FFT spectroscopy seems difficult at these power levels. However, I lack the full picture.
Could you provide more details?
The most relevant are: the area emitting the photons, the required spectral resolution, the estimated measurement time, the expected spectrum, or in other words the total number of photons.
Jacquinot, Fellget and Conne' s advantages for the FTS. However in a photon noise limited system dispersive and FTS spectrometers have equivalent performance (L. W. Schumann and T. S. Lomheim, “Infrared hyperspectral imaging Fourier transform and dispersive spectrometers: comparison of signal-to-noise-based performance,” Proceedings of SPIE, vol. 4480, no. 1, pp. 1–14, Jan. 2002). If your system noise is limited by your detector then the Fellgett advantage quicks-in in favour of FTS.
My bad : the full text is not available in Research Gate. The original paper can be found here https://www.spiedigitallibrary.org/conference-proceedings-of-spie/4480/0000/Infrared-hyperspectral-imaging-Fourier-transform-and-dispersive-spectrometers--comparison/10.1117/12.453326.full
(1) Please find in your e-mail the paper of Lee W. Schumann e.a. suggested by Luis Miguel Gaspar Venancio above.
(2) Since you didn't provide the community with extra details about your application (as requested by Karsten Schuhmann earlier), I dare share only most general (and pactical) thoughts as relevant to your question:
* - the known FT-advantages may be lowered to some extent in VIS or short NIR (500-800 nm) range you've indicated - so dispersive spectrometers may look not so bad alternative here
** - Silicon CCDs perform well in the range you've indicated - especially the so called "intensified", thinned and back-illuminated ones for low-light applications (cf. e.g. Andor catalogues). Certainly, a Pelltier cooling of the CCD is the must
*** - Since we don't know about the resolution you'd like to have (but the higher is the better almost in all instances), I guess an Echelle-type spectrograph would do the job in your case. The constancy of the resolution throughout the measured wavelength range is a favour in Echelle, and the resolution of 1 cm-1 is easily realisable in this case (cf e.g. PE RamanStation 400 based on the Echelle+Andor's cooled CCD optimised for low-light applications). I don't mean that you need namely Raman spectrometer for your application, but using the PE RS400 for some time i'm highly impressed by its sensitivity, resolution and the provided possibility to analyse low-light photon fluxes for very long (many minutes) CCD exposure times.
Hope these notes would be of some help. Good Luck!
thank you alot for your answers. I may provide some more information resulting from rough estimates.
The expected spectrum is rather broad, covering more than 0,5eV range within about 1,7-2,7 eV. The total amount of photons will be some 1-100 photons per minute. At present, I do not know if there will be fine subfeatures.
I expect that the spectral resolution, which may be obtained, is solely limited by the s/n ratio, i.e. technically possible resolution of maybe 10 meV will be sufficient, I cannot think of more than 1meV being possible with the photon flux.