Spectrometer

A spectrometer measures how the power of a light source is distributed over wavelength. Most laboratory instruments do this with a diffraction grating: light enters through a narrow slit, is collimated, diffracted at an angle that depends on wavelength, and focused onto a detector, so that each wavelength lands at a different position. A compact fiber-coupled spectrometer with a silicon detector array covers roughly 200–1100 nm and typically resolves about 0.1–2 nm, depending on slit and grating; a large scanning research instrument can resolve a few hundredths of a nanometer or better.

The Czerny-Turner layout

The most common arrangement is the Czerny-Turner spectrometer. A concave mirror collimates the light from the entrance slit, a plane grating disperses it, and a second concave mirror focuses each wavelength into an image of the slit at the output plane. In a scanning monochromator an exit slit selects one wavelength and the grating rotates to scan; in an array spectrometer a line of detector pixels at the focal plane records all wavelengths at once.

The grating sends wavelength $\lambda$ in order $m$ to the angle $\beta$ given by

$$m\lambda = d\,(\sin\alpha + \sin\beta),$$

where $d$ is the groove spacing and $\alpha$ the angle of incidence. The angular dispersion follows by differentiating:

$$\frac{d\beta}{d\lambda} = \frac{m}{d\cos\beta}.$$

Dispersion, slit width and resolution

Take a 600 line/mm grating used near-symmetrically ($\alpha \approx \beta$) at 500 nm in first order. Then $\sin\beta = 0.15$, $\beta \approx 8.6°$, and the angular dispersion is about 0.61 mrad/nm. With a 100 mm focal length focusing mirror, the reciprocal linear dispersion at the detector is

$$\frac{d\cos\beta}{m f} \approx 16.5\ \text{nm/mm}.$$

With unit magnification the slit is imaged at its own width, so a 25 µm slit spans about 0.41 nm and a 50 µm slit about 0.82 nm. A 3648-pixel array with 8 µm pixels is 29.2 mm long and covers about 480 nm, at about 0.13 nm per pixel. The usable resolution is set by whichever is larger: the slit image, the optical aberrations of the mirrors, or about two to three pixels, here around 0.3–0.4 nm. Narrowing the slit improves resolution in proportion but passes proportionally less light.

Resolving power

The theoretical limit of the grating itself is its resolving power,

$$R = \frac{\lambda}{\Delta\lambda} = mN,$$

where $N$ is the number of illuminated grooves. A 1200 line/mm grating illuminated over 25 mm has $N = 30\,000$, so in first order $R = 30\,000$ and $\Delta\lambda \approx 0.017$ nm at 500 nm. Separating the sodium D lines at 589.0 and 589.6 nm, 0.597 nm apart, needs only $R \approx 990$. A compact instrument is limited by its slit and pixels long before it reaches $mN$; echelle spectrometers work in high orders to approach the grating limit.

Detectors and range

Array spectrometers use silicon CCD or CMOS linear sensors or a photodiode array for the ultraviolet to about 1100 nm, and InGaAs arrays for about 900–1700 nm, with extended InGaAs reaching further into the short-wave infrared. The detector's dark current, read noise and full-well capacity set the signal-to-noise ratio and dynamic range. Cooled CCDs are standard in Raman spectroscopy. In the mid-infrared, where array detectors are expensive, a Fourier-transform instrument usually replaces the grating; see FTIR spectroscopy.

Spectrometer versus optical spectrum analyzer

An optical spectrum analyzer is a grating spectrometer built for fiber-optic work: a scanning double-pass monochromator with a calibrated resolution bandwidth of a few hundredths of a nanometer (0.02 nm is about 2.5 GHz at 1550 nm), high dynamic range and an absolute power scale. The trade-offs are covered in optical spectrum analyzer fundamentals, and the diffraction grating calculator gives diffraction angles for a chosen groove density.

Pitfalls

Higher diffraction orders overlap: second-order 400 nm light falls at the same angle as first-order 800 nm light, so broadband instruments use order-sorting filters. Internal stray light limits how weak a feature next to a strong line can be measured. The wavelength scale must be calibrated with known emission lines, such as mercury-argon lamp lines, and the intensity scale with a lamp of known spectral irradiance, because the raw counts include the wavelength-dependent grating efficiency and detector response. For single-frequency lasers a wavemeter is more accurate.

Common questions

What is the difference between a spectrometer and a spectrophotometer?

A spectrometer measures a spectrum. A spectrophotometer combines a light source, a sample compartment and a spectrometer to measure the transmittance or absorbance of the sample against wavelength, by comparing the light with and without the sample.

How do I choose a slit width?

Choose the narrowest slit that still gives enough signal. Resolution scales with the slit width multiplied by the reciprocal linear dispersion, so halving the slit roughly halves the bandpass until the pixel size or aberrations take over, at a cost of about half the light from an extended source.

What does resolution mean on a spectrometer datasheet?

It is usually the full width at half maximum of a narrow emission line as recorded by the instrument, for a stated slit and grating. It varies across the wavelength range.

References: E. Hecht, Optics, 5th ed. (Pearson, 2017), Ch. 10; M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, 1999), Ch. 8; C. Palmer, Diffraction Grating Handbook (Newport Corporation).