What is an echelle spectrometer?

Many real-world spectroscopic applications benefit from obtaining high-resolution spectra over a very broad wavelength range. The fidelity of a spectral measurement increases with resolution until the spectral features are fully resolved, which produces the highest contrast between spectral lines, and background; at the same time, recording the full spectrum provides a complete picture of the source characteristics.

However, recording broadband spectra at high resolution requires many individual photodetectors - conveniently, pixels in a semiconductor chip. As an example, at a resolution of R = 50,000 at 500 nm wavelength, a single resolution element captures only λ/R=10 picometer wavelength range. Sampling theory dictates that at least two pixels are required to properly sample a resolution element, so each pixel of a detector covers only 5 picometers of the spectrum. A 2000 pixel wide detector can record only 5 nm of wavelength range at such a high resolution. To record spectra from 400 nm to 1000 nm would require a detector of several hundred thousand pixels length, with physical dimensions of meters – and matching optical elements as well.

An elegant solution to matching the format of high-resolution spectra to area detectors that provide the required number of pixels in an approximately square format is the use of echelle gratings (from French for “ladder”). Unlike normal diffraction gratings, which produce a single linear spectrum in diffraction order 1, these gratings make use of the fact that the product of wavelength and diffraction order of a grating is constant – 1000 nm in order 1 are diffracted in the same direction as 500 nm in order 2. An echelle grating is used in very high orders ~100, providing high-resolution, but overlapping spectra. Using the same example, 500 nm in order 100 are diffracted in the same direction as 505 nm in order 99. The orders overlap every 5 nm; this is called the free spectral range (FSR) of the grating.

As described above, 5 nm of spectrum can be conveniently recorded with a readily available 2000-pixel wide CMOS or CCD detector, at a resolution of 50,000. The problem remains that the detector cannot distinguish between the overlapping orders. This is solved by using a second dispersive element, a prism or a low-resolution grating, that is oriented perpendicular to the echelle grating, and fans out the orders on the detector, so they are located in traces above each other. This effectively transforms the source spectrum into a stack of consecutive spectral traces on the detector, each of which covers a short spectral range with very high resolution. This enables the recording of broadband high-resolution spectra in a single shot, which is why echelle gratings have long been the tool of choice for example in astronomical observations.

Dedicated analysis software is required to unwrap the stacked spectral orders, and merge them into a single, calibrated spectrum covering the full range. This requires precise wavelength calibration – matching the location of each pixel to a unique wavelength, and careful flux calibration to remove the intensity variation along each order caused by the wavelength-dependent efficiency of the optics and the detector, and in particular, the intensity profile imprinted on each order by the grating (the so-called blaze profile).

The animation below illustrates the principle of transforming a single spectrum into short, consecutive spectral orders stacked on top of each other, forming a ladder-like spectral format that can be recorded with an area detector providing a high pixel count.