Hello Leonardo Chiappisi ! Depending on the number and increment of the angle you could use e.g. something like the X-RITE MA98, which allows for a set of different angles to be used. More options, but a much higher price, would give a device like the DATACOLOR Multi FX10.

A former colleague of mine did a comparison of different multi angle spectrophotometers, perhaps this is of help for you:

https://www.idd.tu-darmstadt.de/media/fachgebiet_idd/publikationen/kehren2011_performanceofmultianglespectrophotometers.pdf

Thanks Dieter for the suggestion, but I fear the instruments you mentioned are not suited.

I will need to record the reflectance from a thin film (without direct contact with the instrument) as a function of wavelength and incidence angle. I have learned that many UV-Vis instrument can, with the necessary accessory, perform such measurements. (A very nice plot is attached to this message).

I don't think I will need to IR region, but I would like to at least approach the UV range.

I now asked for a quote of the Cary 7000 UMS (the instrument used for the plot attached), but I expect it to be too expensive. Further suggestions are always very welcome.

Leonardo Chiappisi , I have realized instrument, which you need by myself in rather simple way. For gamma/2*gamma rotation (gamma is angle of incidence) I used two arms linked by one belt, simultaneously rotated in opposite directions by step motor. As spectrometer I used one of OceanOptics fiber spectrometer, which is controlled by their Ocean View software. It can pass measured spectrum into computer clipboard. To realize such operation in automatic way, I applied key press emulator, which "press" necessary Ocean View key. Than main experiment controlling program process spectrum and rotates arms to following gamma position. You can see an example of measured spectrum in attached file.