Fig. 4.

Improving the signal-to-noise ratio (SNR) of a feature in the image shown in Fig. 1b at cross section I. a Transverse 1-D fluorescence intensity profiles (arbitrary units, plotted against pixel number) are plotted on top of each other for $m=0$ (black), (0.5 ${\delta }_{\mathrm{y}}/\mathrm{\Delta }\mathrm{y})$ (red), (${\delta }_{\mathrm{y}}/\mathrm{\Delta }y)$ (green) and (1.5 ${\delta }_{\mathrm{y}}/\mathrm{\Delta }\mathrm{y})$ (blue), for judging the smoothening operation. The PSF width in pixels is (${\delta }_{\mathrm{y}}/\mathrm{\Delta }\mathrm{y}\sim 25$) for this image. The jump in the intensity profile beyond pixel no. $y=400$ is an artifact. b Plot of noise variance [${\sigma }^2(y)$] vs. average 1-D fluorescence intensity [($I_{\mathrm{av}}(y)$] of the tube. The red line shows a model fit to the data. c signal-to-noise ratio (SNR) is plotted as a function of the smoothening radius m in the units of $\sim ({\delta }_{\mathrm{y}}/\mathrm{\Delta }\mathrm{y})$. The peak signal-to-noise ratio (SNR) of the feature is improved by six times from $(I_{\mathrm{av}}(y)/\sigma (y))\simeq 500$ up to 3000 by smoothening operation