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Formula for Calculating Optical Resolution

How to Calculate Optical Resolution

Optical resolution of a spectrometer, measured as Full Width Half Maximum (FWHM), depends on the groove density (mm-1) of the grating and the diameter of the entrance optics (optical fiber or slit).

Formula for Calculating Optical Resolution

1. Determine the spectral range of the grating. Look at the grating charts and note the value in the spectral range column in the chart. For example, Grating #3 has a spectral range of ~650 nm. Please note that the spectral range can vary by starting wavelength, which is why 650 nm is an approximation.

2. Determine the number of pixel elements in the spectrometer’s detector. For a USB2000+ spectrometer, the number is 2048. Divide the grating spectral range by the number of pixel elements in the detector. This is your dispersion value. For our example, 650 nm/2048 pixels = 0.32 nm/pixel.

3. Choose a slit width. Each slit has a pixel resolution value. For a USB2000+ with a 10 µm slit, this value is ~3.2 pixels.  You can lookup the pixel resolution for common spectrometer and slit combinations here.

Optical Resolution = Dispersion x Pixel resolution

In our example, the dispersion equals to 0.32 nm/pixel. Multiply it by 3.2 of pixel resolution, and you get that the optical resolution of USB2000+ spectrometer with 10 µm slit is 1.02 nm.