3 The mean set image determination

As explained above, the binary system's instantaneous centers (hence also the residual image motion) are the most reliable parameters derived by fitting the short images. This suggests that the image analysis can be refined by means of the mean set image $i_{\rm m}(x,y)$ obtained by shift-and-add on multiple frames by using the Fourier shift theorem, i.e.,

$$i_{\rm m}(x,y)= {\cal F}^{-1}\left[\frac{1}{N}\,\sum_{k=1}^{... ...\rm e}^{- 2 \pi \, j \,\left(x_{k}u+y_{k}v \right)} \right]$$ (3)

where j is the imaginary unit, I_k(u,v), with $k = 1,2,...,\newline N = 48$, is the Fourier transform ($\cal F$) of the observed image i_k(x,y), ${\cal F}^{-1}$ is the inverse Fourier transform and the pairs (x_k,y_k) are the primary centers found by the above described general fit. When compared to the set images, the mean image is really characterized by a much better known position of the primary center (see Fig. 4), by an improved signal to noise ratio in each pixel, and by a better definition of the relevant details such as the secondary core and the primary bumps.

  

Figure 4: Mean images in the J, H and K bands of the binary system $\tau$ CMa (first row) and their fits (second row). The symmetrical light distribution around the centers of the primary component demonstrates the astrometric accuracy attainable by the shift-and-add algorithm using fit position parameters. The correlation coefficient are 0.98, 0.99 and 0.99, respectively