| Filter | Type of fit |  |  |  |  |  |
| I | unmasked | 13.46 | 0.02 | 0.30 | 0.97 | 12.25 |
| mask of 3'' | 14.05 | 1.76 | 0.29 | 0.79 | 11.56 | |
| mask of 5'' | 13.47 | 3.65 | 0.29 | 0.90 | 11.67 | |
| 64x64 | 14.95 | 1.46 | 0.30 | 0.77 | 5.28 | |
| R | unmasked | 14.08 | 0.26 | 0.30 | 1.00 | 7.86 |
| mask of 3'' | 14.57 | 1.66 | 0.29 | 0.72 | 7.26 | |
| mask of 5'' | 14.03 | 3.65 | 0.30 | 0.90 | 7.42 | |
| 64x64 | 16.83 | 10.50 | 0.34 | 0.50 | 5.17 | |
| V | unmasked | 12.58 | 0.04 | 0.29 | 0.36 | 7.24 |
| mask of 3'' | 12.51 | 8.02 | 0.27 | 0.61 | 6.98 | |
| mask of 5'' | 12.52 | 8.09 | 0.26 | 0.62 | 6.87 | |
| 64x64 | 13.74 | 0.07 | 0.31 | 0.94 | 3.89 |
As noted earlier, the 1D decomposition of a profile involves averaging
of the profile along elliptical isophotes and obtaining a
major axis profile. The averaging smears out
faint features. A 2D fitting scheme overcomes this difficulty.
In the 2D fit
a model galaxy is generated using assumed values of , ,
, and 
. The model is convolved with an appropriate
PSF and a 
minimization
is then made using the minuit routines. The standard deviation
used at each pixel for the
minimization is obtained from the image without subtracting
the sky background.
The iterative minimization
continues till either the maximum number of iterations is exceeded or
till the change in goes below a specified tolerance.
The procedure is described in detail by Wadadekar et al. (1998).
An advantage of the 2D method is the detection of faint features. When the best-fit model is subtracted out from the input image, the features in the residual stand out. In case of the 1D fit, the 2D information has been converted into a 1D profile by averaging along elliptical isophotes. In this process the faint features are also averaged out. Even if the residual (input profile - best fit profile) indicates an excess at the semi-major axis where the feature was, the spatial location of the feature is lost. An example is that of shells in a galaxy. When a 2D fit is made, interleaved shells in an elliptical galaxy will stand out. On the other hand, if one wants to ignore faint features and is only interested in the large scale light distribution of the galaxy, the 1D fits prove more useful.
To be consistent with
the 1D fits, we masked out the central regions of the images before
performing the fit on the sample objects.
The results of the test fits that we carried out for
images
of NGC 661 images are given in Table 
.
The following points can be noted with respect to these results:
values are acceptable for all the
images.
Except for the I images, where we get 
, the
values for
images in the other band
are acceptable too. is not acceptable we find
that a spurious disk has been detected. Though it has a
large scale length ( 
), we have D/B;SPMlt;0.2
indicating that the disk is weak. values are similar to those obtained by the 1D program
(See Table ).
We mention here the functional differences in the 1D and 2D fitting programs.
:
The first noticeable thing is that the size of error bars in the 1D case
are much smaller than the 2D case. Though in both cases a \
minimization was done using the same minimization package, the
definition of was different. In the 1D case the input
parameter was mean intensity, 
, along different ellipses and the
error on
this parameter was that given by the IRAF task ellipse.
is obtained by fitting an isophote with an elliptical shape
and averaging along the best fit ellipse. A large number of
points having approximately the same intensity are used resulting
in the error being small.
In the 2D case the original
photon shot noise is considered for each pixel to evaluate the
. Deviant points (e.g. those arising from faint foreground
stars) are clipped off during the 1D fit. This can not be done in the
2D program. However, unlike in the 1D case,
the features do not get averaged out either.
If left unmasked, they contribute a large part to the
resulting in the 2D case.
The same holds true for the outer regions of the galaxy frame.
In 1D we used points in the profile for
which the error 
.
In 2D when a 
image
is used the noisier regions also get considered during the fit. As seen from
Table , for a galaxy like NGC 661, it does not make too
much of a difference to but the does reduce in the
smaller image.
In both the programs the position angle is not varied with radius during fitting. In case of the 1D fits it poses less of a problem since the profile output by ellipse is along the twisting semi-major axis direction i.e., the position angle itself is output as a function of the semi-major axis and the 'major-axis' profile is not strictly along a fixed direction. Thus, when there is a large position angle twist, the 1D program is still reliable whereas the 2D program will not be. Additionally, the 2D program, since it involves only a single position angle, is capable of finding only disks that are along the major axis.
Neither the 1D program, nor the 2D program fit for changing ellipticity and the results need to be taken with caution when the ellipticity varies a lot. When the ellipticity is approximately constant, the results should be comparable.
We present the results of fitting the program objects with the 1D procedure in the next chapter.