The energy resolution of an energy-loss spectrum (Electron Energy Loss Spectroscopy - EELS) is
determined by several factors, including aberrations of
the electron spectrometer, energy distribution provided by the electron source, and collection angle. An example of aberrations is the non-isochromaticity of the energy filter. The energy resolution can be estimated by FWHM (full width at half maximum) of the zero loss peak.
Generally speaking, large collection angles of EELS will give high
intensity but poor energy resolution. If the EELS spectrum is collected in image mode without
an objective aperture then the energy resolution is not compromised but spatial resolution is
poor. If it is in diffraction mode and the control collection angle (β) is controled by the entrance aperture, then a large aperture (high
intensity, high β) will lower the resolution and vice
versa.Further improvement in energy resolution is possible by
inserting an electron monochromator after the electron source. EELS typically offers an energy resolution of 1 eV but close to 0.1 eV if an electron-beam monochromator is used.
On the other hand, there are some unmeasurable energy losses in EELS due to the limit of energy resolution. First, because the nuclear mass is much more than the rest mass of an electron (e.g. the electron has 1823 times less mass than a proton), the energy exchange is small and usually unmeasurable during the interaction of an incident electron with an atomic nucleus, acting as a physical process of elastic scattering.
Second, phonon scattering broadens the angular width of each Bragg beam and involves an energy transfer of the order of kT (≈25 meV at T ≈ 300 K) that is also unmeasurable in a TEM-EELS system.
Before the application of field emission electron guns in TEM, the energy resolution of EELS systems had been ~1–2 eV, mainly limited by the energy spreading of thermionic electron source (tungsten filament or LaB6). In the late 1990s, Schottky emission sources became available and have been providing energy resolution greater than 0.5 eV.
Furthermore, the energy resolution of the EELS system can also affect the chemical sensitivity of spectroscopy especially when the signals are very weak for some elements and some edges. Figure 4970a shows how the energy resolution affects EELS sensitivity by comparing the C(carbon) 1s spectrum of poly(ethylene terephthalate) (PET) recorded by two different microscopes. The higher energy resolution with a cold field emission gun (VG-HB501) increases the chemical sensitivity of a spectroscopy comparing to a LaB6 thermionic emission electron source.
Figure 4970a. EELS profiles of the C 1s spectrum of poly(ethylene terephthalate) (PET) recorded by two different microscopes.
Adapted from 
Figure 4970b shows experimental EEL spectra of the N (nitrogen) K edge obtained from a GaN film with the three different energy resolutions versus the DFT simulations with the indicated energy broadening. The spectrum with an energy resolution of 1.0 eV was obtained with the JEOL2010F, the spectrum with the resolution of 0.4 eV was obtained with the Cs-corrected Nion VG HB501, and the 0.2 eV spectrum by using the monochromated FEI Tecnai G2. Those profiles indicate the EELS sensitivity to the detection of extended energy loss fine structure (EXELFS) depending on the energy resolution.
Figure 4970b. Experimental EEL spectra of the N (nitrogen) K edge from a GaN film obtained with the three different energy resolutions versus the DFT simulations with the indicated energy broadening.
In many cases, high energy resolution is needed to detect the point defects, grain boundaries and heterointerfaces in materials. An energy resolution of close to 100 meV is required to reveal the spectroscopic details, while an energy resolution of less than 50 meV will most likely not provide additional information.
The energy resolution in thermally assisted field-emission gun (FEG) can be higher in cold-cathode mode (with thermal assistance turned off) than in the normal operation condition. For instance, the energy resolution of 0.7 eV was obtained in cold-cathode mode while it was 0.9 eV in normal condition with Gatan 666 PEELS spectrometer in Philips 400ST-FEG TEM .
Note that, in EELS analysis, high energy-resolution is necessary to observe ELNES for investigating the chemical bonding. However, high energy resolutions (e.g. < 0.5 eV) is not always necessary, for instance, in the case of core-loss spectroscopy, the fine structures in a core-loss spectrum are dominated by lifetime broadening and solid-state effects  that normally does not need high resolutions.
The practical (real) energy resolution of EELS in a TEM depends not only on the energy spread of the electron source, but also on instabilities in accelerating voltage of the electron beam, spectrometer energy dispersion and stray electromagnetic field.
Note that if the EELS energy resolution is poor, then the data at low energy range will be not reliable, for instance, the data below 3 eV are not reliable with an common energy resolution of 1.3 eV.
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