How to select the right instrument

The cost-effective choice of an instrument for a particular spectroscopic application requires a knowledge of the basic principles of monochromator operation.

G. J. Dixon, Contributing Editor

Emission spectroscopy is one of the most common measurement techniques performed in the optics laboratory. By determining the relative spectral-power density of the light emitted by a sample, it is possible to determine its composition and/or the distribution of energy among the available excited states. Depending on the desired resolution, the source brightness, and other factors, several types of instruments, including spectrographs, monochromators, interferometers, and optical spectrum analyzers can be used for spectral analysis (see photo, right).

For example, interferometers (see Laser Focus World, May 1997, p. 159) are typically used for measurements that require high resolution over a narrow spectral range. Determining the longitudinal-mode spectrum of a laser is a good example of this type of measurement. Monochromators and spectrographs cover a broader spectral range than an interferometer with a comparatively lower resolution.

In practice, the terms monochromator, spectrometer, and spectrograph are often used interchangeably, although each term actually refers to a unique class of instruments. Monochromators and spectrographs are both optical spectrometers that collect light and map variations in source wavelength onto changes in grating tilt angle and/or spatial position in the output plane of the instrument. In a scanning monochromator, the grating or prism is rotated, changing the wavelength that is transmitted by a narrow exit slit.

A spectrograph has a much wider output port and uses a photographic plate or optical multichannel analyzer to simultaneously record a range of wavelengths. Because they can only look at one wavelength at a time, monochromators take several minutes to record a spectrum that could be captured in a fraction of second with a spectrograph. Consequently, monochromators are typically used to record the spectrum of a continuous source or the time evolution of a system operating at a single wavelength. Spectrographs, however, are extremely useful for looking at a pulsed emission over a range of wavelengths.

Whether in an undergraduate science course or research laboratory, most of us are given the opportunity to use a spectrograph or monochromator very early in our careers. Unfortunately, the machines used for laboratory flight training rarely embody the newest and most sophisticated technology options. As a result, purchasing a new instrument for a particular application can be a stressful and somewhat confusing experience.

Modern monochromators use diffraction gratings

For many years, spectra were recorded using prism-based instruments. Today, however, almost all commercial instruments use diffraction gratings (see Fig. 1). Light incident on a grating is reflected at an angle that is a function of the density of grooves in the grating G measured in grooves per millimeter, the wavelength of the light in nanometers l, and the diffraction order N. For an incident angle a measured with respect to the normal, the angle of reflection b can be determined by

sin a + sin b = (10-6) N l G (1)

Because the angle of reflection is proportional to the product of wavelength and diffraction order, multiple wavelengths can be reflected at the same angle. For example, the first-order maximum at 1064 nm is coincident with the second-order maximum at 532 nm and the third order at 355 nm. Elimination of higher orders is usually accomplished by filtering the shorter wavelengths from the input.

The basic grating equation also shows that reduced groove densities must be used at longer wavelengths. Because the lefthand side of Eq. 1 is always less than two, the product of the wavelength in nanometers and diffraction order cannot exceed 2 ¥ 106/G. Limiting values for actual instruments are somewhat reduced from this maximum as the angular separation between input and output rays is typically less than 180°.

Modern gratings are blazed to maximize the reflection of light into a particular diffraction order. Grating manufacturers typically specify the blaze angle, in addition to the order and wavelength for which the grating is optimized. Holographic gratings are superior to those produced by a classical ruling engine for most applications in the near-IR, visible, and UV regions because irregularities in conventional gratings that are ruled with high groove densities lead to `ghosts` and an increased level of stray light. At longer wavelengths (that is, lower groove densities), ruled gratings are preferred due to increased diffraction efficiency.

Increased spectral resolution

In a typical scanning monochromator, the input source is focused onto a narrow entrance slit (see Fig. 2). Maximum resolution is typically obtained with slit widths of a few microns, although larger values are used for certain applications. In the ideal case, light entering the entrance port expands to fill a collimating mirror that reflects a parallel bundle of rays toward the grating. This light is diffracted by the grating at a wavelength-dependent angle and is imaged onto the exit slit by the focusing mirror (see Eq. 1). By rotating the grating about an axis that is parallel to its grooves and that lies in the plane defined by the grating`s reflective surface, the narrow range of wavelengths passing through the exit slit is changed. A manual crank or motor drive is used to move the grating, and a detector placed outside the exit slit measures the power of the light leaving the instrument.

Although many variables determine the performance (and price) of a scanning monochromator, the most important of these is the spectral resolution of the instrument. This parameter is equal to the spacing between two lines at which a clear minimum exists between them divided by their wavelength. In those cases in which the line shapes are determined by diffraction alone, Rayleigh`s criteria state that two lines are resolved if the central maximum of one line falls on the first minimum of the other. This corresponds to a dip of approximately 20% between the two lines. This 20% criterion is also applied to real instruments in which the line shape has contributions due to finite slit width and optical aberrations.

The theoretical resolving power R of a monochromator with a collimating mirror of focal length f, measured in centimeters, is

R = (10-2 ) (f l N G)/s (2)

where l is the wavelength of the light in nanometers, N is the diffraction order,

G is the groove density in mm-1, and s is the slit width in microns. This expression shows that, for fixed input slit width, the theoretical resolving power is proportional to the groove density of the grating and the focal length of the collimating mirror.

The other parameter that is key in the selection of a monochromator is the optical throughput. This is a function of the light-gathering power, or étendue, of the instrument and its spectral transmission function. With point-source illumination, an optimized imaging system matches the solid angle of the incoming light to the solid acceptance angle of the spectrometer. The étendue is equal to the product of this angle and the area of the slit.

If a square grating with side dimension l is the limiting aperture inside the spectrometer, the acceptance angle is given by (l/f)2 where f is the focal length of the collimating mirror. Maximum light-gathering power is achieved by using a large grating in combination with a short-focal-length mirror. Because the resolving power of the instrument is directly proportional to the collimating mirror focal length, there is a trade-off between étendue and resolution.

In addition to light-gathering power, the optical throughput of a particular instrument is a function of the grating diffraction efficiency and the reflectivity of the mirrors. The spectral transmission function describes the variation of these parameters with input wavelength. In general, the variation of optical throughput with wavelength is most strongly dependent on the grating design because the collimating and focusing mirrors typically have a flat reflectivity curve in the visible and near-IR regions.

In some applications the reduction of scattered light within an instrument can be a major priority. In these cases, the wavelength of the excitation source lies close to the spectral region of interest, and a significant amount of pump light enters the spectrograph. Double and triple monochromators, in which the output slit of one instrument acts as the input slit for a another, can significantly reduce the amount of stray light reaching the detector and, if configured properly, can significantly increase the instrument resolution (see Fig. 3).

An experiment designed to study the fluorescence of a new, rare-earth solid-state laser material uses two different monochromators (see Fig. 4). Excitation for the sample is provided by emission from a CW arc lamp that is filtered by a low-resolution monochromator. The output of this instrument is focused into the sample, and the resulting fluorescence is imaged into a second spectrograph with good spectral resolution. Because the two monochromators in this experiment are used for different functions, they are quite different in design.

The principal requirement for the first filter monochromator is high optical throughput. An instrument with a high f-number and a short focal length (<0.15 m) is commonly used. Manual wavelength tuning is adequate for the experiment shown in Fig. 4, although it may be desirable to have a motorized drive so that the same instrument can be used for excitation spectroscopy.

The spectrograph used to record the sample emission must be capable of resolving spectral features of interest. Because the linewidths of rare-earth transitions in insulating crystals are a few wavenumbers (cm-1) or greater, an instrument with a focal length between 0.5 and 0.75 m is adequate.

Maximizing the f-number of the instrument will increase its light-gathering power, but the added expense associated with a larger grating is probably not justified for a measurement of this type. A motorized drive is essential for recording a spectrum. A computer-based motor controller and data-acquisition system are not required but are highly desirable in cases in which a number of similar measurements are to be made. In other cases, choosing between a strip chart recorder and a computer-based system is a matter of cost and convenience.

After matching the key features of a monochromator to a particular application, there are still choices to be made. At this point, selecting an instrument is very much like buying a new car. It is often useful to talk to friends who own instruments similar to the one being purchased; beyond that, the final selection is largely dependent on personal taste and budget. o