A diffraction grating is a periodic optical structure that directs different wavelengths into different angles through wave interference.
A diffraction order labels a constructive interference maximum by the integer number of wavelengths in the path difference between adjacent grating elements.
For a reflection diffraction grating with both ray directions measured on the same side of its normal, adjacent grooves have path difference . Constructive interference requires this to be an integer multiple . Signed-angle conventions can turn the sum into a difference; the physical path difference is unchanged.
At fixed incidence angle, differentiating the grating equation gives . A camera with focal length therefore has local focal-plane dispersion near its optical axis. With coordinate , the full derivative is .
At fixed wavelength, the grating equation gives . Thus an incident angular width is magnified by in the dispersion direction. Including the ratio of camera and collimator focal lengths gives the projected slit width. The ESO B&C operating manual, Appendix A explicitly includes this anamorphic factor.
A slit of width at the focus of a collimator subtends . Its projected width is . Dividing this width by the grating dispersion gives . Thus the spectral resolving power is . Omitting the anamorphic factor gives a denominator instead; these agree in the Littrow configuration.
In the Littrow configuration the selected diffracted ray retraces the incident ray, so and the grating equation becomes .
An echelle grating works in high diffraction orders. A separate cross-disperser separates their overlapping optical spectra on a two-dimensional detector.
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A diffraction grating is an optical component with a periodic structure that diffracts light into several beams. The grating consists of multiple closely spaced slits or grooves, which can be either reflective or transmissive. When light waves encounter the grating, they are scattered at specific angles according to the principles of wave interference, producing a spectrum of colors.
