The expected throughput for FHiRE and FHiREbot, as a function of wavelength, is summarized in the figure below.
The throughput has been computed using standard assumptions about high and low reflectivity coatings, as appropriate for the optical surfaces in the spectrograph, and includes both atmospheric extinction and losses in the telescope. Fiber throughput includes seeing, end losses, focal ratio degradation, and attenuation, assuming a 25-m fiber length. Efficiency for the echelle grating has been taken from curves available from the Richardson Grating Laboratory for the selected ruling
Realistic assumptions have been included for wavelength dependencies for the VPH cross disperser and order separating filter, the camera, and the detector. The throughput has been calculated as a function of wavelength for the full spectral coverage provided by the instrument. As see in the figure the total throughput rises from a low of a few percent at the blue end to nearly 10% at the red end of the spectrum. The efficiency of the VPH grating has been optimized in the blue to balance the relatively lower blue efficiency due to the combination of atmospheric extinction, seeing-related slit loss, camera throughput and detector efficiency.
Based on the throughput assumptions described above, FHiRE(FHiREBot) should achieve a S/N ratio at 500 nm of 500 (300) per resolution element on a 9th magnitude star in 20 minutes. With the rapid CCD readout time, FHiRE (FHiREBot) should be able to obtain spectra of at least 30 (30) V=9th magnitude stars per night. Note that target stars for the Hipparcos precision parallax survey are brighter than this limit, allowing greater numbers to be observed each night.