General radiometric equation
L( i, j ) 

A   i  Rc ( i, j )  FFi, j  
(1)
UVIS radiometric equation combines geometric,
responsivity, and bandpass terms
L( i, j ) 

[C ( i, j )  N (C)  D(i, j)  B(i, j)  S( i, j )] t
[C( i, j )  N (C)  D(i, j)  B(i, j)  S( i, j )]  FF (i, j)1 Cal(i, j)
t
(2)
L( i, j ) 

[C( i, j )  N (C)  D(i, j)  B(i, j)  S( i, j )]  FF (i, j)1 Cal(i, j)
t
(2)
• N is the detector dead time correction, applied as a multiplicative
factor to all pixels.
• D and B are the dark count and background corrections and must be
estimated by examining individual spectra.
• S is the scattered light and represents photons scattered out of
relatively bright features (S is negative) or photons scattered into
relatively weak features. S is calculated by deconvolving instrument
point spread function (instrument response to a monochromatic,
collimated source) from the observed spectral-spatial image.
• Cal(i,j) and FF(i,j)-1 are the calibration matrix and the flatfield matrix.
 t is the integration time in seconds.

Some care must be exercised for subtracting dark,
background, and scattered light
If they are estimated from observations then they
should be subtracted before the flatfield correction
L( i, j ) 
[C( i, j )  N (C)  D(i, j)  B(i, j)  S( i, j )]  FF (i, j)1 Cal(i, j)
t
(2)
If they are estimated from averages or smoothed
data then they should be subtracted after the
flatfield correction
L( i, j
C ( i, j )  N (C)  FF (i, j)1  D(i, j)  B(i, j)  S(i, j)Cal(i, j)

)
t
(3)
Calibration evolution
•
Preflight calibration is a single row vector. There is no correction for
row-to-row sensitivity variations.
Cal(i,j)=Cal(i) for all rows
Flatfields derived from Spica observations correct the magnitude of the
row to row variations. The relative column to column calibration is
constant
Cal(I,j)=Cal(I)*FF-1(j)
•
– If the Spica flatfield matrix is used the row-to-row variations are corrected
– Other flatfielding schemes must include terms for row-to-row variations
•
Red patch calibration includes both row to row and column to column
variations. There are no terms for the high frequency flatfield
variations. There are two versions of the red patch.
– Red patch consistent with the explicit row-to-row variations included in the
Spica derived flatfield
CalRP (i, j)  FF 1(i, j )  Cal(i )  FUV _ Red _ Patch_1 FF 1(i, j)
(5)
– Red patch that explicitly corrects row-to-row variations in the flatfield.

 (i, j)  Cal(i)  FUV _ Red _ Patch_ 0
CalRP
(6)
Scattered Light Estimation
A first approximation of the UVIS scattered light can be made by convolving
the observed spectrum with the instrument point spread function
C( )Obs  C ( )True  PSF  C( )True  C( ) Scat
C( )Obs  PSF  (C ( )True  C ( ) Scat)  PSF
C( )Obs  PSF  C( )True  2 C( ) Scat
C( ) Scat  C( )Obs  PSF  C( )Obs
C( )True  C( )Obs [C( )Obs  C ( )Obs  PSF]

Scattered Light Estimation
A first approximation of the UVIS scattered light can be made by convolving
the observed spectrum with the instrument point spread function
C( )Obs  C ( )True  PSF  C( )True  C( ) Scat
C( )Obs  PSF  (C ( )True  C ( ) Scat)  PSF
C( )Obs  PSF  C( )True  2 C( ) Scat
C( ) Scat  C( )Obs  PSF  C( )Obs
C( )True  C( )Obs [C( )Obs  C ( )Obs  PSF]
This is the first term in the expansion of a deconvolution algorithm developed
by van Cittert

C( )1  C( )Obs [C( )Obs  C( )Obs  PSF]
C( ) n  C( ) n1 [C( )Obs  C( ) n1  PSF]
Scattered Light Estimation
Scattered Light Estimation
Scattered Light Estimation
Red
- Instrument PSF
Green-Blue - 1,3,5 iterations
Scattered Light Estimation
Red
- Instrument PSF
Green-Blue - 1,5 iterations
Scattered Light Estimation
Red
- Instrument PSF
Green-Blue - 1,5 iterations