Monochromator

A monochromator transmits a narrow band of wavelengths, selectable over a wide range, and blocks the rest. Light enters through an entrance slit, is collimated, dispersed by a diffraction grating (or, in older and some ultraviolet instruments, a prism), and refocused onto an exit slit; only the wavelengths whose slit image lands on the exit slit pass through. Rotating the grating scans the passband across the spectrum. A bench instrument with a 0.3 m focal length and a 1200 line/mm grating passes a band about 0.26 nm wide at 500 nm with 100 µm slits, and can be set anywhere from the ultraviolet to the near infrared by changing gratings. The output is either a tunable narrowband source, when the input is a lamp, or, with a single detector behind the exit slit, a scanning spectrometer.

Relation to the spectrometer

The optical layout is usually the Czerny-Turner arrangement described in the spectrometer entry: two concave mirrors and a plane grating. The difference lies at the output. An array spectrometer records many wavelengths at once on a line of pixels; a monochromator puts a slit there and records one wavelength at a time with a single detector, typically a photomultiplier tube, photodiode or cooled InGaAs detector. A grating optical spectrum analyzer is a fiber-input scanning monochromator.

Bandpass

The bandpass, the full width at half maximum of the transmitted band, is the product of the reciprocal linear dispersion at the exit slit and the slit width $w$:

$$\Delta\lambda \approx R_d\, w, \qquad R_d = \frac{d \cos\beta}{m F}.$$

Here $d$ is the groove spacing, $\beta$ the diffraction angle, $m$ the order and $F$ the focal length of the focusing mirror; $R_d$ is in nanometers per millimeter. For a 1200 line/mm grating ($d$ = 833 nm) in first order at 500 nm, used near-symmetrically so that $\sin\beta \approx m\lambda/2d = 0.30$, $\cos\beta$ = 0.954, and with $F$ = 300 mm,

$$R_d = \frac{833\ \text{nm} \times 0.954}{300\ \text{mm}} = 2.65\ \text{nm/mm}.$$

A 100 µm slit then gives a bandpass of 0.26 nm, and a 10 µm slit 0.026 nm. When entrance and exit slits are equal, the transmitted band has a triangular profile whose FWHM is $R_d w$; unequal slits give a trapezoid whose FWHM is set by the wider one. The bandpass cannot fall below the grating's resolution limit $\lambda/(mN)$, 0.0083 nm for 60 000 illuminated grooves (50 mm of a 1200 line/mm grating), and aberrations usually stop it short of that.

Throughput from a continuum source scales with the product of entrance and exit slit widths, so halving both slits to halve the bandpass cuts the signal by about four. A fixed bandpass in wavelength corresponds to a bandpass in wavenumber, $\Delta\lambda/\lambda^2$, that widens toward shorter wavelengths, which matters in Raman spectroscopy, where shifts are reported in cm⁻¹.

Double and triple monochromators

The weakness of a single monochromator is stray light: grating scatter and internal reflections deliver a fraction of order $10^{-5}$ of out-of-band light to the exit slit. Two monochromators in series, with the exit slit of the first serving as the entrance of the second, multiply the rejections, to roughly $10^{-10}$. In an additive double the second grating continues the dispersion of the first, halving the reciprocal linear dispersion and therefore the bandpass for the same slits. In a subtractive double the second stage undoes the dispersion, so the output is spatially recombined and the pair acts as a tunable bandpass filter with very steep edges; subtractive stages are used as the filter in front of a triple spectrometer, which in Raman work rejects the elastically scattered laser line within a few wavenumbers of it.

Uses and practice

Monochromators select excitation and emission wavelengths in fluorescence spectrometers, measure the spectral responsivity of detectors and solar cells by illuminating them with a tunable band from an arc lamp or tungsten-halogen lamp, and serve as scanning analyzers for photoluminescence and Raman light. The wavelength scale is calibrated against emission lines of known wavelength, such as the mercury lines at 435.83 nm and 546.07 nm. A grating also passes half the set wavelength in second order (250 nm light exits with 500 nm), so a long-pass order-sorting filter is required whenever the source contains light below half the operating wavelength.

Common questions

What is the difference between a monochromator and a spectrometer?

A monochromator selects one band through an exit slit and needs a single detector; a spectrometer in current usage records the whole spectrum at once on a detector array. A monochromator with a scanning grating and detector behind its exit slit is a scanning spectrometer.

How is bandpass related to resolution?

The bandpass is the width of the band the instrument passes for a given slit setting. Two lines can be distinguished when they are separated by roughly the bandpass or more. Setting the slits for a bandpass about one fifth of the narrowest feature of interest records its shape with little broadening; for a 1 nm feature with $R_d$ = 2.65 nm/mm a bandpass of 0.2 nm needs slits of about 75 µm.

Why use a double monochromator?

For stray-light rejection, when a weak signal lies close to a strong one, as in Raman spectroscopy or measuring optical densities above about 4.

References: E. Hecht, Optics, 5th ed. (Pearson, 2017); J. F. James, Spectrograph Design Fundamentals (Cambridge University Press, 2007); J. R. Lakowicz, Principles of Fluorescence Spectroscopy, 3rd ed. (Springer, 2006).