What’s the aberration, and why do we need to correct it?

An optical aberration is a departure of the performance of an optical system from the predictions of paraxial optics. In the existence of an optical aberration, light from one point of an object does not converge into (or does not diverge from) a single point after transmission through the system. Optical aberrations fall into two classes: monochromatic and chromatic.

Chromatic aberration is a type of distortion in which the lens fails to focus all colors on the same convergence point, due to the dispersion of the lens (different refractive index of the lens for different wavelengths of light).

Monochromatic aberrations are caused by the geometry of the lens and occur both when light is reflected and when it is refracted. Monochromatic aberrations include spherical aberration, coma, astigmatism, and field curvature and image distortion.

Spherically shaped lenses and mirrors share this problem. Parallel light rays that pass through the central region focus farther away than those that pass through the edges. The result is many focal points, which produces a blurry image.

Some aberration affects the images due to off axis rays. The image of a spot looks like several cylinders not centered, like an image of a “comet”, where its name comes from.

An optical system with astigmatism is one where rays that propagate in two perpendicular planes have different focal points.

Field curvature is the aberration that makes a planar object look curved in the image.

Distortion is the most easily recognized aberration as it deforms the image as whole. It arises from the unequal magnification of the peripheral part of a lens (or a mirror) from that of its central part. In “barrel distortion,” image magnification decreases with distance from the optical axis. In “pincushion distortion,” image magnification increases with the distance from the optical axis.

Aberration leads to blurring of the image produced by an image-forming optical system. Makers of optical instruments need to correct optical systems to compensate for aberration.

In order to limit the number of reflections onto optics, concave gratings are often used as single element in VUV spectrometers.

A Rowland demonstrated that the dispersed spectrum of an illuminated point lying on a circle is focused on this circle, if the following setup is respected (see figure). A lot of VUV monochromators use this design.

Unfortunately, gratings suffer from the aberrations of concave mirrors and others due to their diffraction capabilities. Working in the Rowland conditions definitively limits the imaging quality of the instruments. The major aberration here is astigmatism. This aberration can be tolerated with a monochromator since only horizontal focusing is required to separate the wavelengths of spectrum.

At normal incidence (zero order, λ₃), the aberration is minimum and image is straight. But closer the images are from the grating, more stretched and curved are their images. This stretching can be severe, depends on the position of the image on the Rowland circle and hence of the observed wavelength. It results in both loss of signal and loss of resolution, especially in spectrograph mode when CCD detectors are used.

S: Spot source (or slit of the instrument)
λ₃: Zero order position
λ₁, λ₂: Dispersed wavelength positions λ₁> λ₂
i: incidence angle
r: reflectance angle

The spectroscopic images can be improved by using toroidal gratings. A toroidal grating is a form of an elliptic paraboloid with different vertical and horizontal focal distances. It reduces the stretching and the curvature of astigmatism.

Another important advance is the development of Variable Line Spacing (VLS) gratings.

A VLS grating is one whose grooves, when projected onto the tangent plane, form a set of straight parallel lines whose spacing varies from groove to groove. Varying the groove spacing across the surface of the grating moves the tangential focal curve, while keeping the grooves straight and parallel keeps the sagittal focal curve fixed. It corrects for spherical aberration associated with conventional spherical gratings. The VLS technique can also be applied on toroidal grating for an optimum correction.

Two basic types of spectrographs and monochromators are used in the VUV: normal incidence instruments a better design for 100-400 nm, and grazing incidence instruments for 2-100 nm.

The optimization of the image correction of gratings can be calculated for a better image quality on the optical axis of the instrument (monochromator layout) or on a focal plane (spectrograph layout). In the last case, the optimization enlarges the focal plane, the grating of the spectrograph works in fixed position and the wavelength range selection is achieved by sliding the detector in the focal plane of the instrument. The correction is excellent in both cases.

The realization of a real VUV monograph has to be done without a toroidal grating. The Plane Grating Spectrograph (PGS) configuration is one of the best choices. The PGS layout operates with a toroid mirror and a plane grating working at a grazing angle. It also has the advantage of being more affordable grating as they have a plane design.

HORIBA Scientific offers a series of VUV spectrometers and monochromators:

• VHR series monograph in CZ configuration for FUV – IR range in vacuum
• UVL series monochromator or monographs: a single aberration corrected spherical or toroidal grating with middle incidence angle, suitable for 50-600 nm spectral range analysis.
• TGM series monochromators: a single toroidal grating with grazing incidence, coupled with a single channel detector, suitable for 10-300 nm spectral range analysis.
• TGS series spectrographs: a single fixed toroidal grating with grazing incidence, coupled with an array detector, > 40 mm exit flat field.
• PGM-PGS monograph: a rotated plane grating with grazing incidence and a fixed toroidal mirror, able to work down to soft X-ray.

The design of VUV instruments suffers from the constraints of VUV optical materials. Transmission through bulk materials is limited to λ < 105 nm, the short wavelength transmission is limited of LiF or λ < 115 nm for MgF₂. Reflective configuration is used in a VUV optical layout. However, reflectance from metal surfaces also decreases at short wavelengths. Several coating materials are introduced to increase reflectivity, such as Al, Os, Pt, Au, Rh and Ir. Above 120 nm, the main broadband reflector for VUV wavelengths is Al with MgF² coating, having a normal incidence reflectivity of up to 90% under certain conditions. Os, Pt, Au, and Ir have a reflectance of about 60% from 5-200 nm in grazing configuration.

A master grating is an original unit recorded as a unique piece. A master grating can be utilized as the “mother” of multiples copies, called replicas.

Most of the time, VUV monochromators are preferred when equipped with master gratings. But unfortunately, such gratings are extremely expensive and have a long delivery time.