Whereas a traditional grating is designed to operate at low order numbers, an
echelle operates at high blaze angle (the angle between the surface of the
grating and the reflective groove faces, of order 63
) and at high order
numbers typically between 50 and 150. The high blaze angle permits a
comparatively wide spectrograph
entrance slit and therefore better light throughput at a given resolution. The
high order numbers result in many orders overlapping, but these can be separated
by cross--dispersing, thus giving large spectral coverage while maintaining high
spectral resolution. Wavelengths which overlap in the undispersed echelle
spectrum are related by
where 
are the order numbers. The wavelengths 
thus
occupy similar positions in adjacent orders of the cross--dispersed echelle.
A given wavelength will appear in several orders, but each echelle order has
its own intensity profile (blaze profile) resembling a sinc function, so
the intensity at some wavelength will differ in each order.
In practice, a wavelength is concentrated in only one or two orders.
In each order, two wavelengths can be identified some distance from the peak
of the blaze profile that appear equal but opposite
distances off peak in the adjacent orders. These delineate the ends of the
Free Spectral Range (FSR). Observations restricted to the FSR would provide
complete wavelength coverage without any duplication, whereas
if the detector is narrower than the FSR, there
will be gaps in the spectral coverage. The length of the FSR on the
detector increases proportional to the central wavelength of the order,
giving the familiar trapezoidal format of an echelle spectrum,
illustrated in
Appendices 
and .
Note, however, that the spectrum does not terminate at the end of the free
spectral range; rather it continues at lower intensity away from the blaze
peak.
The dispersion in Å mm
is proportional to wavelength,
but the resolving power 
(and consequently the velocity resolution 
) is constant.
Also, the dispersion at a given wavelength depends only on the angle at which
the grating is used, not on its groove-spacing. Thus, the two echelle gratings
available in UCLES (with 31.6 and 79 lines mm
) give the SAME
dispersion because their blaze angles are the same. The primary difference is
in FSR and order separation.