Monochromator and spectrometer systems form an image of the entrance slit in the exit plane at the wavelengths present in the light source. There are numerous configurations by which this may be achieved; only the most common are discussed in this document, including Plane Grating Systems (PGS) and Aberration Corrected Holographic Grating (ACHG) systems.
LA - entrance arm length
LB - exit arm length
h - height of entrance slit
h' - height of image of the entrance slit
α - angle of incidence
β - angle of diffraction
w - width of entrance slit
w' - width of entrance slit image
Dg - diameter of a circular grating
Wg - width of a rectangular grating
Hg - height of a rectangular grating
A Fastie-Ebert instrument consists of one large spherical mirror and one plane diffraction grating (see Fig. 9).
A portion of the mirror first collimates the light which will fall upon the plane grating. A separate portion of the mirror then focuses the dispersed light from the grating into images of the entrance slit in the exit plane.
The Czerny-Turner (CZ) monochromator consists of two concave mirrors and one planar diffraction grating (see Fig. 10 ).
Although the two mirrors function in the same separate capacities as the single spherical mirror of the Fastie-Ebert configuration, i.e., first collimating the light source (mirror 1), and second, focusing the dispersed light from the grating (mirror 2), the geometry of the mirrors in the Czerny-Turner configuration is flexible.
By using an asymmetrical geometry, a Czerny-Turner configuration may be designed to produce a flattened spectral field and good coma correction at one wavelength. Spherical aberration and astigmatism will remain at all wavelengths.
It is also possible to design a system that may accommodate very large optics.
In the common Czerny-Turner design, the broad band illumination source (A) is aimed at an entrance slit (B). The amount of light energy available for use depends on the intensity of the source in the space defined by the slit (width x height) and the acceptance angle of the optical system. The slit is placed at the effective focus of a curved mirror (the collimator, C) so that the light from the slit reflected from the mirror is collimated (focused at infinity). The collimated light is diffracted from the grating (D) and then is collected by another mirror (E) which refocuses the light, now dispersed, on the exit slit (F).
CZ Monochromator: Output narrow monochromatic light through the slit.
CZ Spectrograph: Instead of using a slit on the exit slit, there will be an array detector placed on the exit slit, in this case, the spectrograph will cover a certain spectral range in one shot.
PGS spectrometers exhibit certain aberrations that degrade spectral resolution, spatial resolution, or signal-to-noise ratio. The most significant are astigmatism, coma, spherical aberration and defocusing. PGS systems are used off-axis, so the aberrations will be different in each plane. It is not within the scope of this document to review the concepts and details of these aberrations, (4) however, it is useful to understand the concept of Optical Path Difference (OPD) when considering the effects of aberrations.
Basically, an OPD is the difference between an actual wavefront produced and a "reference wavefront” that would be obtained if there were no aberrations. This reference wavefront is a sphere centered at the image, or a plane if the image is at infinity.
For example: Defocusing results in rays finding a focus outside the detector surface producing a blurred image that will degrade bandpass, spatial resolution, and optical signal-tonoise ratio. A good example could be the spherical wavefront illuminating mirror M1 in Fig. 10. Defocusing should not be a problem in a PGS monochromator used with a single exit slit and a PMT detector. However, in an uncorrected PGS there is field curvature that would display defocusing towards the ends of a planar linear diode array. Geometrically corrected CZ configurations such as that shown in Fig. 10 nearly eliminate the problem. The OPD due to defocusing varies as the square of the numerical aperture.
Coma is the result of the off-axis geometry of a PGS and is seen as a skewing of rays in the dispersion plane enlarging the base on one side of a spectral line as shown in Fig. 13. Coma may be responsible for both degraded bandpass and optical signal-to-noise ratio. The OPD due to coma varies as the cube of the numerical aperture. Coma may be corrected at one wavelength in a CZ by calculating an appropriate operating geometry as shown in Fig. 13.
Spherical aberration is the result of rays emanating away from the center of an optical surface failing to find the same focal point as those from the center (see Fig. 14). The OPD due to spherical aberration varies with the fourth power of the numerical aperture and cannot be corrected without the use of aspheric optics.
Astigmatism is characteristic of off-axis geometry. In this case, a spherical mirror illuminated by a plane wave incident at an angle to the normal (such as mirror M2 in Fig. 10) will present two foci: the tangential focus, Ft, and the sagittal focus, FS.
Astigmatism has the effect of taking a point at the entrance slit and imaging it as a line perpendicular to the dispersion plane at the exit (see Fig. 15), thereby preventing spatial resolution and increasing slit height with subsequent degradation of optical signal-to-noise ratio.
The OPD due to astigmatism varies with the square of numerical aperture and the square of the off-axis angle, and cannot be corrected without employing aspheric optics.
A toroidal mirror corrects for astigmatism, allowing the tangential (resolution optimized) and sagittal (imaging optimized) focal planes to cross at the center of the focal plane.
This provides the flexibility to choose between imaging and resolution optimization (with a CCD detector) by selecting the desired detection angle. It will make the spectrograph having the largest flat fields available in an imaging spectrograph.
Recent advances in holographic grating technology now permit complete correction of ALL aberrations present in a spherical mirror-based CZ spectrometer at one wavelength, with excellent mitigation over a wide wavelength range (12).
Both monochromators and spectrographs of this type use a single holographic grating with no ancillary optics.
In these systems, the grating both focuses and diffracts the incident light.
With only one optic in their design, these devices are inexpensive and compact. Fig. 18 illustrates an ACHG monochromator. Fig. 19 illustrates an ACHG spectrograph in which the location of the focal plane is established by:
βH - Angle between perpendicular to spectral plane and grating normal.
LH - Perpendicular distance from spectral plane to grating.
*Use Equations (19) and (2) to determine α and β respectively.
See Table 3 for worked examples.
Note: In practice the highest wavelength attainable is limited by the mechanical rotation of the grating. This means that doubling the groove density of the grating will halve the spectral range.