**Abstract**

In this Post we provide a calculator to compute the amount of flux of the image of a star passing through a pinhole or slit in a conventional spectrograph.

The calculator is embedded in an excel document that can be downloaded as SlitPinholeFluxCalculator.xlsx or SlitPinholeFluxCalculator.xls. It is also available as a Java applet that can be executed here (it requires Java plug-in’s in your browser) or downloaded (including Java sources) here.

**Description**

The width of a slit in a spectrograph compromises the amount of luminous flux on the detector against the resolving power of the spectrograph. On the one hand, wider is the slit of the spectrograph higher the number of photons on the detector. Therefore higher will be the signal to noise ratio of the recorded spectrum. On the other hand, wider is the slit, lower will be the resolving power of the spectrograph. This trade-off is affected as well by the local seeing. Better is the seeing, narrow can be slit.

The same trade-off appears when optical fibres are used to link telescopes to spectrographs. Circular apertures would give the impression that they just increase flux losses with respect to the slits. especially when the diameter equals the slit width. However, this flux reduction is compensated by an increase of the resolving power of the spectrograph. Indeed, the full width half maximum (FWHM) of the point spread function (PSF) on the detector is smaller for a fibre than for a slit. The gain in resolution with a fibre is around the same as the reduction in luminous flux. Empirically is about 20% in both cases.

The flux distribution of the image of a star on the focal plane of the telescope is defined by the convolution of the telescope aberrations and by the seeing function. If the aberrations are small, the image of a star may be simulated with good approximation to a bi-dimmensional Gaussian function (*Figure 1a*). The size of this gaussian function is basically defined by the FWHM (Full Width Half Maximum) of the *seeing *function() and scaled by the *scale plate *()of the telescope.

At the telescope focal plane we can project either, a pinhole or a slit, and center our gaussian star representation on them. *Figure 1b* shows the top view (from telescope beam) of our gaussian star centered in a pinhole, while *Figure 1c * shows the same view with a slit. *Figure 1d* would represent the flux coming through the pinhole and entering the instrument (view from behind), while *Figure 1e* would represent the flux through the slit.

The calculators compute the efficiency ratio (partial flux/total flux) for both alternatives: pinhole and slit.

**Mathematical functions**

**Input parameters:**

Seeing FWHM in arcseconds

Telescope diameter in cm

Telescope Focal Number (F/#)

Pinhole diameter in um

Slit width in um

Slit lenght in um

**Equations:**

**Plate**** Scale ** (in microns per arcsec)