Optimizing the Czerny-Turner imaging spectrometer

Introduction

The Czerny-Turner arrangement is one of the most common designs for a spectrometer or monochromator. It consists of an input slit, a focusing optic for collimation, a dispersive element such as a grating or a prism, another focusing optic, and a detector or exit slit. An image of the input plane is formed at the exit plane, dispersed by wavelength.

Astigmatism caused by spherical optics

A simple and common choice of focusing optics is spherical mirrors. However, the off-axis reflections on the spherical mirrors cause astigmatism, so that image in the exit plane is out of focus either horizontally or vertically. For example, if the entrance slit is replaced by a pinhole and illuminated with a spectral calibration lamp, then one should observe a pattern of spots corresponding to the various wavelengths:

However, with spherical optics, one typically observes something like the following:

Correcting for this effect typically requires nonspherical or additional optics, or a curved grating. Alternatively one may use divergent illumination, in which the distance form the entrance slit to the collimating optic is reduced so that a divergent beam falls upon the grating [1]. However, early work suggested that divergent illumination was only effective for rather narrowband \Delta \lambda/\lambda < 0.03.

Broadband correction with divergent illumination

With Dr Tobias Witting and Professor Ian Walmsley, I showed that divergent illumination could in fact compensate for astigmatism over \Delta \lambda/\lambda\approx 0.2, a much broader range than previously thought [2]. The trick is careful selection of distances and angles which enables the zero-astigmatism condition to be satisfied to first order in wavelength, rather than to zeroth order in the original proposal [1]. The following figure, acquired on a spectrometer designed in this fashion, demonstrates the power of the technique. It shows a “spatio-spectral spot pattern”, produced by illuminating a pinhole with a spectral calibration lamp and scanning the pinhole in the entrance plane. Near diffraction limited performance is achieved over 100 nm.

References

[1] [doi] B. Bates, M. McDowell, and A. C. Newton, “Correction of astigmatism in a Czerny-Turner spectrograph using a plane grating in divergent illumination,” J. phys. e: sci. instrum., vol. 3, iss. 3, pp. 206-210, 1970.
[Bibtex]
@Article{Bates-1970-Correction,
Title = {{Correction of astigmatism in a Czerny-Turner spectrograph using a plane grating in divergent illumination}},
Author = {B Bates and M McDowell and A C Newton},
Journal = {J. Phys. E: Sci. Instrum.},
Year = {1970},
Number = {3},
Pages = {206-210},
Volume = {3},
Abstract = {A method for eliminating the astigmatism of a Czerny-Turner spectrograph is described in which the grating is used in divergent illumination. Expressions are given for the distances of the tangential and sagittal astigmatic images from the camera mirror in terms of the separation between the entrance slit and the collimating mirror and the condition for the elimination of astigmatism is derived. These results are compared with ray tracing data for a practical instrument. Experimental tests of spatial and spectral resolution for an f/15 spectrograph of 0*6 m focal length are given at wavelengths 5461 and 2800 A. Over a spectral range of 100 A centred on 2800 A a spatial resolution along the slit in excess of 50 cycles mm[?]1 has been achieved for a flat inclined image plane. For the same spectrograph with the grating in collimated light the spatial resolution is only 3 cycles mm[?]1.},
Doi = {10.1088/0022-3735/3/3/310},
File = {Bates-1970-Correction.pdf:Bates-1970-Correction.pdf:PDF},
Owner = {dane_austin},
Timestamp = {2012.04.25},
Url = {http://stacks.iop.org/0022-3735/3/206}
}
[2] [doi] D. R. Austin, T. Witting, and I. A. Walmsley, “Broadband astigmatism-free Czerny-Turner imaging spectrometer using spherical mirrors,” Appl. Opt., vol. 48, iss. 19, pp. 3846-3853, 2009.
[Bibtex]
@Article{Austin-2009-Broadband,
author = {Dane R. Austin and Tobias Witting and Ian A. Walmsley},
title = {{Broadband astigmatism-free Czerny-Turner imaging spectrometer using spherical mirrors}},
journal = {{Appl. Opt.}},
year = {2009},
volume = {48},
number = {19},
pages = {3846--3853},
abstract = {We describe the elimination of the astigmatism of a Czerny?Turner imaging spectrometer, built using spherical optics and a plane grating, over a broad spectral region. Starting with the principle of divergent illumination of the grating, which removes astigmatism at one chosen wavelength, we obtain design equations for the distance from the grating to the focusing mirror and the detector angle that remove the astigmatism to first order in wavelength. Experimentally, we demonstrate near diffraction-limited performance from 740 to 860 nm and over a 5 mm transverse spatial extent, while ray-tracing calcula- tions show that barring finite-aperture and detector size limitations, this range extends from 640 to 900 nm and over 10 mm transversely. Our technique requires no additional optics and uses standard off-the- shelf components.},
doi = {10.1364/AO.48.003846},
file = {Austin-2009-Broadband.pdf:A/Austin-2009-Broadband.pdf:PDF},
keywords = {Diffraction gratings; Remote sensing and sensors ; Optical design of instruments; Spectrometers and spectroscopic instrumentation; Spectrometers; Ultrafast measurements},
owner = {dane_austin},
publisher = {OSA},
timestamp = {2012.03.30},
url = {http://ao.osa.org/abstract.cfm?URI=ao-48-19-3846},
}