Depends on what resolution you want, but the simplest way is starting with a simple diffraction grating.
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Is a grating blazed for 1.6 microns, cost is 72.00.
On Line Grating Calculators are wonderful, soL At a zero degree angle of incidence, no slits, no focusing mirrors, not a Czerny Turner setup, just a collimated beam input, the deflection angle of the first order beam is
1550 nm = 68.4'
1450 nm = 60.4'
1350 nm = 54.1'
1250 nm = 48.5'
How ever you want to detect and measure is up to you, put a diode with a p inhole on a sliding stage, IR viewer card, a crude sine bar with a bearing and micrometer plus a photodiode, just a protractor, bolt it to a table and mark spots on the wall, there are a lot of possibilities.
A quick check of the NIST spectral data base shows NE-I has a few distinct very strong lines, from 1200 to 1500, so a Neon glow lamp could be used as a reference.
These folks claim to have stretched the silicon spectrum out to nearly 1550 and the price is not that bad.
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If you want to measure the center wavelength accurately, Ocean Insight's fi ber coupled USB spectrometer is still your best shot.
Steve