SARINCD

Description

Creates an array segment of incident angles to use with a RADARSAT gain scaling table. This function cannot be used for ASAR images.

Parameters

sarincd(file, orbit, a0seg, incidseg)

Name	Type	Caption	Length
FILE *	str	Input file name	1 -
ORBIT *	List[int]	Input satellite orbital ephemeris segment	1 - 1
A0SEG *	List[int]	Input SAR Offset segment	1 - 1
INCIDSEG	List[int]	Output SAR incident angle segment	0 - 1

* Required parameter

Parameter descriptions

FILE

Specifies the name of the PCIDSK file that contains the orbit segment and SAR Gain array segment to process.

ORBIT

Specifies the input segment that contains the satellite orbital ephemeris data.

The orbital segment is created when the satellite image is read from CD using CDSAR.

A0SEG

Specifies the input array segment that contains the SAR Offset data.

The segment is created when the satellite image is read from CD using CDSAR; it is typically labeled "SAR Offset" or "A0Scale".

INCIDSEG

Upons successful completion of SARINCD, this parameter receives the number of the new array segment of incident angles.

Details

SARINCD produces a table of incident angles that correspond to the table of SAR gain scaling values produced when an image is read from a CD using CDSAR. The input image file (FILE) contains the orbit segment (ORBIT) and the SAR Offset array segment (A0SEG) required as input.

SARINCD is not required for ENVISAT ASAR images. For ASAR images, the incident angle information is extracted from the ESA-format image and stored in the Incident Angle segment by the CDASAR function.

Example

Create an Array Segment of Incidence Angles (incidseg) using asarapp.pix.

from pci.sarincd import sarincd

file	=	'radarbeam2.pix'	# input file
orbit	=	[2]	# input orbit segment
a0seg	=	[3]	# input SAR Offset segment

incidseg =   sarincd ( file, orbit, a0seg )

Algorithm

SARINCD calculates the incident angle for each column required to convert pixel values to the radar backscatter in the SARSIGM function. The incident angles are calculated as follows:

Calculate the earth radius (r) at the image center (start of image for swath products) and the orbit altitude (h).
```
 tan_plat_lat = ( tan(plat_lat * PI/180) )**2

                 sqrt(1 + tan_plat_lat)
 r = ellip_min * ---------------------------------------------- * 1000
                 sqrt(ellip_min**2/ellip_maj**2 + tan_plat_lat)

 h = eph_orb(1) * 1000 - r
```
where:
- tan_plat_lat: an intermediate term in the calculation
- plat_lat: the platform geodetic latitude, in degrees, read from the CEOS "Data Set Summary" record and stored as element 2 in the SAR Offset segment
- PI/180: converts degrees to radians
- ()**2: the square of a value
- r: the radius of the earth at the image center, in meters
- ellip_min: the semi-minor (or polar) axis for the Earth ellipsoid, in kilometers, read from the CEOS "Data Set Summary" record and stored in the ORBIT segment
- sqrt(): the square root of a value
- ellip_maj: the semi-major (or equatorial) axis for the Earth ellipsoid, in kilometers, read from the CEOS "Data Set Summary" record and stored in the ORBIT segment
- h: the orbit altitude, in meters
- eph_orb(1): the first of the equinoctial orbit elements (the semi-major axis of the orbit, in kilometers) read from the CEOS "Detailed Processing Parameters" record and stored as element 3 in the SAR Offset segment
For each image column, calculate the slant range (RSi).

For detected products stored in ground range (not SLC):
```
			 RSi = SRGR(1) + (i * dRg)    * SRGR(2) + (i * dRg)**2 * SRGR(3) 
						   + (i * dRg)**3 * SRGR(4) + (i * dRg)**4 * SRGR(5) 
						   + (i * dRg)**5 * SRGR(6) 
			
```
where:
- RSi: the Slant Range at a given image column, in meters
- SRGR(): the Slant Range/Ground Range coefficients read from the CEOS "Detailed Processing Parameters" record stored as elements 4 to 9 in the SAR Gain segment
- i: the column offset, where (i = 0 to Number of Columns in the image minus one)
- dRg: the pixel width, in meters, read from the CEOS "Data Set Summary" record and stored in the ORBIT segment
- ()**2: the square of a value
- ()**3: the third power of a value
- ()**4: the forth power of a value
- ()**5: the fifth power of a value
For SLC products (stored in slant range):
```
RSi = SRfirst + (i * dRg)
```
where:
- RSi: the Slant Range at a given image column, in meters
- SRfirst: the slant range of the first image pixel of the first scanline, read from the first "Processed Data" record and stored in the ORBIT segment
- i: the column offset, where (i = 0 to Number of Columns in the image minus one)
- dRg: the pixel width, in meters, read from the CEOS "Data Set Summary" record and stored in the ORBIT segment
For each image column, calculate the incident angle (Ii):
```
Ii = acos( (h*h - RSi*RSi + 2*r*h)/(2*RSi*r) ) * 180/PI
```
where:
- Ii: the incident angle at a given column
- acos(): the arccosine function
- h: the orbit altitude, in meters, from Step 1
- RSi: the Slant Range at a given image column, in meters, from Step 2
- r: the radius of the Earth at the image center, in meters, from Step 1
- 180/PI: converts radians to degrees

References

The calculations in the Algorithm come from:

"4.4 Conversion to Sigma Nought" and "Appendix A, Supporting calculations" of Technical Note No. 4.2 CDPF Output Data Calibration", N.W.Shepherd and Associates, February 26, 1996.

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