Extension 2 - Sigma of data

This extension contains the sigma (error) of the data. It replaces the weights extension. The header keyword SIGMADAT must be used to define either a function to calculate sigma, or a pointer to an extension that contains the sigma values.

The relation between sigma and WEIGHTS is:

SIGMA = 1 / sqrt(WEIGHT)

WEIGHT = SIGMA ^ 2

The sigma can be given in one of three ways. However, only the Function method has been implemented so far.

A function

The sigma values can be defined as a function specifying how to calculate the standard deviation sigma of each pixel. The formula should be given as a human-readable string in the header keyword SIGMADAT, e.g.,

SIGMADAT = 'sqrt( data^2 + (2*GAIN*XPOSURE)^2 )',

where data is the pixel value. Header keywords (e.g., XPOSURE) may be used directly in the formula. Since keyword names may contain dashes, actual minus signs in the formula must be surrounded by spaces. To increase the readability and interpretability of the formula, try to avoid using "magical constants" (i.e., add instead descriptive keywords in the header to use in the formula, with comments). If formula parameters are not constant for the entire data cube (e.g., for different readout quadrants), variable keywords can be used (Appendix I). Even the formula itself can be specified as a pixel-to-pixel variable keyword (Appendix I-b)

A curve

If it's not practical to give a formula at all (e.g., if the sigma values as a function of data is discontinuous), it may be specified as a curve in a separate extension using an EXTNAME name that starts with 'CURVE:', e.g.,

SIGMADAT = 'CURVE:SIGMA-TABLE'.

The contents of this extension should be a data cube with dimension [2,n], functioning as a lookup table where (1,*) are data values and (2,*) are the corresponding sigma values. The table is subject to linear interpolation. The sigma values may also be specified on a pixel-by-pixel basis.

Pixel-by-pixel representation

If it is necessary to specify sigma directly for each individual pixel, values can be specified in an extension with an EXTNAME that starts with 'VALUES:', e.g.,

SIGMADAT``='VALUES:SIGMA-VALUES'.

The extension should have the same dimensions as the original data.

Data cube

The dimension of the data cube depends on the method used.

A function

No extension.

A curve

• 2, n

Pixel-by-pixel representation

• Lambda, X, Y, Time

General Keywords

EXTNAME  = Extension name              
RESEXT   = Extension name of the results extension
DATAEXT  = Extension name of the data extension (this is a link to an external extension)
XDIMXT1  = Extension name of the 1st dimension absorbed by analysis
WGTSEXT  = Extension name of the weights extension
INCLEXT  = Extension name of the include extension
CONSTEXT = Extension name of the constant extension

World Coordinate System (WCS) keywords

WCSNAME = Name of coordinate system                                            
LONPOLE = Native longitude of the celestial pole                                             
SPECSYS = Spectral coord. not corrected for S/C velocity                                               
VELOSYS = [m/s] Default for SPECSYS='TOPOCENT'                                               

CTYPE1   = Type of 1st coordinate (SPICE: WAVE)                       
CNAME1   = Name of 1st coordinate                        
CUNIT1   = Units for 1st coordinate (for CRVAL1, CDELT1)  
CRVAL1   = [nm] 1st coordinate of reference point          
CDELT1   = [nm] Increment of 1st coord at ref point        
CRPIX1   = [pixel] 1st pixel index of reference point    
PC1_1    = Contribution of dim 1 to coord 1                    
                                                                            
CTYPE2   = Type of 2nd coordinate (SPICE: HPLN-TAN)                        
CNAME2   = Name of 2nd coordinate  
CUNIT2   = Units for 2nd coordinate (for CRVAL2, CDELT2)  
CRVAL2   = [arcsec] 2nd coordinate of reference point    
CDELT2   = [arcsec] Increment of 2nd coord at ref point  
CRPIX2   = [pixel] 2nd pixel index of reference point    
PC2_2    = Contribution of dim 2 to coord 2   
PC2_3    = Contribution of dim 3 to coord 2  
                                                                            
CTYPE3   = Type of 3rd coordinate (SPICE: HPLT-TAN)                       
CNAME3   = Name of 3rd coordinate  
CUNIT3   = Units for 3rd coordinate (for CRVAL3, CDELT3)  
CRVAL3   = [arcsec] 3rd coordinate of reference point    
CDELT3   = [arcsec] Increment of 3rd coord at ref point  
CRPIX3   = [pixel] 3rd pixel index of reference point    
PC3_2    = Contribution of dim 2 to coord 3 due to roll  
PC3_3    = Contribution of dim 3 to coord 3  
                                                                            
CTYPE4   = Type of 4th coordinate (SPICE: UTC)                        
CNAME4   = Description of 4th coordinate                  
CUNIT4   = Units for 4th coordinate (for CRVAL4, CDELT4)  
CRVAL4   = [s] 4th coord of ref point, relative to DATEREF  
CDELT4   = [s] Increment of 4th coord at ref point        
CRPIX4   = [pixel] 4th pixel index of reference point     
PC4_2    = Contribution of dim 2 to coord 4 due to roll  ; _optional, only for rasters_  
PC4_4    = Contribution of dim 4 to coord 4                    

BTYPE    = Type of data                                   
UCD      = Unified Content Descriptors v1.23           
BUNIT    = Physical units of calibrated data