  NNNNNNNN
        2    NUMBER OF HEADER RECORDS =                NNNNNNNN
        3    NUMBER OF SAMPLES PER RECORD =            NNNNNNNN
        4    NUMBER OF LINES IN IMAGE =                NNNNNNNN
        5    NUMBER OF BYTES PER SAMPLE =              NNNNNNNN
        6    JPL AIRCRAFT SAR PROCESSOR VERSION       XXXX.XXXX
        7    DATA TYPE =                             CCCCCCCCCC
        8    RANGE PROJECTION =                          CCCCCC
        9    RANGE PIXEL SPACING (METERS) =           XXXX.XXXX
        10   AZIMUTH PIXEL SPACING (METERS) =         XXXX.XXXX
        11   BYTE OFFSET OF OLD HEADER =               NNNNNNNN
        12   BYTE OFFSET OF USER HEADER =              NNNNNNNN
        13   BYTE OFFSET OF FIRST DATA RECORD =        NNNNNNNN
        14*  UPPER LEFT CORNER X (0-1023) =            NNNNNNNN
        15*  UPPER LEFT CORNER Y (0-1023) =            NNNNNNNN
        16*  AVERAGING (1,2,4) =                       NNNNNNNN

Printers

Differences Between MacSigma0 and Sigma0

Known Bugs

References

1. Sensor/Mission Description

   
   
   
   

JPL AIRSAR (A. Freeman)

1. Getting Started

   
   
   

Copying the application

Starting the application

Tutorial

Getting the most out of Sigma0

Low memory conditions

1. The File Menu

   
   
   

About the File Menu

Open compressed Stokes...

Open Byte Image..

Open Mac PICT...

Open Win BMP...

After the image is opened

About this data...

Close

Save as Byte, Save as BMP, Save as TIFF...

Quit

1. The Edit Menu

   
   
   

Copy

1. The View Menu

   
   
   

View Coordinates

Draw Selected On All

1. The Image Menu

   
   
   

Display Sigma_0's

Add Captions...

Normal size

Zoom in

Zoom out

1. The Statistics Menu

   
   
   

Select rectangles

Select lines

Select polygons

Mean and std dev

Image name:  SANFRANL.STK_TP (L-BAND)
(0) Center incidence angle:  39.7 degrees
Number of pixels: 1974
Selected rect:  (73,87) (119,128)
(1) TP mean: -15.80 dB
(2) TP relative standard deviation: 2.53
(3) HH mean:  -13.05 dB
(4) HH relative standard deviation:  2.70
(5) HV mean:  -22.13 dB
(6) HV relative standard deviation: 2.46
(7) VV mean:  -13.62 dB
(8) VV relative standard deviation:  2.61
(9) HHVV* phase mean:  -172.60 degrees
(10) HHVV* phase standard deviation:  115.96 degrees
(11) Correlation coefficient mean:  0.23
(12) Correlation coefficient relative standard deviation:  2.86
(0)	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)... 39.7	-15.80	2.53	-13.05	2.70	-22.13	2.46	-13.62... 
 
Histogram type:  TP
Units:  dBs
-100.00	0.00000
-99.00	0.00000
-98.00	0.00000
...
-29.00	0.00152
-28.00	0.00608
-27.00	0.04863
-26.00	0.08511
-25.00	0.06383
-24.00	0.03698
-23.00	0.03445
-22.00	0.02989
-21.00	0.03597
-20.00	0.05978
-19.00	0.05471
-18.00	0.05370
-17.00	0.06383
-16.00	0.06738
-15.00	0.08055
-14.00	0.07700
-13.00	0.06130
-12.00	0.05471
-11.00	0.03141
-10.00	0.02077
...
95.00	0.00000
96.00	0.00000
97.00	0.00000
98.00	0.00000
99.00	0.00000

Image name:  image256x274.byte
Number of pixels:  1570
Polygon's frame:  (109,58) (159,104)
(0) Mean:  183.43
(1) Standard deviation:  28.75
(0)	(1)
183.43	28.75
Histogram type:  BYTE
Units:  pixel  values
0.00	0.00000
1.00	0.00000
2.00	0.00000
3.00	0.00000
...
124.00	0.00127
125.00	0.00064
126.00	0.00318
127.00	0.00191
128.00	0.00064
129.00	0.00127
130.00	0.00255
131.00	0.00127
132.00	0.00191
133.00	0.00318
134.00	0.00446
135.00	0.00191
136.00	0.00064
137.00	0.00255
138.00	0.00510
139.00	0.00382
...
250.00	0.00000
251.00	0.00000
252.00	0.00000
253.00	0.00000
254.00	0.00000
255.00	0.00000

Analyze Reflector..

Line options...

Introduction

Compressed Stokes Matrix Data

sc0

sc1

sc0

	extended e		

	extended sc0[160]	

	int i			

	e = pow (2.0,-100.0);
		for (i=-100; i<60; i++) {
		sc0[i+100] = e;
		e *= 2.0;
	}

sc1

	extended sc1[256]	

	extended gen_sca	

	int i			

	for (i=-128; i<128; i++) 
		sc1[i+128] = (i/254.0 + 1.5)*scale;

b[10]

	char b[10]		

	extern extended sc0[]	

	
	extern extended sc1[]	

	extended p11		

	if (b[0]<-100) b[0] = -100;
	if (b[0]>59) b[0] = 59;
	p11 = sc0[b[0]+100]*sc1[b[1]+128];

	char b[10]  	

	extended p[16]  	

	extended p11	

	p[0] = p11;                        // element 1,1
	p[1] = b[2]/127.0;                 // 1,2
	p[2] = b[3]*b[3]/16129.0;
	if (b[3] < 0) p[2] = -p[2];        // 1,3
	p[3] = b[4]*b[4]/16129.0;
	if (b[4] < 0) p[3] = -p[3];        // 1,4
	p[6] = b[5]*b[5]/16129.0;
	if (b[5] < 0) p[6] = -p[6];        // 2,3
	p[7] = b[6]*b[6]/16129.0;
	if (b[6] < 0) p[7] = -p[7];        // 2,4
	p[10] = b[7]/127.0;                // 3,3
	p[11] = b[8]/127.0;                // 3,4
	p[15] = b[9]/127.0;                // 4,4
	p[5]  = p[0]-p[10]-p[15];          // 2,2
	p[4]  = p[1];                      // 2,1
	p[8]  = p[2];                      // 3,1
	p[12] = p[3];                      // 4,1
	p[9]  = p[6];                      // 3,2
	p[13] = p[7];                      // 4,2
	p[14] = p[11];                     // 4,3

	TP = p11		10 log (TP)
	HH = p11+p22+2p12	10 log (HH)
	VV = p11+p22-2p12	10 log (VV)
	HV = p11-p22	10 log (HV)
	RL = p11-p44	10 log (RL)
	RR = p11+p44+2p14	10 log (RR)
	|HHVV*| =		10 log (|HHVV*|)
	   |(p33-p44,-2p34)|

	HHVV* phase = 	N/A
	   tan-1(-2p34/(p33-p44)
	|HHHV*| =		10 log (|HHHV*|)
	   |(p13+p23,-p14-p24)|
	HHHV* phase =	N/A
	   tan-1((-p14-p24)/(p13+p23)
	|HHHV*| =		10 log (|HHHV*|)
	   |(p13+p23,-p14-p24)|
	HHHV* phase =	N/A
	   tan-1((-p14-p24)/(p13+p23)
	correlation coefficient =	N/A
	   |HHVV*|/(sqrt(HH) sqrt(VV))
	

	int start_line	

	int skip_line	

	short line,samp	

	short xsize,ysize	

	extended max	

	extended min	

	extended value	

	start_line = ysize/10;
	skip_line = (ysize-start_line)/8;
	for (line=start_line; line<ysize; line+=skip_line) {
		for (samp=0; samp<xsize; samp+=10) {
			get the 10 compressed bytes for pixel (samp,line)

			value = parameter being calculated (e.g. HH)

			if (value < 0.0) value = 0.0;
			if (line == start_line && samp == 0) {
			   max = value;
			   min = value;
			}
			if (value > max) max = value;
			if (value < min) min = value;
		}
	}

	short line,samp	

	short xsize,ysize	

	int start_line	

	int skip_line	

	int k			

	extended value	

	extended max	

	extended min	

	extended bin	

	short hist[256]	

	bin = (max-min) / 256.0;
	for (k=0; k<256; k++) hist[k] = 0;
	for (line=start_line; line<ysize; line+=skip_line) {
		for (samp=0; samp<xsize; samp+=10) {
			get the 10 compressed bytes for pixel (samp,line)

			value = parameter being calculated (e.g. HH)

			if (value < 0.0) value = 0.0;
			k = floor((value-min)/bin);
			if (k <= 0) k = 0;
			if (k >= 256) k = 255;
			hist[k]++;
		}
	}

max

min

max

min

max

min

	short line,samp	

	short xsize,ysize	

	int theint		

	int thesigma	

	extended value	

	extended max	

	extended min	

	extended scale	

	scale = 255.0 / (max-min);
	for (line=0; line<ysize; line++) {
		for (samp=0; samp<xsize; samp++) {
			get the 10 compressed bytes for pixel (samp,line)

			value = parameter being calculated (e.g. HH)

			if (value < 0.0) value = 0.0;
			theint = (value-min)*scale;
			if (theint>255) theint = 255;
			if (theint<0) theint = 0;
			value = (value==0.0) ? -100 : 10.0*log10 (value);
			if (value >= 0.0) thesigma = value+0.5;
			else thesigma = value-0.5;
			if (thesigma < -99) thesigma = -100;
			if (thesigma > 99) thesigma = 99;
		}
	}

theint

thesigma

Thesigma

	int start_line	

	int skip_line	

	short line,samp	

	short xsize,ysize	

	extended max	

	extended min	

	extended value	

	start_line = ysize/10;
	skip_line = (ysize-start_line)/8;
	for (line=start_line; line<ysize; line+=skip_line) {
		for (samp=0; samp<xsize; samp+=10) {
			get the 10 compressed bytes for pixel (samp,line)

			value = magnitude of parameter being calculated

		            (e.g. |HHHV*|)

			if (line == start_line && samp == 0) {
			   max = value;
			   min = value;
			}
			if (value > max) max = value;
			if (value < min) min = value;
		}
	}

	short line,samp	

	short xsize,ysize	

	int start_line	

	int skip_line	

	int k			

	extended value	

	extended max	

	extended min	

	extended bin	

	short hist[256]	

	bin = (max-min) / 256.0;
	for (k=0; k<256; k++) hist[k] = 0;
	for (line=start_line; line<ysize; line+=skip_line) {
		for (samp=0; samp<xsize; samp+=10) {
			get the 10 compressed bytes for pixel (samp,line)

			value = magnitude of parameter being calculated

		            (e.g. |HHHV*|)

			k = floor((value-min)/bin);
			if (k <= 0) k = 0;
			if (k >= 256) k = 255;
			hist[k]++;
		}
	}

max

min

max

min

sc2

	int i			

	extended sc2[45]	

	for (i=0; i<45; i++) 
		sc2[i] = tan((float)i*3.141592654/90.0);

	extended x		

	extended real	

	extended imag	

	extended phase	

	int start		

	int end		

	int mid		

	int n			

	if (imag == 0.0 && real == 0.0) return 0.0;
	if (real == 0.0 && imag >  0.0) return 1.570796327;
	if (real == 0.0 && imag <  0.0) return 4.71238898;

	x = fabs (imag/real);

	if (x > sc2[44])  n = 45;
	else {
		n = -1;
		start = 0;
		end = 44;
		mid = (start+end)/2;
		while (n == -1) {
			if (x == sc2[mid]) n = mid;
			else if (x < sc2[mid]) end = mid;
			else start = mid;
			if (end-start == 1) {
				if ((sc2[end]-x) > (x-sc2[start])) n = start;
				else n = end;
			} else mid = (start+end)/2;
		}	
	}

	if (real < 0.0) n = 90 - n;
	if (imag < 0.0) n = 180 - n;

	phase = (float)n*3.141592654/90.0;

	short line,samp	

	short xsize,ysize	

	int theint		

	int themag		

	int thesigma	

	int thephase	

	extended a		

	extended b		

	extended value	

	extended phase	

	extended max	

	extended min	

	extended scale	

	scale = 15.0 / (max-min);
	for (line=0; line<ysize; line++) {
		for (samp=0; samp<xsize; samp++) {
			get the 10 compressed bytes for pixel (samp,line)

			a = real component of parameter being calculated

			   (e.g. HHHV*)

			b = imaginary component of parameter being 

			   calculated (e.g. HHHV*)


			/* -- calculate phase and magnitude -- */
			value = sqrt(a*a+b*b);
			phase = myatan (b,a);   // 0 -> 2*PI

			/* -- convert magnitude to 0->15 -- */
			theint = (value-min)*scale;
			if (themag>15) themag = 15;
			if (themag<0) themag = 0;

			/* -- convert phase to 0->15 -- */
			phase *= 2.387324146;
			thephase = phase;
			if (thephase>15) thephase = 15;
			if (thephase< 0) thephase = 0;

			/* -- calculate output pixel -- */
			theint = themag + (thephase<<4);

			/* -- calculate magnitude in dBs -- */
			value = (value==0.0) ? -100 : 10.0*log10 (value);
			if (value >= 0.0) thesigma = value+0.5;
			else thesigma = value-0.5;
			if (thesigma < -99) thesigma = -100;
			if (thesigma > 99) thesigma = 99;

			/* -- calculate phase in degrees/2 -- */
			phase *= 12.0;
			if (phase > 90.0) phase += -180.0;
			if (phase >= 0.0) thephase = phase+0.5;
			else thephase = phase-0.5;
			if (thephase < -90) thephase = -90;
			if (thephase > 90) thephase = 90;
		}
	}

theint

Thesigma 

Thesigma

Thephase

myatan

	short line,samp	

	short xsize,ysize	

	int thephase	

	extended a		

	extended b		

	extended phase	

	scale = 255.0 / (max-min);
	for (line=0; line<ysize; line++) {
		for (samp=0; samp<xsize; samp++) {
			get the 10 compressed bytes for pixel (samp,line)

			a = real component of HHVV*

			b = imaginary component of HHVV*


			/* -- calculate phase -- */
			phase = myatan (b,a);   // 0 -> 2*PI

			/* -- convert phase to 0->255 -- */
			phase *= 40.58451049;
			theint = phase;
			if (theint>255) theint = 255;
			if (theint<  0) theint = 0;

			/* -- calculate phase in degrees/2 -- */
			phase *= 0.705882352;
			if (phase > 90.0) phase += -180.0;
			if (phase >= 0.0) thephase = phase+0.5;
			else thephase = phase-0.5;
			if (thephase < -90) thephase = -90;
			if (thephase > 90) thephase = 90;
		}
	}

theint

Thephase

	short line,samp	

	short xsize,ysize	

	int theint		

	int theCC		

	extended a		

	extended b		

	extended r		

	extended value	

	scale = 255.0 / (max-min);
	for (line=0; line<ysize; line++) {
		for (samp=0; samp<xsize; samp++) {
			get the 10 compressed bytes for pixel (samp,line)

			a = real component of HHVV* or HHHV* or HVVV*

			b = imaginary component of HHVV* or HHHV* or HVVV*


			r = sqrt(a*a + b*b);

			value = HH or HV

			if (value > 0.0) r /= sqrt(value);
			else r = 0.0;

			value = VV or HV 

			if (value > 0.0) r /= sqrt(value);
			else r = 0.0;

			theint = 255.0*r;
			if (theint > 255) theint = 255;
			if (theint < 0  ) the int = 0;

			theCC = 100*r;
			if (theCC > 100) theCC = 100;
			if (theCC > 0  ) theCC = 0;
		}
	}

theint

TheCC

	Rect rect		

	Rect line		

	int y			

	int averaging	

	int uly		

	if selected area is a rectangle

		y = (rect.top + rect.bottom)/2;
	else if selected area is a line

		y = (line.top + line.bottom)/2;
	y = y*averaging + uly

	extended nearrange	

	extended altitude		

	extended incidence_angle

	extended groundrange	

	extended slantrange	

	extended rspace		

	int y				

	if ground range projection
 {
		if (nearrange <= altitude) incidence_angle = -1.0;
		else {
			groundrange = sqrt (nearrange*nearrange-altitude*
				altitude)
			groundrange += rspace*(extended)y
			incidence_angle = atan (groundrange/altitude);
		}
	} else {
		slantrange = nearrange + rspace*(extended)y;
		if (slantrange <= altitude) incidence_angle = -1.0;
		else {
			incidence_angle = acos (altitude/slantrange);
		}
	}

rect

	Rect rect			

	long count			

	extended sum_angle	

	extended incidence_angle

	short line			

	short sample		

	count = 0;
	sum_angle = 0;
	for (line=rect.top; line<=rect.bottom; line++) {
		incidence_angle = calculated incidence angle for line

			y = line*averaging + uly

		for (sample=rect.left; sample<=sample.right; sample++) {
			if (incidence_angle != -1.0 && 
			    sta_PtInRegion(sample, line)) {
				count++;
				sum_angle += incidence_angle;
			}
		}
	}
	if (count > 0) incidence_angle = sum_angle/(extended)count;

sta_PtInRegion 

((rect.right + rect.left)/2, (rect.top + rect.bottom)/2)

rect

TP, HH, HV, VV, RL, RR, |HHVV*|, |HHHV*|, |HVVV*|

	short line,samp	

	Rect theframe	-

	extended value	

	extended mean	

	extended stddev	

	extended relstddev

	int n 		

	mean = stddev = 0.0;
	n = 0;
	for (line=theFrame.top; line<=theFrame.bottom; line++) {
		for (samp=theFrame.left; samp<=theFrame.right; samp++) {
			if (sta_PtInRegion(samp, line)) {
				get the 10 compressed bytes for 

				   pixel (samp,line)

				value = parameter being calculated 

				   (e.g. HH or |HHVV*|)

				if (value < 0.0) value = 0.0;
				mean += value;
				stddev += value*value;
				n++;
			}
		}
	}
	if (n > 0) {
		mean /= (extended)n;
		stddev /= (extended)n;
		stddev -= mean*mean;
		stddev = (stddev > 0.0) ? sqrt(stddev) : 0.0;
		relstddev = (mean != 0.0) ? (mean+stddev)/mean : 0.0;
	}

HHVV* phase, HHHV* phase, HVVV* phase

	short line,samp	

	Rect theframe	

	extended a		

	extended b		

	extended suma	

	extended sumb	

	extended mean	

	extended stddev	

	int n 		

	suma = sumb = 0.0;
	n = 0;
	for (line=theFrame.top; line<=theFrame.bottom; line++) {
		for (samp=theFrame.left; samp<=theFrame.right; samp++) {
			if (sta_PtInRegion(samp, line)) {
				get the 10 compressed bytes for 

				   pixel (samp,line)

				a = real component of, say, HHVV*

				b = imaginary component of, say, HHVV*

				suma += a;
				sumb += b;
				n++;
			}
		}
	}
	mean = atan2(sumb,suma); // -PI -> PI
	mean *= 57.29577951;     // -180 -> 180

	short line,samp	

	Rect theframe	

	extended a		

	extended b		

	extended mean	

	extended stddev	

	extended phase	

	int n 		

	stddev = 0.0;
	for (line=theFrame.top; line<=theFrame.bottom; line++) {
		for (samp=theFrame.left; samp<=theFrame.right; samp++) {
			if (sta_PtInRegion(samp, line)) {
				get the 10 compressed bytes for 

				   pixel (samp,line)

				a = real component of, say, HHVV*

				b = imaginary component of, say, HHVV*

				phase = atan2 (b,a);   // -PI -> PI
				phase *= 57.29577951;  // -180 -> 180 deg
				phase = mean - phase;
				if (phase < 0.0) phase = -phase;
				if (360.0-phase < phase) phase = 360-phase;
				stddev += phase*phase;
			}
		}
	}
	if (n > 0) {
		stddev /= (extended)n;
		stddev = (stddev > 0.0) ? sqrt(stddev) : 0.0;
	}

Correlation coefficient

	short line,samp	

	Rect theframe	

	extended a		

	extended b		

	extended meana	

	extended meanb	

	int n 		

	suma = sumb = 0.0;
	n = 0;
	for (line=theFrame.top; line<=theFrame.bottom; line++) {
		for (samp=theFrame.left; samp<=theFrame.right; samp++) {
			if (sta_PtInRegion(samp, line)) {
				get the 10 compressed bytes for 

				   pixel (samp,line)

				a = real component of HHVV*, HHHV*, or HVVV*

				b = imag component of HHVV*, HHHV*, or HVVV*

				meana += a;
				meanb += b;
				n++;
			}
		}
	}
	meana /= (extended)n;
	meanb /= (extended)n;

	if (meanHH != 0.0 && meanVV != 0.0)
		meanCC = sqrt(meana*meana+meanb*meanb)/
		         sqrt(meanHH)/sqrt(meanVV);
	else 
		meanCC = 0.0;

Now the relative standard deviation of the correlation coefficient is calculated as 
follows:

	short line,samp	

	Rect theframe	

	extended a		

	extended b		

	extended meanCC	

	extended stddev	

	extended relstddev

	extended value	

	extended r		

	int n 		

	stddev = 0.0;
	for (line=theFrame.top; line<=theFrame.bottom; line++) {
		for (samp=theFrame.left; samp<=theFrame.right; samp++) {
			if (sta_PtInRegion(samp, line)) {
				get the 10 compressed bytes for 

				   pixel (samp,line)

				a = real component of, say, HHVV*

				b = imaginary component of, say, HHVV*

				r = sqrt(a*a+b*b);

				value = HH

				if (value > 0.0) r /= sqrt(value);
				else r = 0.0;

				value = VV

				if (value > 0.0) r /= sqrt(value);
				else r = 0.0;

				stddev += r*r;
			}
		}
	}
	if (n > 0) {
		stddev /= (extended)n;
		stddev -= meanCC*meanCC;
		stddev = (stddev > 0.0) ? sqrt(stddev) : 0.0;
		relstddev = (meanCC != 0.0) ? (meanCC+stddev)/meanCC :



0;


}

Incidence Angle

Histogram Generation

	extended hist[256]	

	short i			

	extended value		

	int theInt			

	extended total		

	for (i=0; i<256; i++) hist[i] = 0.0;
	while looping over selected region
 {
		if current pixel is in selected region
 {
			value = TP, HH, etc. or |HHVV*|, etc. as

				appropriate

			theInt = (value > 0.0) ? 10.0 * log10 (value) :
				-100;
			if (theInt > 99) theInt = 99;
			if (theInt < -100) theInt = -100;
			hist[intInt] ++;
		}
	}
	total = 0.0;
	for (i=0; i<256; i++) total += hist[i];
	for (i=0; i<256; i++) hist[i] /= total;

	extended hist[256]	

	short i			

	extended phase		

	int theInt			

	extended total		

	for (i=0; i<256; i++) hist[i] = 0.0;
	while looping over selected region
 {
		if current pixel is in selected region
 {
			phase = HHVV* phase (0 -> 2

)

			phase *= 28.64788976; // rad -> deg
			if (phase > 90.0) phase -= 180.0;
			theInt = phase;
			if (theInt < -90) theInt = -90;
			if (theInt >  90) theInt = 90;
			hist[intInt+90] ++;
		}
	}
	total = 0.0;
	for (i=0; i<256; i++) total += hist[i];
	total *= 2.0;
	for (i=0; i<256; i++) hist[i] /= total;

	extended hist[256]	

	short i			

	extended r			

	int theInt			

	extended total		

	for (i=0; i<256; i++) hist[i] = 0.0;
	while looping over selected region
 {
		if current pixel is in selected region
 {
			r = correlation coefficient (0.0->1.0)

			r *= 100; // 0.0 -> 100.0
			theInt = r;
			if (theInt < 0) theInt = 0;
			if (theInt > 100 theInt = 100;
			hist[intInt]++;
		}
	}
	total = 0.0;
	for (i=0; i<256; i++) total += hist[i];
	total *= 0.01;
	for (i=0; i<256; i++) hist[i] /= total;

Mouse Tracking

	extended value		

	extended valueDB		

	int theInt			

	signed char outByte	

	valueDB = (value > 0.0) ? 10.0 * log10 (value) : -100.0;
	theInt = (valueDB > 0.0) ? valueDB + 0.5 : value - 0.5;
	if (theInt < -99) theInt = -100;
	if (theInt > 99) theInt = 99;
	outByte = (signed char)theInt;

valueDB

outByte

	extended phase		

	extended phaseDeg		

	int theInt			

	signed char outByte	

	phaseDeg = phase * 28.64788972;
	if (phaseDeg > 90.0) phaseDeg += (-180.0);
	theInt = (phaseDeg >= 0.0) ? phaseDeg+0.5 : phaseDeg-0.5;
	if (theInt < -90) theInt = -90;
	if (theInt > 90) theInt = 90;
	outByte = (signed char)theInt;

outByte

	extended r			

	extended rBig		

	int theInt			

	signed char outByte	

	rBig = r*100.0;
	if (rBig > 100.0) rBig = 100.0;
	if (rBig < 0.0) rBig = 0.0;
	theInt = rBig + 0.5;
	outByte = (signed char)theInt;

outByte

Overlaid Values

outByte

outByte

outByte

Byte Images

theFrame

	short line		

	short samp		

	int n			

	Rect theFrame	

	extended mean	

	extended stddev	

	int theint		

	extended x		

	n = 0;
	mean = stddev = 0.0;
	for (line=theFrame.top; line<=theFrame.bottom; line++) {
		for (samp=theFrame.left;samp=theFrame.right; samp++) {
			if (sta_PtInRegion(samp, line)) {
				n++;
				theint = pixel value
 & 255;
				x = (extended)theint;
				mean += x;
				stddev += x*x;
			}
		}
	}
	if (n > 0) {
		mean /= (extended)n;
		stddev = stddev/(extended)n - mean*mean;
		stddev = (stddev > 0.0) ? sqrt(stddev) : 0.0;
	}

sta_PtInRegion()

pixel value

pixel value

Histogram Generation

	extended hist[256]	

	short i			

	int theInt			

	extended total		

	for (i=0; i<256; i++) hist[i] = 0.0;
	while looping over selected region
 {
		if current pixel is in selected region
 {
			theInt = byte image value

			intInt = theInt & 255;
			hist[intInt] += 1.0;
		}
	}
	total = 0.0;
	for (i=0; i<256; i++) total += hist[i];
	for (i=0; i<256; i++) hist[i] /= total;

Data to the Macintosh

Data Transfer

Data Reduction

             <<< Reduce >>>

Enter input data file name -->
dud2:[data]cm3181l.dat


Enter input file physical record length (bytes) -->
10240


Samples in input file:         1024
Lines in input file:           1279

Enter width and height of output data 
(width must be multiple of 256) -->
256, 256


Enter amount of averaging (1..4)
(e.g. N = average every NxN pixels) -->
4


Enter x,y of upper left corner
((0,0)=uppermost left pixel) -->
0,0


Enter output file name -->
dud2:[data]cm3181l.small


Enter output file physical record length (bytes) -->
512


Writing variable header...

Storing old header...

Writing file...

line           0
...
line        1020
...done

dud2:[data]cm3181l.dat

10240

256, 256

4

0,0

dud2:[data]cm3181l.small

512

"Reduce.for" Program Listing

cccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
c
c	PROGRAM:	reduce.for
c	AUTHORS:	Lynne Norikane
c	  		Howard Zebker
c
c	DESCRIPTION:
c
c	This program program allows you to store a subset
c	and/or averaged down version of an "original" JPL
c	AIRSAR data set into a separate file.  "Original"
c	implies that the geometry of the data is the same
c	as that of the original processor output.
c
c	The AIRSAR data MUST have both a variable format
c	header and an "old" header.
c
c	Variable format header fields 14 through 16 are
c	used to store the upper left (x,y) coordinates and
c	the averaging.  Note that this program will
c	overwrite anything which may already exist in
c	those fields.
c
c	The upper left corner of the original data set
c	corresponds to coordinate (0,0).
c
c	COPYRIGHT
c
c	Copyright (c) 1992, 1993, California Institute of
c	Technology.  All rights Reserved.  U.S. Government
c	Sponsorship under NASA Contract NAS7-918 is
c	acknowledged.
c
ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc

	program reduce

	implicit none

	character*40	file
	character*10	cbyte

	byte		b(10,1024,4)
	byte		b2(10240,4)
	byte		bb(10240)
	byte		a(10)
	byte		oldhead(10240)

	equivalence	(b, b2)

	real		xxx(-50:50,-127:127)
	real		expscale

	common		b,xxx

	logical		exists

	integer		ichan,ochan
	integer		inreclen, outreclen
	integer		i,j,k,l,jj
	integer		iheadlines, ivarlines
	integer		iw, ih, isub
	integer		ix, iy
	integer		inoff, outoff
	integer		ibytesoldhead
	integer		ibytesdata
	integer		ireclen
	integer		icount

	common /header/	xxreclen,		! bytes per record
     +				xxhead,		! number of header lines
     +				xxsamp,		! number of samples per record
     +				xxline,		! number of lines in image
     +				xxbytesamp,		! bytes per sample
     +				xxversion,		! processor version number
     +   			xxdatatype,		! data type
     +				xxprojection,	! slant/ground range proj.
     +				xxrspace,		! range pixel spacing
     +				xxazspace,		! azimuth pixel spacing
     +				xxbytesoldhead,	! byte offset to old header
     +				xxbytesuserhead,	! byte offset to user header
     +				xxbytesdata		! byte offset to data

	integer*4 	xxreclen
	integer*4	xxhead
	integer*4	xxsamp
	integer*4	xxline
	integer*4	xxbytesamp
	integer*4	xxbytesoldhead
	integer*4 	xxbytesuserhead
	integer*4	xxbytesdata

	real*4    		xxversion
	real*4		xxrspace
	real*4		xxazspace

	character*20 	xxprojection
	character*20	xxdatatype

c	WELCOME

	type *
	type *,'             <<< Reduce >>>'
	type *

C	GET INPUT DATA FILE NAME

100	type *,'Enter input data file name --> '
	accept '(a)',file
	type *

C	SEE IF INPUT DATA FILE EXISTS

	inquire (file=file,exist=exists)
	if (.not.exists) then
	   type *, '*** ERROR - input file does not exist ***'
	   type *
	   stop
	end if

C	GET THE INPUT FILE RECORD LENGTH

	type *,'Enter input file physical record length (bytes) --> '
	accept *, inreclen
	type *

C	OPEN INPUT DATA FILE

	ichan = 40
	open (ichan, file=file, status='old', readonly,
     +     form='unformatted', access='direct', recl=inreclen/4)

C	GET THE INPUT FILE VARIABLE HEADER

	call readheadshort (ichan, inreclen)
	ibytesoldhead = xxbytesoldhead
	ibytesdata = xxbytesdata
	ireclen = xxreclen
	type *,'Samples in input file: ',xxsamp
	type *,'Lines in input file:   ',xxline
	type *

C	GET OUTPUT FILE SPECIFICATIONS

200	type *,'Enter width and height of output data set'
	type *,'(width must be multiple of 256) --> '
	accept *,iw,ih
	type *
	if (iw.lt.256.or.mod(iw,256).ne.0.or.iw.gt.xxsamp) then
	   type *,'*** ERROR - Width must be a multiple of 256 ***'
	   type *
	   goto 200
	end if
	if (ih.lt.1.or.ih.gt.xxline) then
	   type *,' *** ERROR - Height must be between 1 and ',
     +		xxline,' ***'
	   type *
	   goto 200
	end if

400	type *,'Enter amount of averaging (1..4)'
     	type *,'(e.g. N = average every NxN pixels) --> '
	accept *,isub
	type *
	if (isub.lt.1) then
	   type *,'** INPUT ERROR ** Averaging must be >= 1'
	   type *
	   goto 400
	end if
	if (isub.gt.4) then
	   type *,'** INPUT ERROR ** Averaging must be <= 4'
	   type *
	   goto 400
	end if
	if (isub*iw.gt.xxsamp) then
	   type *,' ** INPUT ERROR ** Width times averaging is > ',
     +		xxsamp
	   goto 200
	end if
	if (isub*ih.gt.xxline) then
	   type *,' ** INPUT ERROR ** Height times averaging is > ',
     +		xxline
	   goto 200
	end if

300	type *,'Enter x,y of upper left corner'
        type *,'((0,0)=uppermost left pixel) --> '
	accept *,ix,iy
	type *
	if (ix.lt.0.or.iy.lt.0)
     +	   type *,'** INPUT ERROR ** X and y must be >= 0'
	if (ix.lt.0.or.iy.lt.0) goto 300
	if (ix.gt.xxsamp-iw*isub) then
           type *,'** INPUT ERROR ** X is too large for the requested'
	   type *,'                  image'
	   type *
	   goto 300
	end if
	if (iy.gt.xxline-ih*isub) then
           type *,'** INPUT ERROR ** Y is too large for the requested'
	   type *,'                  image'
	   type *
	   goto 300
	end if

C	GET OUTPUT FILE NAME

500	continue
	type *,'Enter output file name --> '
	accept '(a)', file
	type *

C	GET THE OUTPUT FILE RECORD LENGTH

	type *,'Enter output file physical record length (bytes) --> '
	accept *, outreclen
	type *

C	OPEN NEW FILE

	ochan = 41
	open (ochan, file=file, form='unformatted',
     +     status='unknown', access='direct', recl=outreclen/4)

C	STORE VARIABLE FORMAT HEADER

	iheadlines = 1023/(iw*10)+8191/(iw*10)+2
	ivarlines  = 1023/(iw*10)+1

	xxreclen = iw * 10
	xxhead = iheadlines
	xxsamp = iw
	xxline = ih
	xxbytesamp = 10
	xxbytesoldhead = ivarlines*iw*10
	xxbytesuserhead = 0		! ASSUME NO USER HEADER!!!!
	xxbytesdata = iheadlines*iw*10

	call writehead (ochan,ix,iy,isub,outreclen)
	type *

C	STORE OLD HEADER

	type *,'Storing old header...'
	inoff = (ibytesoldhead-1) /inreclen+1
	outoff= (xxbytesoldhead-1)/outreclen+1
	do i = 1, 8191/inreclen+1
	   read  (ichan, rec=i+inoff) 
     +        (oldhead(j),j=(i-1)*inreclen+1,i*inreclen)
	end do
	do i = 1, 8191/outreclen+1
	   write (ochan, rec=i+outoff) 
     +        (oldhead(j),j=(i-1)*outreclen+1,i*outreclen)
	end do
	type *

C	STORE DATA

	if (isub.ne.1) then
	   do i = -50,50
	      expscale=2.**i
	      do j = -127,127
		 xxx(i,j)=(j/254.+1.5)*expscale
	      end do
	   end do
	end if

	type *,'Writing file...'
	type *

	inoff  = (ibytesdata-1) /inreclen+1+iy*((ireclen-1)/inreclen+1)
	outoff = (xxbytesdata-1)/outreclen+1

	do i = iy,iy+ih*isub-1,isub
	   if (mod(i,10).eq.0) type *, 'line', i
	   do j = 1,isub
	      do k = 1, (ireclen-1)/inreclen+1
	         read (ichan, rec=k+inoff) 
     +              (b2(l,j),l=(k-1)*inreclen+1,k*inreclen)
	      end do
	      inoff = inoff + (ireclen-1)/inreclen+1
	   end do
	   icount = 0
	   if (isub.eq.1) then
	      do j = ix,ix+iw-1
	         do jj = 1,10
		    icount = icount + 1
		    bb(icount) = b(jj,j+1,1)
	         end do
	      end do
	   else
	      do j = ix,ix+iw*isub-1,isub
		 call average (j,a,isub)
		 do jj = 1,10
		    icount = icount + 1
		    bb(icount) = a(jj)
		 end do
	      end do
	   end if
	   do k = 1, (xxreclen-1)/outreclen+1
	      write (ochan, rec=k+outoff)
     +           (bb(l),l=(k-1)*outreclen+1,k*outreclen)
	   end do  
	   outoff = outoff + (xxreclen-1)/outreclen+1
	end do

	type *,'...done'
	type *

	end

cccccccccccccccccccccccccccccccccccccccccccccccccccccc
c
c	AVERAGE
c
c	This subroutine uncompresses the 10 bytes
c	stored in the common array b to form a Stokes
c	matrix.  The parameter isub indicates how much
c	averaging is to be done.  The input parameter
c	ix indicates the starting pixel for averaging
c	(the first pixel = 0).  The array a contains the
c	compressed results.
c
ccccccccccccccccccccccccccccccccccccccccccccccccccccccccc

	subroutine average (ix,a,isub)

	implicit none

	integer		i,j,ii,jj
	integer		ix, isub
	integer		iexp, imant
	integer		i12, i33, i44, i13, i14, i23,  i24, i34
	byte			a(10)
	byte			b(10,1024,4)
	real			xxx(-50:50,-127:127)
	common		b,xxx

	real		p(4,4),sump(4,4),ph11
	real		alog2
	real		scale, sca
	real		exp

	alog2 = alog10(2.0)

c	CLEAR STOKES MATRIX

	do i = 1,4
	   do j = 1,4
	      sump(i,j) = 0
	   end do
	end do

c	DECOMPRESS AND ACCUMULATE

	do i = ix,ix+isub-1
	   do j = 1,isub	
	      call pmatrix(b(1,i+1,j),p)
	      do ii=1,4
		 do jj=1,4
		    sump(ii,jj) = sump(ii,jj)+p(ii,jj)
		 end do
	      end do
	   end do
	end do

c	AVERAGE

	do i = 1,4
	   do j = 1,4
	      sump(i,j) = sump(i,j)/(isub*isub)
	   end do
	end do

c	RECOMPRESS

	do i = 1, 10
	   a(i) = 0
	end do

	scale = sump(1,1)

	if (scale.gt.0.0) then

	   exp = alog10(scale)/alog2
	   iexp = exp
	   if (exp.lt.0) iexp = exp-1
	   imant = nint((scale*2.0**(-iexp)-1.5)*254.0)

	   sca = xxx(iexp,imant)/127.

	   if (sca.gt.0) then

	      ph11 = xxx(iexp,imant)
	      sump(1,3) = sign(sqrt(abs(sump(1,3))/ph11),sump(1,3))
	      sump(1,4) = sign(sqrt(abs(sump(1,4))/ph11),sump(1,4))
	      sump(2,3) = sign(sqrt(abs(sump(2,3))/ph11),sump(2,3))
	      sump(2,4) = sign(sqrt(abs(sump(2,4))/ph11),sump(2,4))
		 
	      i12 = nint(sump(1,2)/sca)
	      i33 = nint(sump(3,3)/sca)
	      i44 = nint(sump(4,4)/sca)
	      i13 = nint(sump(1,3)*127.)
	      i14 = nint(sump(1,4)*127.)
	      i23 = nint(sump(2,3)*127.)
	      i24 = nint(sump(2,4)*127.)
	      i34 = nint(sump(3,4)/sca)

	      a(1) = iexp
	      a(2) = imant
	      a(3) = i12
	      a(4) = i13
	      a(5) = i14
	      a(6) = i23
	      a(7) = i24
	      a(8) = i33
	      a(9) = i34
	      a(10) = i44

	   end if

        end if

	end

ccccccccccccccccccccccccccccccccccccccccc
c
c	PMATRIX
c
c	This subroutine uncompresses the
c	10 bytes to form the 4x4 real
c	Stokes matrix.
c
ccccccccccccccccccccccccccccccccccccccccc

	subroutine pmatrix (data,p)

	implicit none

	real 		p(4,4)
	real		sc, r
	byte 		data(10)

	byte		b(10,1024,4)
	real		xxx(-50:50,-127:127)
	common	b,xxx

	sc = xxx(data(1),data(2))/127.
	p(1,1) = 127*sc
	p(1,2) = data(3)*sc
	r = data(4)
	p(1,3) = sign(r*r,r)*sc/127.
	r = data(5)
	p(1,4) = sign(r*r,r)*sc/127.
	p(2,1) = p(1,2)
	r = data(6)
	p(2,3) = sign(r*r,r)*sc/127.
	r = data(7)
	p(2,4) = sign(r*r,r)*sc/127.
	p(3,1) = p(1,3)
	p(3,2) = p(2,3)
	p(3,3) = data(8)*sc
	p(3,4) = data(9)*sc
	p(4,1) = p(1,4)
	p(4,2) = p(2,4)
	p(4,3) = p(3,4)
	p(4,4) = data(10)*sc
	p(2,2) = p(1,1)-p(3,3)-p(4,4)

	return
	end

ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
c
c  READHEADSHORT -- 
c 	This subroutine decodes the variable data header used
c	by JPL Aircraft data output products as described
c	below and saves the results in a common block.
c
c  Version 1.1  
c  by Howard Zebker, Lynne Norikane
c  14-AUG-89
c
c  This subroutine should be used to decode the variable data header
c  which exists at the beginning of each JPL Aircraft data output
c  product.  The header exists at the beginning of the file and is
c  composed of 20 50-byte ASCII fields.  The format of each field is as
c  follows:
c
c     Byte 1                                            Byte 50
c     DESCRIPTIVE TEXT  -- blanks (ascii 32) -- NUMERICAL VALUE
c
c  The descriptive text is left justified, and the numerical values are
c  right justified.  Intermediate characters are assumed to be blanks.
c
c  The fields contained in the header are as follows:
c
c	field	contents
c	-----   --------
c	1  	RECORD LENGTH IN BYTES =                   XXXXXXXX
c	2	NUMBER OF HEADER RECORDS =                 XXXXXXXX
c	3	NUMBER OF SAMPLES PER RECORD =             XXXXXXXX
c	4	NUMBER OF LINES IN IMAGE =                 XXXXXXXX
c	5	NUMBER OF BYTES PER SAMPLE =               XXXXXXXX
c	6	JPL AIRCRAFT SAR PROCESSOR VERSION            XX.XX
c	7	DATA TYPE =                       CCCCCCCCCCCCCCCCC
c	8	RANGE PROJECTION =                           CCCCCC
c	9	RANGE PIXEL SPACING (METERS) =            XXXX.XXXX
c	10	AZIMUTH PIXEL SPACING (METERS) =          XXXX.XXXX
c	11	BYTE OFFSET OF OLD HEADER =                XXXXXXXX
c	12	BYTE OFFSET OF USER HEADER =               XXXXXXXX
c	13	BYTE OFFSET OF FIRST DATA RECORD =         XXXXXXXX
c	14-20   TBD
c
c  where 'X's are replaced by numerical values and 'C's are replaced by
c  character strings.
c
c  This implementation returns all of the header information in the
c  common block. 
c
ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc

	subroutine readheadshort (ichan, reclen)

	implicit none

	common /header/	ireclen,	! bytes per record
     +				nhead,	! number of header lines
     +				nsamp,	! number of samples per record
     +				nline,	! number of lines in image
     +				nbytesamp,	! bytes per sample
     +				version,	! processor version number
     +   			datatype,	! data type
     +				projection,	! slant/ground range projection
     +				rspace,	! range pixel spacing
     +				azspace,	! azimuth pixel spacing
     +				ibytesoldhead,	! byte offset to old header
     +				ibytesuserhead,	! byte offset to user header
     +				ibytesdata	! byte offset to data

	integer*4	ireclen
	integer*4	nhead
	integer*4	nsamp
	integer*4	nline
	integer*4	nbytesamp
	integer*4	ibytesoldhead
	integer*4 	ibytesuserhead
	integer*4	ibytesdata	
	integer	reclen
	integer	i,j
	integer	ichan

	real*4    	version
	real*4	rspace
	real*4	azspace

	character*20 	projection
	character*20	datatype
	character*20	tt

	byte		head(10240)
	byte		t(25)

	equivalence (t,tt)

c  READ HEADER (1024 BYTES)

	do i = 1, 1023/reclen+1
	   read (ichan,rec=i) (head(j),j=(i-1)*reclen+1,i*reclen)
	end do

c  STRIP INTEGER VALUES FIRST

	decode(8,'(i8)',head(1*50-7))ireclen
	decode(8,'(i8)',head(2*50-7))nhead
	decode(8,'(i8)',head(3*50-7))nsamp
	decode(8,'(i8)',head(4*50-7))nline
	decode(8,'(i8)',head(5*50-7))nbytesamp

	decode(8,'(i8)',head(11*50-7))ibytesoldhead
	decode(8,'(i8)',head(12*50-7))ibytesuserhead
	decode(8,'(i8)',head(13*50-7))ibytesdata

c  STRIP REAL VALUES

	decode(8,'(f9.0)',head(6*50-8))version
	decode(8,'(f9.0)',head(9*50-8))rspace
	decode(8,'(f9.0)',head(10*50-8))azspace

c  STRIP CHARACTER VALUES

	do i=1,20
	   t(i)=head(8*50-20+i)
	end do
	projection=tt

	do i=1,20
	   t(i)=head(7*50-20+i)
	end do
	datatype=tt

	return

	end

cccccccccccccccccccccccccccccccccccccccccccccccccccccc
c
c  WRITEHEAD - 
c	This subroutine writes the variable data header used
c	by JPL Aircraft data output products.  It uses the
c	values stored in the variables in the common block.
c	It also adds the x,y offset and amount
c	of averaging to the header.
c
c  < see comments from READHEADSHORT >
c
c  THIS SUBROUTINE DOES NOT STORE THE OLD HEADER!
c
ccccccccccccccccccccccccccccccccccccccccccccccccccccccccc

	subroutine writehead (outchan,iulx,iuly,iavg, reclen)

	implicit none

	common /header/	ireclen,	! bytes per record
     +			nhead,		! number of header lines
     +			nsamp,		! number of samples per record
     +			nline,		! number of lines in image
     +			nbytesamp,		! bytes per sample
     +			version,		! processor version number
     +			datatype,		! data type
     +			projection,		! slant/ground range projection
     +			rspace,		! range pixel spacing
     +			azspace,		! azimuth pixel spacing
     +			ibytesoldhead,	! byte offset to old header
     +			ibytesuserhead,	! byte offset to user header
     +			ibytesdata		! byte offset to data

	integer*4 	ireclen
	integer*4	nhead
	integer*4	nsamp
	integer*4	nline
	integer*4	nbytesamp
	integer*4	ibytesoldhead
	integer*4 	ibytesuserhead
	integer*4	ibytesdata

	integer		outchan
	integer		reclen
	integer		i,j,k
	integer		iulx, iuly, iavg

	real*4		version
	real*4		rspace
	real*4		azspace

	character*20 	projection
	character*20	datatype

	character*50	header(16)
	character*10	string
	character*20	string20

	byte		bheader(50,16)
	byte		oneline(10240)
	byte		bstring(10),bstring20(20)

	equivalence	(header,bheader),(string,bstring),(string20,bstring20)

c	CREATE HEADER

	type *,'Writing variable header...'

	header(1) = 'RECORD LENGTH IN BYTES =                          '
	header(2) = 'NUMBER OF HEADER RECORDS =                        '
	header(3) = 'NUMBER OF SAMPLES PER RECORD =                    '
	header(4) = 'NUMBER OF LINES IN IMAGE =                        '
	header(5) = 'NUMBER OF BYTES PER SAMPLE =                      '
	header(6) = 'JPL AIRCRAFT SAR PROCESSOR VERSION                '
	header(7) = 'DATA TYPE =                                       '
	header(8) = 'RANGE PROJECTION =                                '
	header(9) = 'RANGE PIXEL SPACING (METERS) =                    '
	header(10) = 'AZIMUTH PIXEL SPACING (METERS) =                  '
	header(11) = 'BYTE OFFSET OF OLD HEADER =                       '
	header(12) = 'BYTE OFFSET OF USER HEADER =                      '
	header(13) = 'BYTE OFFSET OF FIRST DATA RECORD =                '
	header(14) = 'UPPER LEFT CORNER X (0-1023) =                    '
	header(15) = 'UPPER LEFT CORNER Y (0-1023) =                    '
	header(16) = 'AVERAGING (1,2,4) =                               '

c	SAVE RECORD LENGTH IN BYTES

	encode (10,'(i10)',string) ireclen
	do i = 1,8
	   bheader(i+42,1) = bstring(i+2)
	end do

c	SAVE NUMBER OF HEADER LINES

	encode (10,'(i10)',string) nhead
	do i = 1,8
	   bheader(i+42,2) = bstring(i+2)
	end do

c	SAVE NUMBER OF SAMPLES

	encode (10,'(i10)',string) nsamp
	do i = 1,8
	   bheader(i+42,3) = bstring(i+2)
	end do

c	SAVE NUMBER OF LINES

	encode (10,'(i10)',string) nline
	do i = 1,8
	   bheader(i+42,4) = bstring(i+2)
	end do

c	SAVE NUMBER OF BYTES PER SAMPLE

	encode (10,'(i10)',string) nbytesamp
	do i = 1,8
	   bheader(i+42,5) = bstring(i+2)
	end do

c	SAVE SAR PROCESSOR VERSION NUMBER

	encode (10,'(f10.4)',string) version
	do i = 1,9
	   bheader(i+41,6) = bstring(i+1)
	end do

c	SAVE DATA TYPE

	string20(1:20) = datatype(1:20)
	do i = 1,20
	   bheader(i+30,7) = bstring20(i)
	end do

c	SAVE PROJECTION

	string20(1:20) = projection(1:20)
	do i = 1,20
	   bheader(i+30,8) = bstring20(i)
	end do

c	SAVE RANGE PIXEL SPACING

	encode (10,'(f10.4)',string) rspace
	do i = 1,9
	   bheader(i+41,9) = bstring(i+1)
	end do

c	SAVE AZIMUTH PIXEL SPACING

	encode (10,'(f10.4)',string) azspace
	do i = 1,9
	   bheader(i+41,10) = bstring(i+1)
	end do

c	SAVE BYTE OFFSET TO OLD HEADER

	encode (10,'(i10)',string) ibytesoldhead
	do i = 1,8
	   bheader(i+42,11) = bstring(i+2)
	end do

c	SAVE BYTE OFFSET TO USER HEADER

	encode (10,'(i10)',string) ibytesuserhead
	do i = 1,8
	   bheader(i+42,12) = bstring(i+2)
	end do

c	SAVE BYTE OFFSET TO DATA

	encode (10,'(i10)',string) ibytesdata
	do i = 1,8
	   bheader(i+42,13) = bstring(i+2)
	end do

c	SAVE UPPER LEFT CORNER X

	encode (10,'(i10)',string) iulx
	do i = 1,8
	   bheader(i+42,14) = bstring(i+2)
	end do

c	SAVE UPPER LEFT CORNER Y

	encode (10,'(i10)',string) iuly
	do i = 1,8
	   bheader(i+42,15) = bstring(i+2)
	end do

c	SAVE AVERAGING

	encode (10,'(i10)',string) iavg
	do i = 1,8
	   bheader(i+42,16) = bstring(i+2)
	end do

c	WRITE HEADER TO FILE

	do i = 1,1024
	   oneline(i) = 32
	end do

	k = 1
	do i = 1,16
	   do j = 1,50
	      oneline(k) = bheader(j,i)
	      k = k + 1
	   end do
	end do

	do i = 1, 1023/reclen+1
	   write (outchan, rec=i) (oneline(j),j=(i-1)*reclen+1,i*reclen)
	end do

	return

	end

	

Format Header

             Column numbers:
      Field  12345678901234567890123456789012345678901234567890

        1    RECORD LENGTH IN BYTES =                  NNNNNNNN
        2    NUMBER OF HEADER RECORDS =                NNNNNNNN
        3    NUMBER OF SAMPLES PER RECORD =            NNNNNNNN
        4    NUMBER OF LINES IN IMAGE =                NNNNNNNN
        5    NUMBER OF BYTES PER SAMPLE =              NNNNNNNN
        6    JPL AIRCRAFT SAR PROCESSOR VERSION       XXXX.XXXX
        7    DATA TYPE =                             CCCCCCCCCC
        8    RANGE PROJECTION =                          CCCCCC
        9    RANGE PIXEL SPACING (METERS) =           XXXX.XXXX
        10   AZIMUTH PIXEL SPACING (METERS) =         XXXX.XXXX
        11   BYTE OFFSET OF OLD HEADER =               NNNNNNNN
        12   BYTE OFFSET OF USER HEADER =              NNNNNNNN
        13   BYTE OFFSET OF FIRST DATA RECORD =        NNNNNNNN
        14   UPPER LEFT CORNER X (0-1023) =            NNNNNNNN
        15   UPPER LEFT CORNER Y (0-1023) =            NNNNNNNN
        16   AVERAGING (1,2,4) =                       NNNNNNNN
        17   (unused)
        18   (unused)
        19   (unused)
        20   (unused)

record length

number of header records

number of samples

number of lines

number of bytes per sample

SAR processor version number

data type

range projection

range pixel spacing

azimuth pixel spacing

byte offset of the old header

byte offset of the user header

byte offset of the data

upper left corner x

upper left corner y

amount of averaging

Field   1:  CORRELATION DATE: 21-MAR-92
Field   2:  NEAR RANGE (METERS):    8963.794
Field   3:  SLANT RANGE PIXEL (M.):  6.662
Field   4:  AZIMUTH PIXEL (M.):      12.16
Field   5:  INCID.ANG.(NEAR RANGE)(DEG.):    23.00957
Field   6:  MULTIPOLARIZATION L-BAND
Field   7:  POLARIZATION = Quad Pol Mode
Field   8:  NUMBER OF ERRORS DETECTED =     0
Field   9:  FIRST FRAME COUNT =         1703204
Field  10:  DISTANCE TO GO         32.0 NAUTICAL MILES
Field  11:  TIME TO GO             4.7 MIN
Field  12:  CROSS TRACK DEV.        0.1 FEET
Field  13:  DESIRED TRACK ANG.   115.3 DEGREES
Field  14:  TRACK ANG. ERROR       0.2 DEGREES
Field  15:  DRIFT ANGLE          -8.1 DEGREES
Field  16:  ALIGN STATUS        34
Field  17:  LAT    52 DEG.18.2 MIN. N.
Field  18:  LONG   5  DEG.10.9 MIN. E.
Field  19:  GROUND SPEED         407 KNOTS
Field  20:  TRACK ANGLE         115.5 DEGREES
Field  21:  TRUE HEADING        123.5 DEGREES
Field  22:  WIND SPEED           83 KNOTS
Field  23:  WIND ANGLE          260 DEGREES
Field  24:  DAY OF YEAR:  166
Field  25:  TIME GMT:   9:38:44
Field  26:  RADAR ALTITUDE (M.):    8250
Field  27:  RADAR ALTITUDE      27069 FEET
Field  28:  AIRCRAFT PITCH        3.3 DEGREES
Field  29:  AIRCRAFT ROLL         -1.0 DEGREES
Field  30:  DIGITAL DELAY      87 MICROSECONDS
Field  31:  MONTH/DAY/YEAR     06/15/91
Field  32:  DIGITAL RUN NUMBER 0 / 0 / 0
Field  33:  DIGITAL REC. WINDOW  66 MICROSECONDS
Field  34:  ANTENNA =          Standard Modes
Field  35:  PRF FREQUENCY IS CONTROLLED BY: INS
Field  36:  TARGET LATITUDE    +52 17.8 DEGREES
Field  37:  TARGET LONGITUDE   +005 32.7 DEGREES
Field  38:  TARGET ELEVATION   0000 FEET
Field  39:  TARGET LOOK ANGLE  45 DEGREES
Field  40:  SCENE TITLE: Flevoland116-1

frequency

near range

altitude

general scale factor

track angle

drift angle